ExpList.cpp

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//////////////////////////////////////////////////////////////////////////////
//
// File: ExpList.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Expansion list definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <iomanip>
 
#include <boost/core/ignore_unused.hpp>
 
#include <LibUtilities/Communication/Comm.h>
#include <MultiRegions/ExpList.h>
#include <MultiRegions/GlobalLinSys.h>
 
#include <LibUtilities/Foundations/Interp.h>
#include <LocalRegions/Expansion3D.h>
#include <LocalRegions/HexExp.h>
#include <LocalRegions/MatrixKey.h> // for MatrixKey
#include <LocalRegions/NodalTriExp.h>
#include <LocalRegions/PointExp.h>
#include <LocalRegions/PrismExp.h>
#include <LocalRegions/PyrExp.h>
#include <LocalRegions/QuadExp.h>
#include <LocalRegions/SegExp.h>
#include <LocalRegions/TetExp.h>
#include <LocalRegions/TriExp.h>
 
#include <MultiRegions/AssemblyMap/AssemblyMapCG.h> // for AssemblyMapCG, etc
#include <MultiRegions/AssemblyMap/AssemblyMapDG.h> // for AssemblyMapCG, etc
#include <MultiRegions/GlobalLinSysKey.h>           // for GlobalLinSysKey
#include <MultiRegions/GlobalMatrix.h>              // for GlobalMatrix, etc
#include <MultiRegions/GlobalMatrixKey.h>           // for GlobalMatrixKey
 
#include <LibUtilities/Foundations/Interp.h>
#include <LibUtilities/Foundations/ManagerAccess.h> // for PointsManager, etc
#include <LibUtilities/Foundations/PhysGalerkinProject.h>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
#include <LibUtilities/LinearAlgebra/NekTypeDefs.hpp>
#include <LibUtilities/LinearAlgebra/SparseMatrixFwd.hpp>
#include <LibUtilities/Polylib/Polylib.h>
 
#include <Collections/CollectionOptimisation.h>
#include <Collections/Operator.h>
 
#include <LibUtilities/BasicUtils/Likwid.hpp>
#include <LibUtilities/BasicUtils/Timer.h>
 
using namespace std;
 
namespace Nektar
{
namespace MultiRegions
{
/**
 * @class ExpList
 * All multi-elemental expansions \f$u^{\delta}(\boldsymbol{x})\f$ can
 * be considered as the assembly of the various elemental contributions.
 * On a discrete level, this yields,
 * \f[u^{\delta}(\boldsymbol{x}_i)=\sum_{e=1}^{{N_{\mathrm{el}}}}
 * \sum_{n=0}^{N^{e}_m-1}\hat{u}_n^e\phi_n^e(\boldsymbol{x}_i).\f]
 * where \f${N_{\mathrm{el}}}\f$ is the number of elements and
 * \f$N^{e}_m\f$ is the local elemental number of expansion modes.
 * As it is the lowest level class, it contains the definition of the
 * common data and common routines to all multi-elemental expansions.
 *
 * The class stores a vector of expansions, \a m_exp, (each derived from
 * StdRegions#StdExpansion) which define the constituent components of
 * the domain.
 */
 
/**
 * Creates an empty expansion list.
 */
ExpList::ExpList(const ExpansionType type)
    : m_expType(type), m_ncoeffs(0), m_npoints(0), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
}
 
/*----------------------------------------------------------------*/
/*                       Copy Construtor                           */
/*-----------------------------------------------------------------*/
 
/**
 * Copies an existing expansion list.
 * @param   in              Source expansion list.
 */
ExpList::ExpList(const ExpList &in, const bool DeclareCoeffPhysArrays)
    : std::enable_shared_from_this<ExpList>(in), m_expType(in.m_expType),
 
      m_comm(in.m_comm), m_session(in.m_session), m_graph(in.m_graph),
      m_ncoeffs(in.m_ncoeffs), m_npoints(in.m_npoints), m_physState(false),
      m_exp(in.m_exp), m_collections(in.m_collections),
      m_collectionsDoInit(in.m_collectionsDoInit),
      m_coll_coeff_offset(in.m_coll_coeff_offset),
      m_coll_phys_offset(in.m_coll_phys_offset),
      m_coeff_offset(in.m_coeff_offset), m_phys_offset(in.m_phys_offset),
      m_blockMat(in.m_blockMat), m_WaveSpace(false),
      m_elmtToExpId(in.m_elmtToExpId)
{
 
    // Set up m_coeffs, m_phys and offset arrays.
    // use this to keep memory declaration in one place
    SetupCoeffPhys(DeclareCoeffPhysArrays, false);
}
 
ExpList::ExpList(const ExpListSharedPtr &in, const bool DeclareCoeffArrays,
                 const bool DeclarePhysArrays)
    : m_expType(in->m_expType),
 
      m_comm(in->m_comm), m_session(in->m_session), m_graph(in->m_graph),
      m_ncoeffs(in->m_ncoeffs), m_npoints(in->m_npoints),
      m_physState(in->m_physState), m_exp(in->m_exp),
      m_collections(in->m_collections),
      m_collectionsDoInit(in->m_collectionsDoInit),
      m_coll_coeff_offset(in->m_coll_coeff_offset),
      m_coll_phys_offset(in->m_coll_phys_offset),
      m_coeff_offset(in->m_coeff_offset), m_phys_offset(in->m_phys_offset),
      m_coeffsToElmt(in->m_coeffsToElmt), m_blockMat(in->m_blockMat),
      m_WaveSpace(in->m_WaveSpace), m_elmtToExpId(in->m_elmtToExpId)
{
    if (DeclareCoeffArrays)
    {
        m_coeffs = Array<OneD, NekDouble>(m_ncoeffs, 0.0);
    }
    if (DeclarePhysArrays)
    {
        m_phys = Array<OneD, NekDouble>(m_npoints, 0.0);
    }
}
 
/**
 * Copies the eIds elements from an existing expansion list.
 * @param   in              Source expansion list.
 * @param   in              elements that will be in the new exp list.
 */
ExpList::ExpList(const ExpList &in, const std::vector<unsigned int> &eIDs,
                 const bool DeclareCoeffPhysArrays,
                 const Collections::ImplementationType ImpType)
    : m_expType(in.m_expType), m_comm(in.m_comm), m_session(in.m_session),
      m_graph(in.m_graph), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    for (int i = 0; i < eIDs.size(); ++i)
    {
        (*m_exp).push_back((*(in.m_exp))[eIDs[i]]);
    }
 
    // Set up m_coeffs, m_phys and offset arrays.
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    // set up collections
    CreateCollections(ImpType);
}
 
/**
 * Given a meshgraph \a graph, containing information about
 * the domain and the spectral/hp element expansion, this
 * constructor fills the list of local expansions
 * \texttt{m_exp} with the proper expansions, calculates the
 * total number of quadrature points \f$x_i\f$ and local
 * expansion coefficients \f$\hat{u}^e_n\f$ and
 *
 * @param  pSession    A session within information about expansion
 *
 * @param  graph       A meshgraph, containing information about the
 *                      domain and the spectral/hp element expansion.
 *
 * @param DeclareCoeffPhysArrays Declare the coefficient and
 *                               phys space arrays
 *
 * @param  ImpType     Detail about the implementation type to use
 *                     in operators
 */
ExpList::ExpList(const LibUtilities::SessionReaderSharedPtr &pSession,
                 const SpatialDomains::MeshGraphSharedPtr &graph,
                 const bool DeclareCoeffPhysArrays, const std::string &var,
                 const Collections::ImplementationType ImpType)
    : m_comm(pSession->GetComm()), m_session(pSession), m_graph(graph),
      m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    // Retrieve the list of expansions
    const SpatialDomains::ExpansionInfoMap &expansions =
        graph->GetExpansionInfo(var);
 
    // Initialise Expansionn Vector
    InitialiseExpVector(expansions);
 
    // Setup phys coeff space
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    // Initialise collection
    CreateCollections(ImpType);
}
 
/**
 * Given an expansion vector \a expansions, containing
 * information about the domain and the spectral/hp element
 * expansion, this constructor fills the list of local
 * expansions \texttt{m_exp} with the proper expansions,
 * calculates the total number of quadrature points
 * \f$\boldsymbol{x}_i\f$ and local expansion coefficients
 * \f$\hat{u}^e_n\f$.
 *
 * @param  pSession      A session within information about expansion
 * @param expansions     A vector containing information about the
 *                       domain and the spectral/hp element
 *                       expansion.
 * @param DeclareCoeffPhysArrays Declare the coefficient and
 *                               phys space arrays
 * @param  ImpType       Detail about the implementation type to use
 *                       in operators
 */
ExpList::ExpList(const LibUtilities::SessionReaderSharedPtr &pSession,
                 const SpatialDomains::ExpansionInfoMap &expansions,
                 const bool DeclareCoeffPhysArrays,
                 const Collections::ImplementationType ImpType)
    : m_comm(pSession->GetComm()), m_session(pSession), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
 
    // Initialise expansion vector
    InitialiseExpVector(expansions);
 
    // Set up m_coeffs, m_phys and offset arrays.
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    // Setup Collection
    CreateCollections(ImpType);
}
 
//----------------------------------------------------------------------
//                        0D Expansion Constructors
//----------------------------------------------------------------------
ExpList::ExpList(const SpatialDomains::PointGeomSharedPtr &geom)
    : m_expType(e0D), m_ncoeffs(1), m_npoints(1), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    LocalRegions::PointExpSharedPtr Point =
        MemoryManager<LocalRegions::PointExp>::AllocateSharedPtr(geom);
    (*m_exp).push_back(Point);
 
    SetupCoeffPhys();
}
 
/**
 * Store expansions for the trace space expansions used in
 * DisContField
 *
 * @param  pSession      A session within information about expansion
 * @param  bndConstraint Array of ExpList1D objects each containing a
 *                       1D spectral/hp element expansion on a single
 *                       boundary region.
 * @param  bndCond       Array of BoundaryCondition objects which contain
 *                       information about the boundary conditions on the
 *                       different boundary regions.
 * @param  locexp        Complete domain expansion list.
 * @param  graph         mesh corresponding to the expansion list.
 * @param  DeclareCoeffPhysArrays Declare the coefficient and
 *                               phys space arrays
 * @param  variable      The variable name associated with the expansion
 * @param  ImpType       Detail about the implementation type to use
 *                       in operators
 */
ExpList::ExpList(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const Array<OneD, const ExpListSharedPtr> &bndConstraint,
    const Array<OneD, const SpatialDomains::BoundaryConditionShPtr> &bndCond,
    const LocalRegions::ExpansionVector &locexp,
    const SpatialDomains::MeshGraphSharedPtr &graph,
    const LibUtilities::CommSharedPtr &comm, const bool DeclareCoeffPhysArrays,
    const std::string variable, const Collections::ImplementationType ImpType)
    : m_comm(comm), m_session(pSession), m_graph(graph), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    boost::ignore_unused(variable, ImpType);
    int i, j, id, elmtid = 0;
    set<int> tracesDone;
 
    SpatialDomains::PointGeomSharedPtr PointGeom;
    SpatialDomains::Geometry1DSharedPtr segGeom;
    SpatialDomains::Geometry2DSharedPtr ElGeom;
    SpatialDomains::Geometry2DSharedPtr FaceGeom;
    SpatialDomains::QuadGeomSharedPtr QuadGeom;
    SpatialDomains::TriGeomSharedPtr TriGeom;
 
    LocalRegions::ExpansionSharedPtr exp;
    LocalRegions::Expansion0DSharedPtr exp0D;
    LocalRegions::Expansion1DSharedPtr exp1D;
    LocalRegions::Expansion2DSharedPtr exp2D;
    LocalRegions::Expansion3DSharedPtr exp3D;
 
    // First loop over boundary conditions to reorder
    // Dirichlet boundaries
    for (i = 0; i < bndCond.size(); ++i)
    {
        if (bndCond[i]->GetBoundaryConditionType() ==
            SpatialDomains::eDirichlet)
        {
            for (j = 0; j < bndConstraint[i]->GetExpSize(); ++j)
            {
                if ((exp0D =
                         std::dynamic_pointer_cast<LocalRegions::Expansion0D>(
                             bndConstraint[i]->GetExp(j))))
                {
                    m_expType = e0D;
 
                    PointGeom = exp0D->GetGeom()->GetVertex(0);
                    exp       = MemoryManager<
                        LocalRegions::PointExp>::AllocateSharedPtr(PointGeom);
                    tracesDone.insert(PointGeom->GetVid());
                }
                else if ((exp1D = std::dynamic_pointer_cast<
                              LocalRegions::Expansion1D>(
                              bndConstraint[i]->GetExp(j))))
                {
                    m_expType = e1D;
 
                    LibUtilities::BasisKey bkey =
                        exp1D->GetBasis(0)->GetBasisKey();
                    segGeom = exp1D->GetGeom1D();
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            bkey, segGeom);
                    tracesDone.insert(segGeom->GetGlobalID());
                }
                else if ((exp2D = std::dynamic_pointer_cast<
                              LocalRegions::Expansion2D>(
                              bndConstraint[i]->GetExp(j))))
                {
                    m_expType = e2D;
 
                    LibUtilities::BasisKey bkey0 =
                        exp2D->GetBasis(0)->GetBasisKey();
                    LibUtilities::BasisKey bkey1 =
                        exp2D->GetBasis(1)->GetBasisKey();
                    FaceGeom = exp2D->GetGeom2D();
 
                    // if face is a quad
                    if ((QuadGeom = std::dynamic_pointer_cast<
                             SpatialDomains::QuadGeom>(FaceGeom)))
                    {
                        exp = MemoryManager<
                            LocalRegions::QuadExp>::AllocateSharedPtr(bkey0,
                                                                      bkey1,
                                                                      QuadGeom);
                        tracesDone.insert(QuadGeom->GetGlobalID());
                    }
                    // if face is a triangle
                    else if ((TriGeom = std::dynamic_pointer_cast<
                                  SpatialDomains::TriGeom>(FaceGeom)))
                    {
                        exp = MemoryManager<
                            LocalRegions::TriExp>::AllocateSharedPtr(bkey0,
                                                                     bkey1,
                                                                     TriGeom);
                        tracesDone.insert(TriGeom->GetGlobalID());
                    }
                    else
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "dynamic cast to a "
                                 "proper face geometry failed");
                    }
                }
                // Assign next id
                exp->SetElmtId(elmtid++);
 
                // Add the expansion
                (*m_exp).push_back(exp);
            }
        }
    }
 
    map<int, pair<SpatialDomains::Geometry1DSharedPtr, LibUtilities::BasisKey>>
        edgeOrders;
 
    map<int, pair<SpatialDomains::Geometry2DSharedPtr,
                  pair<LibUtilities::BasisKey, LibUtilities::BasisKey>>>
        faceOrders;
 
    for (i = 0; i < locexp.size(); ++i)
    {
        if ((exp1D = std::dynamic_pointer_cast<LocalRegions::Expansion1D>(
                 locexp[i])))
        {
            m_expType = e0D;
 
            for (j = 0; j < 2; ++j)
            {
                PointGeom = (exp1D->GetGeom1D())->GetVertex(j);
                id        = PointGeom->GetVid();
 
                // Ignore Dirichlet edges
                if (tracesDone.count(id) != 0)
                {
                    continue;
                }
 
                exp = MemoryManager<LocalRegions::PointExp>::AllocateSharedPtr(
                    PointGeom);
                tracesDone.insert(id);
                exp->SetElmtId(elmtid++);
                (*m_exp).push_back(exp);
            }
        }
        else if ((exp2D = std::dynamic_pointer_cast<LocalRegions::Expansion2D>(
                      locexp[i])))
        {
            m_expType = e1D;
            for (j = 0; j < locexp[i]->GetNtraces(); ++j)
            {
                segGeom = exp2D->GetGeom2D()->GetEdge(j);
                id      = segGeom->GetGlobalID();
                // Ignore Dirichlet edges
                if (tracesDone.count(id) != 0)
                {
                    continue;
                }
 
                auto it = edgeOrders.find(id);
 
                if (it == edgeOrders.end()) // not exist, insert new one
                {
                    edgeOrders.insert(std::make_pair(
                        id, std::make_pair(segGeom,
                                           locexp[i]->GetTraceBasisKey(j))));
                }
                else // already exist, check if we need to update it
                {
                    LibUtilities::BasisKey edge =
                        locexp[i]->GetTraceBasisKey(j);
                    LibUtilities::BasisKey existing = it->second.second;
 
                    int np1 = edge.GetNumPoints();
                    int np2 = existing.GetNumPoints();
                    int nm1 = edge.GetNumModes();
                    int nm2 = existing.GetNumModes();
 
                    // if the existing edge has less points/modes than the
                    // present edge, then we update the existing edge with
                    // present one (trace should always have highest order)
 
                    // The pointsType is always GLL for edges
                    // So we can directly compare them.
                    if (np2 >= np1 && nm2 >= nm1)
                    {
                        continue;
                    }
                    else if (np2 <= np1 && nm2 <= nm1)
                    {
                        it->second.second = edge;
                    }
                    else
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "inappropriate number of points/modes (max"
                                 "num of points is not set with max order)");
                    }
                }
            }
        }
        else if ((exp3D = dynamic_pointer_cast<LocalRegions::Expansion3D>(
                      locexp[i])))
        {
            m_expType = e2D;
            for (j = 0; j < exp3D->GetNtraces(); ++j)
            {
                FaceGeom = exp3D->GetGeom3D()->GetFace(j);
                id       = FaceGeom->GetGlobalID();
                // Ignore Dirichlet edges
                if (tracesDone.count(id) != 0)
                {
                    continue;
                }
                auto it = faceOrders.find(id);
 
                if (it == faceOrders.end()) // not exist, insert new one
                {
                    // GetTraceBasisKey does not take into account
                    // the orientaion. It is w.r.t local face axes.
                    LibUtilities::BasisKey face_dir0 =
                        locexp[i]->GetTraceBasisKey(j, 0);
                    LibUtilities::BasisKey face_dir1 =
                        locexp[i]->GetTraceBasisKey(j, 1);
 
                    // If the axes 1, 2 of the local face correspond to
                    // the axes 2, 1 of global face, respectively,
                    // then swap face0 and face1
                    if (locexp[i]->GetTraceOrient(j) >= 9)
                    {
                        std::swap(face_dir0, face_dir1);
                    }
 
                    faceOrders.insert(std::make_pair(
                        id,
                        std::make_pair(FaceGeom,
                                       std::make_pair(face_dir0, face_dir1))));
                }
                else // already exist, check if we need to update it
                {
                    LibUtilities::BasisKey face0 =
                        locexp[i]->GetTraceBasisKey(j, 0);
                    LibUtilities::BasisKey face1 =
                        locexp[i]->GetTraceBasisKey(j, 1);
                    LibUtilities::BasisKey existing0 = it->second.second.first;
                    LibUtilities::BasisKey existing1 = it->second.second.second;
 
                    // np -- number of points; nm -- number of modes;
                    // np_I_J --- I=1 current; I=2 existing; J=1 dir0; J=2 dir1;
                    int np11 = face0.GetNumPoints();
                    int np12 = face1.GetNumPoints();
                    int np21 = existing0.GetNumPoints();
                    int np22 = existing1.GetNumPoints();
                    int nm11 = face0.GetNumModes();
                    int nm12 = face1.GetNumModes();
                    int nm21 = existing0.GetNumModes();
                    int nm22 = existing1.GetNumModes();
 
                    // If the axes 1, 2 of the current face correspond to
                    // the axes 2, 1 of existing face, respectively,
                    // then swap face0 and face1
                    // eDir1FwdDir2_Dir2FwdDir1 = 9
                    // eDir1FwdDir2_Dir2BwdDir1 = 10
                    // eDir1BwdDir2_Dir2FwdDir1 = 11
                    // eDir1BwdDir2_Dir2BwdDir1 = 12
                    if (locexp[i]->GetTraceOrient(j) >= 9)
                    {
                        std::swap(np11, np12);
                        std::swap(nm11, nm12);
                        std::swap(face0, face1);
                    }
 
                    // The baiskey return by GetTraceBasisKey should always
                    // have GLL for eModified_A and GR for eModified_B.
                    // But we still use GetPointsType to check this.
                    if (existing1.GetPointsType() ==
                        LibUtilities::eGaussRadauMAlpha1Beta0)
                    {
                        if (face1.GetPointsType() ==
                            LibUtilities::eGaussLobattoLegendre)
                        {
                            np12--; // make np12 comparable to np22
                        }
                    }
                    else
                    {
                        if (face1.GetPointsType() ==
                            LibUtilities::eGaussRadauMAlpha1Beta0)
                        {
                            np12++; // make np12 comparable to np22
                        }
                    }
 
                    if (existing0.GetPointsType() ==
                        LibUtilities::eGaussRadauMAlpha1Beta0)
                    {
                        if (face0.GetPointsType() ==
                            LibUtilities::eGaussLobattoLegendre)
                        {
                            np11--; // make np11 comparable to np21
                        }
                    }
                    else
                    {
                        if (face0.GetPointsType() ==
                            LibUtilities::eGaussRadauMAlpha1Beta0)
                        {
                            np11++; // make np11 comparable to np21
                        }
                    }
 
                    // if the existing face_i has less points/modes than the
                    // present face_i, then we update the existing face_i with
                    // present one (trace should always have highest order)
                    if (np22 >= np12 && nm22 >= nm12)
                    {
                        // keep existing face_i and do nothing
                    }
                    else if (np22 <= np12 && nm22 <= nm12)
                    {
                        // Instead of using face0 directly, We create new
                        // basiskey with original Type but higher order.
                        LibUtilities::BasisKey newbkey(
                            existing1.GetBasisType(), nm12,
                            LibUtilities::PointsKey(np12,
                                                    existing1.GetPointsType()));
                        it->second.second.second = newbkey;
                    }
                    else // np22 > np12 but nm22 < nm12
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "inappropriate number of points/modes (max"
                                 "num of points is not set with max order)");
                    }
 
                    if (np21 >= np11 && nm21 >= nm11)
                    {
                        // keep existing face_i and do nothing
                    }
                    else if (np21 <= np11 && nm21 <= nm11)
                    {
                        // Instead of using face0 directly, We create new
                        // basiskey with original Type but higher order.
                        LibUtilities::PointsKey newpkey(
                            np11, existing0.GetPointsType());
                        LibUtilities::BasisKey newbkey(existing0.GetBasisType(),
                                                       nm11, newpkey);
                        it->second.second.first = newbkey;
                    }
                    else // np21 > np11 but nm21 < nm11
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "inappropriate number of points/modes (max"
                                 "num of points is not set with max order)");
                    }
                }
            }
        }
    }
 
    int nproc   = m_comm->GetRowComm()->GetSize(); // number of processors
    int tracepr = m_comm->GetRowComm()->GetRank(); // ID processor
 
    if (nproc > 1)
    {
        int tCnt = 0;
 
        // Count the number of traces on each partition
        for (i = 0; i < locexp.size(); ++i)
        {
            tCnt += locexp[i]->GetNtraces();
        }
 
        // Record the number traces on each partition,
        // then reduce this across processors.
        Array<OneD, int> tracesCnt(nproc, 0);
        tracesCnt[tracepr] = tCnt;
        m_comm->GetRowComm()->AllReduce(tracesCnt, LibUtilities::ReduceSum);
 
        // Set up offset array.
        int totTraceCnt = Vmath::Vsum(nproc, tracesCnt, 1);
        Array<OneD, int> tTotOffsets(nproc, 0);
 
        for (i = 1; i < nproc; ++i)
        {
            tTotOffsets[i] = tTotOffsets[i - 1] + tracesCnt[i - 1];
        }
 
        // Set up arrays that are large enough to hold all traces
        // in the domain, not just those in local partition.
        Array<OneD, int> TracesTotID(totTraceCnt, 0);
        Array<OneD, int> TracesTotNm0(totTraceCnt, 0);
        Array<OneD, int> TracesTotNm1(totTraceCnt, 0);
        Array<OneD, int> TracesTotPnts0(totTraceCnt, 0);
        Array<OneD, int> TracesTotPnts1(totTraceCnt, 0);
        Array<OneD, int> TracesPointsType0(totTraceCnt, 0);
        Array<OneD, int> TracesPointsType1(totTraceCnt, 0);
        // convert enum PointsType to integer, so that MPI can handle it
 
        // TODO: Change this design to save memory and improve performance.
        //
        // In the current design, After AllReduce, each processor will
        // store a full copy these large arrays, which might be too
        // expensive when nproc and mesh are large. So basically, this
        // design is just a naive implementation and we need to redesign it
        // in the future.
 
        int cntr = tTotOffsets[tracepr];
 
        for (i = 0; i < locexp.size(); ++i)
        {
            if ((exp2D = locexp[i]->as<LocalRegions::Expansion2D>()))
            {
 
                int nedges = locexp[i]->GetNtraces();
 
                for (j = 0; j < nedges; ++j, ++cntr)
                {
                    LibUtilities::BasisKey bkeyEdge =
                        locexp[i]->GetTraceBasisKey(j);
                    TracesTotID[cntr]    = exp2D->GetGeom2D()->GetEid(j);
                    TracesTotNm0[cntr]   = bkeyEdge.GetNumModes();
                    TracesTotPnts0[cntr] = bkeyEdge.GetNumPoints();
                    TracesPointsType0[cntr] =
                        static_cast<int>(bkeyEdge.GetPointsType());
                    // Althought for edges, we only have GLL points, we still
                    // keep this design for backup.
                }
            }
            else if ((exp3D = locexp[i]->as<LocalRegions::Expansion3D>()))
            {
                int nfaces = locexp[i]->GetNtraces();
 
                for (j = 0; j < nfaces; ++j, ++cntr)
                {
                    LibUtilities::BasisKey face_dir0 =
                        locexp[i]->GetTraceBasisKey(j, 0);
                    LibUtilities::BasisKey face_dir1 =
                        locexp[i]->GetTraceBasisKey(j, 1);
 
                    // If the axes 1, 2 of the local face correspond to
                    // the axes 2, 1 of global face, respectively,
                    // then swap face0 and face1
                    if (locexp[i]->GetTraceOrient(j) >= 9)
                    {
                        std::swap(face_dir0, face_dir1);
                    }
 
                    TracesTotID[cntr]    = exp3D->GetGeom3D()->GetFid(j);
                    TracesTotNm0[cntr]   = face_dir0.GetNumModes();
                    TracesTotNm1[cntr]   = face_dir1.GetNumModes();
                    TracesTotPnts0[cntr] = face_dir0.GetNumPoints();
                    TracesTotPnts1[cntr] = face_dir1.GetNumPoints();
                    TracesPointsType0[cntr] =
                        static_cast<int>(face_dir0.GetPointsType());
                    TracesPointsType1[cntr] =
                        static_cast<int>(face_dir1.GetPointsType());
                }
            }
        }
 
        m_comm->GetRowComm()->AllReduce(TracesTotID, LibUtilities::ReduceSum);
        m_comm->GetRowComm()->AllReduce(TracesTotNm0, LibUtilities::ReduceSum);
        m_comm->GetRowComm()->AllReduce(TracesTotPnts0,
                                        LibUtilities::ReduceSum);
        m_comm->GetRowComm()->AllReduce(TracesPointsType0,
                                        LibUtilities::ReduceSum);
        if (m_expType == e2D) // 2D face
        {
            m_comm->GetRowComm()->AllReduce(TracesTotNm1,
                                            LibUtilities::ReduceSum);
            m_comm->GetRowComm()->AllReduce(TracesTotPnts1,
                                            LibUtilities::ReduceSum);
            m_comm->GetRowComm()->AllReduce(TracesPointsType1,
                                            LibUtilities::ReduceSum);
        }
        // TracesTotXXX has collected traces info of entire domain
        // Now compare them with current traces info - edgeOrders
        // and update traces basiskey. This step is to ensure the
        // m_trace has highest order even on parition interfaces.
 
        if (edgeOrders.size())
        {
            for (i = 0; i < totTraceCnt; ++i)
            {
                auto it = edgeOrders.find(TracesTotID[i]);
 
                if (it == edgeOrders.end())
                {
                    continue;
                }
 
                LibUtilities::BasisKey existing = it->second.second;
 
                int np1 = TracesTotPnts0[i];
                int np2 = existing.GetNumPoints();
                int nm1 = TracesTotNm0[i];
                int nm2 = existing.GetNumModes();
 
                // The pointsType is always GLL for edges
                // So we can directly compare them.
                if (np2 >= np1 && nm2 >= nm1)
                {
                    continue;
                }
                else if (np2 <= np1 && nm2 <= nm1)
                {
                    // We have to rebuild the basis key locally because
                    // MPI::AllReduce does not support BasisKey directly.
                    LibUtilities::BasisKey newbkey(
                        existing.GetBasisType(), nm1,
                        LibUtilities::PointsKey(np1, existing.GetPointsType()));
                    it->second.second = newbkey;
                }
                else
                {
                    NEKERROR(ErrorUtil::efatal,
                             "inappropriate number of points/modes (max "
                             "num of points is not set with max order)");
                }
            }
        }
        else if (faceOrders.size())
        {
            for (i = 0; i < totTraceCnt; ++i)
            {
                auto it = faceOrders.find(TracesTotID[i]);
 
                if (it == faceOrders.end())
                {
                    continue;
                }
 
                LibUtilities::BasisKey existing0 = it->second.second.first;
                LibUtilities::BasisKey existing1 = it->second.second.second;
 
                // np -- number of points; nm -- number of modes;
                // np_I_J --- I=1 current; I=2 existing; J=1 dir0; J=2 dir1;
                int np11 = TracesTotPnts0[i];
                int np12 = TracesTotPnts1[i];
                int np21 = existing0.GetNumPoints();
                int np22 = existing1.GetNumPoints();
                int nm11 = TracesTotNm0[i];
                int nm12 = TracesTotNm1[i];
                int nm21 = existing0.GetNumModes();
                int nm22 = existing1.GetNumModes();
 
                // The orientation is already aligned
                // Here we only need to compare pointsType
                // and adjust np
                if (existing1.GetPointsType() ==
                    LibUtilities::eGaussRadauMAlpha1Beta0)
                {
                    if (static_cast<LibUtilities::PointsType>(
                            TracesPointsType1[i]) ==
                        LibUtilities::eGaussLobattoLegendre)
                    {
                        np12--; // make np12 comparable to np22
                    }
                }
                else
                {
                    if (static_cast<LibUtilities::PointsType>(
                            TracesPointsType1[i]) ==
                        LibUtilities::eGaussRadauMAlpha1Beta0)
                    {
                        np12++; // make np12 comparable to np22
                    }
                }
 
                if (existing0.GetPointsType() ==
                    LibUtilities::eGaussRadauMAlpha1Beta0)
                {
                    if (static_cast<LibUtilities::PointsType>(
                            TracesPointsType0[i]) ==
                        LibUtilities::eGaussLobattoLegendre)
                    {
                        np11--; // make np11 comparable to np21
                    }
                }
                else
                {
                    if (static_cast<LibUtilities::PointsType>(
                            TracesPointsType0[i]) ==
                        LibUtilities::eGaussRadauMAlpha1Beta0)
                    {
                        np11++; // make np11 comparable to np21
                    }
                }
 
                // if the existing face_i has less points/modes than the
                // present face_i, then we update the existing face_i with
                // present one (trace should always have highest order)
                if (np22 >= np12 && nm22 >= nm12)
                {
                    // keep existing face_i and do nothing
                }
                else if (np22 <= np12 && nm22 <= nm12)
                {
                    LibUtilities::BasisKey newbkey(
                        existing1.GetBasisType(), nm12,
                        LibUtilities::PointsKey(np12,
                                                existing1.GetPointsType()));
                    it->second.second.second = newbkey;
                }
                else // np22 > np12 but nm22 < nm12
                {
                    NEKERROR(ErrorUtil::efatal,
                             "inappropriate number of points/modes (max "
                             "num of points is not set with max order)");
                }
 
                if (np21 >= np11 && nm21 >= nm11)
                {
                    // keep existing face_i and do nothing
                }
                else if (np21 <= np11 && nm21 <= nm11)
                {
                    LibUtilities::BasisKey newbkey(
                        existing0.GetBasisType(), nm11,
                        LibUtilities::PointsKey(np11,
                                                existing0.GetPointsType()));
                    it->second.second.first = newbkey;
                }
                else // np21 > np11 but nm21 < nm11
                {
                    NEKERROR(ErrorUtil::efatal,
                             "inappropriate number of points/modes (max"
                             "num of points is not set with max order)");
                }
            }
        }
    }
 
    if (edgeOrders.size())
    {
        for (auto &it : edgeOrders)
        {
            exp = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                it.second.second, it.second.first);
            exp->SetElmtId(elmtid++);
            (*m_exp).push_back(exp);
        }
    }
    else
    {
        for (auto &it : faceOrders)
        {
            FaceGeom = it.second.first;
 
            if ((QuadGeom = std::dynamic_pointer_cast<SpatialDomains::QuadGeom>(
                     FaceGeom)))
            {
                exp = MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                    it.second.second.first, it.second.second.second, QuadGeom);
            }
            else if ((TriGeom =
                          std::dynamic_pointer_cast<SpatialDomains::TriGeom>(
                              FaceGeom)))
            {
                exp = MemoryManager<LocalRegions::TriExp>::AllocateSharedPtr(
                    it.second.second.first, it.second.second.second, TriGeom);
            }
            exp->SetElmtId(elmtid++);
            (*m_exp).push_back(exp);
        }
    }
 
    // Set up m_coeffs, m_phys and offset arrays.
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    // Set up collections
    if (m_expType != e0D)
    {
        CreateCollections(ImpType);
    }
 
    // Setup element to expansion ID maps for the trace elements
    // Loop in reverse order so that in case where using a
    // Homogeneous expansion it sets geometry ids to first part of
    // m_exp list. Otherwise will set to second (complex) expansion
    for (int i = (*m_exp).size() - 1; i >= 0; --i)
    {
        m_elmtToExpId[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
    }
}
 
/**
 * Set  expansions for localtrace space expansions used in
 * DisContField as part of Gradient Jump Penalisation
 *
 * @param  pSession      A session within information about expansion
 * @param  locexp        Complete domain expansion list.
 * @param  graph         mesh corresponding to the expansion list.
 * @param  DeclareCoeffPhysArrays Declare the coefficient and
 *                               phys space arrays
 * @param  variable      The variable name associated with the expansion
 * @param  ImpType       Detail about the implementation type to use
 *                       in operators
 */
ExpList::ExpList(const LibUtilities::SessionReaderSharedPtr &pSession,
                 const LocalRegions::ExpansionVector &locexp,
                 const SpatialDomains::MeshGraphSharedPtr &graph,
                 const bool DeclareCoeffPhysArrays, const std::string variable,
                 const Collections::ImplementationType ImpType)
    : m_comm(pSession->GetComm()), m_session(pSession), m_graph(graph),
      m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    boost::ignore_unused(variable, ImpType);
    int i, j, elmtid = 0;
 
    SpatialDomains::PointGeomSharedPtr PointGeom;
    SpatialDomains::Geometry1DSharedPtr segGeom;
    SpatialDomains::Geometry2DSharedPtr ElGeom;
    SpatialDomains::Geometry2DSharedPtr FaceGeom;
    SpatialDomains::QuadGeomSharedPtr QuadGeom;
    SpatialDomains::TriGeomSharedPtr TriGeom;
 
    LocalRegions::ExpansionSharedPtr exp;
    LocalRegions::Expansion0DSharedPtr exp0D;
    LocalRegions::Expansion1DSharedPtr exp1D;
    LocalRegions::Expansion2DSharedPtr exp2D;
    LocalRegions::Expansion3DSharedPtr exp3D;
 
    for (i = 0; i < locexp.size(); ++i)
    {
        if ((exp1D = std::dynamic_pointer_cast<LocalRegions::Expansion1D>(
                 locexp[i])))
        {
            m_expType = e0D;
 
            for (j = 0; j < 2; ++j)
            {
                PointGeom = (exp1D->GetGeom1D())->GetVertex(j);
 
                exp = MemoryManager<LocalRegions::PointExp>::AllocateSharedPtr(
                    PointGeom);
                exp->SetElmtId(elmtid++);
                (*m_exp).push_back(exp);
            }
        }
        else if ((exp2D = std::dynamic_pointer_cast<LocalRegions::Expansion2D>(
                      locexp[i])))
        {
            m_expType = e1D;
            LibUtilities::BasisKey edgeKey0 =
                locexp[i]->GetBasis(0)->GetBasisKey();
 
            for (j = 0; j < locexp[i]->GetNtraces(); ++j)
            {
                segGeom = exp2D->GetGeom2D()->GetEdge(j);
 
                int dir = exp2D->GetGeom2D()->GetDir(j);
 
                if (locexp[i]->GetNtraces() == 3)
                {
                    LibUtilities::BasisKey edgeKey =
                        locexp[i]->GetBasis(dir)->GetBasisKey();
 
                    LibUtilities::BasisKey nEdgeKey(edgeKey0.GetBasisType(),
                                                    edgeKey.GetNumModes(),
                                                    edgeKey.GetPointsKey());
 
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            nEdgeKey, segGeom);
                }
                else
                {
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            locexp[i]->GetBasis(dir)->GetBasisKey(), segGeom);
                }
 
                exp->SetElmtId(elmtid++);
                (*m_exp).push_back(exp);
            }
        }
        else if ((exp3D = dynamic_pointer_cast<LocalRegions::Expansion3D>(
                      locexp[i])))
        {
            m_expType = e2D;
 
            LibUtilities::BasisKey face0_dir0 =
                locexp[i]->GetBasis(0)->GetBasisKey();
            LibUtilities::BasisKey face0_dir1 =
                locexp[i]->GetBasis(1)->GetBasisKey();
 
            for (j = 0; j < exp3D->GetNtraces(); ++j)
            {
                FaceGeom = exp3D->GetGeom3D()->GetFace(j);
 
                int dir0 = exp3D->GetGeom3D()->GetDir(j, 0);
                int dir1 = exp3D->GetGeom3D()->GetDir(j, 1);
 
                LibUtilities::BasisKey face_dir0 =
                    locexp[i]->GetBasis(dir0)->GetBasisKey();
                LibUtilities::BasisKey face_dir1 =
                    locexp[i]->GetBasis(dir1)->GetBasisKey();
 
                if ((QuadGeom =
                         std::dynamic_pointer_cast<SpatialDomains::QuadGeom>(
                             FaceGeom)))
                {
                    exp =
                        MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                            face_dir0, face_dir1, QuadGeom);
                }
                else if ((TriGeom = std::dynamic_pointer_cast<
                              SpatialDomains::TriGeom>(FaceGeom)))
                {
 
                    LibUtilities::BasisKey nface_dir0(face0_dir0.GetBasisType(),
                                                      face_dir0.GetNumModes(),
                                                      face_dir0.GetPointsKey());
                    LibUtilities::BasisKey nface_dir1(face0_dir1.GetBasisType(),
                                                      face_dir1.GetNumModes(),
                                                      face_dir1.GetPointsKey());
                    exp =
                        MemoryManager<LocalRegions::TriExp>::AllocateSharedPtr(
                            nface_dir0, nface_dir1, TriGeom);
                }
                exp->SetElmtId(elmtid++);
                (*m_exp).push_back(exp);
            }
        }
    }
 
    // Set up m_coeffs, m_phys and offset arrays.
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    // Set up collections
    if (m_expType != e0D)
    {
        CreateCollections(ImpType);
    }
}
 
/**
 * Fills the list of local expansions with the trace from the mesh
 * specified by \a domain. This CompositeMap contains a list of
 * Composites which define the boundary. It is also used to set up
 * expansion domains in the 1D Pulse Wave solver.
 *
 * @param  pSession     A session within information about expansion
 * @param  domain       A domain, comprising of one or more composite
 *                      regions,
 * @param  graph        A mesh, containing information about the
 *                      domain and the spectral/hp element expansion.
 * @param DeclareCoeffPhysArrays Declare the coefficient and
 *                               phys space arrays. Default is true.
 * @param  variable     The variable name associated with the expansion
 * @param  SetToOneSpaceDimension Reduce to one space dimension expansion
 * @param  comm         An optional communicator that can be used with the
 *                      boundary expansion in case of more global
 *                      parallel operations. Default to a Null Communicator
 * @param  ImpType      Detail about the implementation type to use
 *                      in operators. Default is eNoImpType.
 *
 */
ExpList::ExpList(const LibUtilities::SessionReaderSharedPtr &pSession,
                 const SpatialDomains::CompositeMap &domain,
                 const SpatialDomains::MeshGraphSharedPtr &graph,
                 const bool DeclareCoeffPhysArrays, const std::string variable,
                 bool SetToOneSpaceDimension,
                 const LibUtilities::CommSharedPtr comm,
                 const Collections::ImplementationType ImpType)
    : m_comm(comm), m_session(pSession), m_graph(graph), m_physState(false),
      m_exp(MemoryManager<LocalRegions::ExpansionVector>::AllocateSharedPtr()),
      m_blockMat(MemoryManager<BlockMatrixMap>::AllocateSharedPtr()),
      m_WaveSpace(false)
{
    int j, elmtid = 0;
    SpatialDomains::PointGeomSharedPtr PtGeom;
    SpatialDomains::SegGeomSharedPtr SegGeom;
    SpatialDomains::TriGeomSharedPtr TriGeom;
    SpatialDomains::QuadGeomSharedPtr QuadGeom;
 
    LocalRegions::ExpansionSharedPtr exp;
 
    LibUtilities::PointsType TriNb;
 
    int meshdim = graph->GetMeshDimension();
 
    // Retrieve the list of expansions (element exp)
    const SpatialDomains::ExpansionInfoMap &expansions =
        graph->GetExpansionInfo(variable);
 
    // Retrieve the list of expansions
    // Process each composite region.
    for (auto &compIt : domain)
    {
        // Process each expansion in the region.
        for (j = 0; j < compIt.second->m_geomVec.size(); ++j)
        {
            if ((PtGeom = std::dynamic_pointer_cast<SpatialDomains::PointGeom>(
                     compIt.second->m_geomVec[j])))
            {
                m_expType = e0D;
 
                exp = MemoryManager<LocalRegions::PointExp>::AllocateSharedPtr(
                    PtGeom);
            }
            else if ((SegGeom =
                          std::dynamic_pointer_cast<SpatialDomains::SegGeom>(
                              compIt.second->m_geomVec[j])))
            {
                m_expType = e1D;
 
                // Retrieve the basis key from the expansion.
                LibUtilities::BasisKey bkey = LibUtilities::NullBasisKey;
 
                if (meshdim == 1)
                {
                    // map<int, ExpansionInfoShPtr>
                    auto expIt = expansions.find(SegGeom->GetGlobalID());
                    ASSERTL0(expIt != expansions.end(),
                             "Failed to find basis key");
                    bkey = expIt->second->m_basisKeyVector[0];
                }
                else // get bkey from Tri or Quad
                {
                    // First, create the element stdExp that the edge belongs to
                    SpatialDomains::GeometryLinkSharedPtr elmts =
                        graph->GetElementsFromEdge(SegGeom);
                    // elmts -> std::vector<std::pair<GeometrySharedPtr, int> >
                    // Currently we assume the elements adjacent to the edge
                    // have the same type. So we directly fetch the first
                    // element.
                    SpatialDomains::GeometrySharedPtr geom = elmts->at(0).first;
                    int edge_id = elmts->at(0).second;
                    SpatialDomains::ExpansionInfoShPtr expInfo =
                        graph->GetExpansionInfo(geom, variable);
                    LibUtilities::BasisKey Ba = expInfo->m_basisKeyVector[0];
                    LibUtilities::BasisKey Bb = expInfo->m_basisKeyVector[1];
                    StdRegions::StdExpansionSharedPtr elmtStdExp;
 
                    if (geom->GetShapeType() == LibUtilities::eTriangle)
                    {
                        elmtStdExp = MemoryManager<
                            StdRegions::StdTriExp>::AllocateSharedPtr(Ba, Bb);
                    }
                    else if (geom->GetShapeType() ==
                             LibUtilities::eQuadrilateral)
                    {
                        elmtStdExp = MemoryManager<
                            StdRegions::StdQuadExp>::AllocateSharedPtr(Ba, Bb);
                    }
                    else
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "Fail to cast geom to a known 2D shape.");
                    }
                    // Then, get the trace basis key from the element stdExp,
                    // which may be different from Ba and Bb.
                    bkey = elmtStdExp->GetTraceBasisKey(edge_id);
                }
 
                if (SetToOneSpaceDimension)
                {
                    SpatialDomains::SegGeomSharedPtr OneDSegmentGeom =
                        SegGeom->GenerateOneSpaceDimGeom();
 
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            bkey, OneDSegmentGeom);
                }
                else
                {
 
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            bkey, SegGeom);
                }
            }
            else if ((TriGeom =
                          std::dynamic_pointer_cast<SpatialDomains::TriGeom>(
                              compIt.second->m_geomVec[j])))
            {
                m_expType = e2D;
 
                // First, create the element stdExp that the face belongs to
                SpatialDomains::GeometryLinkSharedPtr elmts =
                    graph->GetElementsFromFace(TriGeom);
                // elmts -> std::vector<std::pair<GeometrySharedPtr, int> >
                // Currently we assume the elements adjacent to the face have
                // the same type. So we directly fetch the first element.
                SpatialDomains::GeometrySharedPtr geom = elmts->at(0).first;
                int face_id                            = elmts->at(0).second;
                SpatialDomains::ExpansionInfoShPtr expInfo =
                    graph->GetExpansionInfo(geom, variable);
                LibUtilities::BasisKey Ba = expInfo->m_basisKeyVector[0];
                LibUtilities::BasisKey Bb = expInfo->m_basisKeyVector[1];
                LibUtilities::BasisKey Bc = expInfo->m_basisKeyVector[2];
                StdRegions::StdExpansionSharedPtr elmtStdExp;
 
                if (geom->GetShapeType() == LibUtilities::ePrism)
                {
                    elmtStdExp = MemoryManager<
                        StdRegions::StdPrismExp>::AllocateSharedPtr(Ba, Bb, Bc);
                }
                else if (geom->GetShapeType() == LibUtilities::eTetrahedron)
                {
                    elmtStdExp =
                        MemoryManager<StdRegions::StdTetExp>::AllocateSharedPtr(
                            Ba, Bb, Bc);
                }
                else if (geom->GetShapeType() == LibUtilities::ePyramid)
                {
                    elmtStdExp =
                        MemoryManager<StdRegions::StdPyrExp>::AllocateSharedPtr(
                            Ba, Bb, Bc);
                }
                else // hex cannot have tri surface
                {
                    NEKERROR(ErrorUtil::efatal,
                             "Fail to cast geom to a known 3D shape.");
                }
                // Then, get the trace basis key from the element stdExp,
                // which may be different from Ba, Bb and Bc.
                LibUtilities::BasisKey TriBa =
                    elmtStdExp->GetTraceBasisKey(face_id, 0);
                LibUtilities::BasisKey TriBb =
                    elmtStdExp->GetTraceBasisKey(face_id, 1);
                // swap TriBa and TriBb orientation is transposed
                if (geom->GetForient(face_id) >= 9)
                {
                    std::swap(TriBa, TriBb);
                }
 
                if (graph->GetExpansionInfo()
                        .begin()
                        ->second->m_basisKeyVector[0]
                        .GetBasisType() == LibUtilities::eGLL_Lagrange)
                {
                    NEKERROR(ErrorUtil::efatal, "This method needs sorting");
                    TriNb = LibUtilities::eNodalTriElec;
 
                    exp = MemoryManager<
                        LocalRegions::NodalTriExp>::AllocateSharedPtr(TriBa,
                                                                      TriBb,
                                                                      TriNb,
                                                                      TriGeom);
                }
                else
                {
                    exp =
                        MemoryManager<LocalRegions::TriExp>::AllocateSharedPtr(
                            TriBa, TriBb, TriGeom);
                }
            }
            else if ((QuadGeom =
                          std::dynamic_pointer_cast<SpatialDomains::QuadGeom>(
                              compIt.second->m_geomVec[j])))
            {
                m_expType = e2D;
 
                // First, create the element stdExp that the face belongs to
                SpatialDomains::GeometryLinkSharedPtr elmts =
                    graph->GetElementsFromFace(QuadGeom);
                // elmts -> std::vector<std::pair<GeometrySharedPtr, int> >
                // Currently we assume the elements adjacent to the face have
                // the same type. So we directly fetch the first element.
                SpatialDomains::GeometrySharedPtr geom = elmts->at(0).first;
                int face_id                            = elmts->at(0).second;
                SpatialDomains::ExpansionInfoShPtr expInfo =
                    graph->GetExpansionInfo(geom, variable);
                LibUtilities::BasisKey Ba = expInfo->m_basisKeyVector[0];
                LibUtilities::BasisKey Bb = expInfo->m_basisKeyVector[1];
                LibUtilities::BasisKey Bc = expInfo->m_basisKeyVector[2];
                StdRegions::StdExpansionSharedPtr elmtStdExp;
 
                if (geom->GetShapeType() == LibUtilities::ePrism)
                {
                    elmtStdExp = MemoryManager<
                        StdRegions::StdPrismExp>::AllocateSharedPtr(Ba, Bb, Bc);
                }
                else if (geom->GetShapeType() == LibUtilities::eHexahedron)
                {
                    elmtStdExp =
                        MemoryManager<StdRegions::StdHexExp>::AllocateSharedPtr(
                            Ba, Bb, Bc);
                }
                else if (geom->GetShapeType() == LibUtilities::ePyramid)
                {
                    elmtStdExp =
                        MemoryManager<StdRegions::StdPyrExp>::AllocateSharedPtr(
                            Ba, Bb, Bc);
                }
                else // Tet cannot have quad surface
                {
                    NEKERROR(ErrorUtil::efatal,
                             "Fail to cast geom to a known 3D shape.");
                }
                // Then, get the trace basis key from the element stdExp,
                // which may be different from Ba, Bb and Bc.
                LibUtilities::BasisKey QuadBa =
                    elmtStdExp->GetTraceBasisKey(face_id, 0);
                LibUtilities::BasisKey QuadBb =
                    elmtStdExp->GetTraceBasisKey(face_id, 1);
                // swap Ba and Bb if the orientation is transposed
                if (geom->GetForient(face_id) >= 9)
                {
                    std::swap(QuadBa, QuadBb);
                }
 
                exp = MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                    QuadBa, QuadBb, QuadGeom);
            }
            else
            {
                NEKERROR(ErrorUtil::efatal,
                         "dynamic cast to a Geom (possibly 3D) failed");
            }
 
            exp->SetElmtId(elmtid++);
            (*m_exp).push_back(exp);
        }
    }
 
    // Set up m_coeffs, m_phys and offset arrays.
    SetupCoeffPhys(DeclareCoeffPhysArrays);
 
    if (m_expType != e0D)
    {
        CreateCollections(ImpType);
    }
}
 
/**
 * Each expansion (local element) is processed in turn to
 * determine the number of coefficients and physical data
 * points it contributes to the domain. Two arrays,
 * #m_coeff_offset are #m_phys_offset are also initialised and
 * updated to store the data offsets of each element in the
 * #m_coeffs and #m_phys arrays, and the element id that each
 * consecutive block is associated respectively.
 * Finally we initialise #m_coeffs and #m_phys
 */
void ExpList::SetupCoeffPhys(bool DeclareCoeffPhysArrays, bool SetupOffsets)
{
    if (SetupOffsets)
    {
        int i;
 
        // Set up offset information and array sizes
        m_coeff_offset = Array<OneD, int>(m_exp->size());
        m_phys_offset  = Array<OneD, int>(m_exp->size());
 
        m_ncoeffs = m_npoints = 0;
 
        for (i = 0; i < m_exp->size(); ++i)
        {
            m_coeff_offset[i] = m_ncoeffs;
            m_phys_offset[i]  = m_npoints;
            m_ncoeffs += (*m_exp)[i]->GetNcoeffs();
            m_npoints += (*m_exp)[i]->GetTotPoints();
        }
    }
 
    if (DeclareCoeffPhysArrays)
    {
        m_coeffs = Array<OneD, NekDouble>(m_ncoeffs, 0.0);
        m_phys   = Array<OneD, NekDouble>(m_npoints, 0.0);
    }
 
    m_coeffsToElmt = Array<OneD, pair<int, int>>{size_t(m_ncoeffs)};
 
    for (int i = 0; i < m_exp->size(); ++i)
    {
        int coeffs_offset = m_coeff_offset[i];
 
        int loccoeffs = (*m_exp)[i]->GetNcoeffs();
 
        for (int j = 0; j < loccoeffs; ++j)
        {
            m_coeffsToElmt[coeffs_offset + j].first  = i;
            m_coeffsToElmt[coeffs_offset + j].second = j;
        }
    }
}
 
void ExpList::InitialiseExpVector(
    const SpatialDomains::ExpansionInfoMap &expmap)
{
 
    SpatialDomains::SegGeomSharedPtr SegmentGeom;
    SpatialDomains::TriGeomSharedPtr TriangleGeom;
    SpatialDomains::QuadGeomSharedPtr QuadrilateralGeom;
    SpatialDomains::TetGeomSharedPtr TetGeom;
    SpatialDomains::HexGeomSharedPtr HexGeom;
    SpatialDomains::PrismGeomSharedPtr PrismGeom;
    SpatialDomains::PyrGeomSharedPtr PyrGeom;
 
    int id = 0;
    LocalRegions::ExpansionSharedPtr exp;
 
    m_expType = eNoType;
    // Process each expansion in the graph
    for (auto &expIt : expmap)
    {
        const SpatialDomains::ExpansionInfoShPtr expInfo = expIt.second;
 
        switch (expInfo->m_basisKeyVector.size())
        {
            case 1: // Segment Expansions
            {
                ASSERTL1(m_expType == e1D || m_expType == eNoType,
                         "Cannot mix expansion dimensions in one vector");
                m_expType = e1D;
 
                if ((SegmentGeom =
                         std::dynamic_pointer_cast<SpatialDomains::SegGeom>(
                             expInfo->m_geomShPtr)))
                {
                    // Retrieve basis key from expansion
                    LibUtilities::BasisKey bkey = expInfo->m_basisKeyVector[0];
 
                    exp =
                        MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
                            bkey, SegmentGeom);
                }
                else
                {
                    NEKERROR(ErrorUtil::efatal,
                             "dynamic cast to a 1D Geom failed");
                }
            }
            break;
            case 2:
            {
                ASSERTL1(m_expType == e2D || m_expType == eNoType,
                         "Cannot mix expansion dimensions in one vector");
                m_expType = e2D;
 
                LibUtilities::BasisKey Ba = expInfo->m_basisKeyVector[0];
                LibUtilities::BasisKey Bb = expInfo->m_basisKeyVector[1];
 
                if ((TriangleGeom =
                         std::dynamic_pointer_cast<SpatialDomains ::TriGeom>(
                             expInfo->m_geomShPtr)))
                {
 
                    // This is not elegantly implemented needs re-thinking.
                    if (Ba.GetBasisType() == LibUtilities::eGLL_Lagrange)
                    {
                        LibUtilities::BasisKey newBa(LibUtilities::eOrtho_A,
                                                     Ba.GetNumModes(),
                                                     Ba.GetPointsKey());
 
                        LibUtilities::PointsType TriNb =
                            LibUtilities::eNodalTriElec;
                        exp = MemoryManager<LocalRegions::NodalTriExp>::
                            AllocateSharedPtr(newBa, Bb, TriNb, TriangleGeom);
                    }
                    else
                    {
                        exp = MemoryManager<LocalRegions::TriExp>::
                            AllocateSharedPtr(Ba, Bb, TriangleGeom);
                    }
                }
                else if ((QuadrilateralGeom = std::dynamic_pointer_cast<
                              SpatialDomains::QuadGeom>(expInfo->m_geomShPtr)))
                {
                    exp =
                        MemoryManager<LocalRegions::QuadExp>::AllocateSharedPtr(
                            Ba, Bb, QuadrilateralGeom);
                }
                else
                {
                    NEKERROR(ErrorUtil::efatal,
                             "dynamic cast to a 2D Geom failed");
                }
            }
            break;
            case 3:
            {
                ASSERTL1(m_expType == e3D || m_expType == eNoType,
                         "Cannot mix expansion dimensions in one vector");
                m_expType = e3D;
 
                LibUtilities::BasisKey Ba = expInfo->m_basisKeyVector[0];
                LibUtilities::BasisKey Bb = expInfo->m_basisKeyVector[1];
                LibUtilities::BasisKey Bc = expInfo->m_basisKeyVector[2];
 
                if ((TetGeom =
                         std::dynamic_pointer_cast<SpatialDomains::TetGeom>(
                             expInfo->m_geomShPtr)))
                {
 
                    if (Ba.GetBasisType() == LibUtilities::eGLL_Lagrange ||
                        Ba.GetBasisType() == LibUtilities::eGauss_Lagrange)
                    {
                        NEKERROR(ErrorUtil::efatal,
                                 "LocalRegions::NodalTetExp is not implemented "
                                 "yet");
                    }
                    else
                    {
                        exp = MemoryManager<
                            LocalRegions::TetExp>::AllocateSharedPtr(Ba, Bb, Bc,
                                                                     TetGeom);
                    }
                }
                else if ((PrismGeom = std::dynamic_pointer_cast<
                              SpatialDomains ::PrismGeom>(
                              expInfo->m_geomShPtr)))
                {
                    exp = MemoryManager<
                        LocalRegions::PrismExp>::AllocateSharedPtr(Ba, Bb, Bc,
                                                                   PrismGeom);
                }
                else if ((PyrGeom = std::dynamic_pointer_cast<
                              SpatialDomains::PyrGeom>(expInfo->m_geomShPtr)))
                {
 
                    exp =
                        MemoryManager<LocalRegions::PyrExp>::AllocateSharedPtr(
                            Ba, Bb, Bc, PyrGeom);
                }
                else if ((HexGeom = std::dynamic_pointer_cast<
                              SpatialDomains::HexGeom>(expInfo->m_geomShPtr)))
                {
                    exp =
                        MemoryManager<LocalRegions::HexExp>::AllocateSharedPtr(
                            Ba, Bb, Bc, HexGeom);
                }
                else
                {
                    NEKERROR(ErrorUtil::efatal,
                             "dynamic cast to a Geom failed");
                }
            }
            break;
            default:
                NEKERROR(ErrorUtil::efatal,
                         "Dimension of basis key is greater than 3");
        }
 
        // Assign next id
        exp->SetElmtId(id++);
 
        // Add the expansion
        (*m_exp).push_back(exp);
    }
}
 
/**
 *
 */
ExpansionType ExpList::GetExpType(void)
{
    return m_expType;
}
 
ExpList::~ExpList()
{
}
 
/**
 * Retrieves the block matrix specified by \a bkey, and computes
 * \f$ y=Mx \f$.
 * @param   gkey        GlobalMatrixKey specifying the block matrix to
 *                      use in the matrix-vector multiply.
 * @param   inarray     Input vector \f$ x \f$.
 * @param   outarray    Output vector \f$ y \f$.
 */
void ExpList::MultiplyByBlockMatrix(const GlobalMatrixKey &gkey,
                                    const Array<OneD, const NekDouble> &inarray,
                                    Array<OneD, NekDouble> &outarray)
{
    // Retrieve the block matrix using the given key.
    const DNekScalBlkMatSharedPtr &blockmat = GetBlockMatrix(gkey);
    int nrows                               = blockmat->GetRows();
    int ncols                               = blockmat->GetColumns();
 
    // Create NekVectors from the given data arrays
    NekVector<NekDouble> in(ncols, inarray, eWrapper);
    NekVector<NekDouble> out(nrows, outarray, eWrapper);
 
    // Perform matrix-vector multiply.
    out = (*blockmat) * in;
}
 
/**
 * multiply the metric jacobi and quadrature weights
 */
void ExpList::MultiplyByQuadratureMetric(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> e_outarray;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        (*m_exp)[i]->MultiplyByQuadratureMetric(inarray + m_phys_offset[i],
                                                e_outarray = outarray +
                                                             m_phys_offset[i]);
    }
}
 
/**
 * Divided by the metric jacobi and quadrature weights
 */
void ExpList::DivideByQuadratureMetric(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> e_outarray;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        (*m_exp)[i]->DivideByQuadratureMetric(inarray + m_phys_offset[i],
                                              e_outarray =
                                                  outarray + m_phys_offset[i]);
    }
}
 
/**
 * The operation is evaluated locally for every element by the function
 * StdRegions#Expansion#IProductWRTDerivBase.
 *
 * @param   dir             {0,1} is the direction in which the
 *                          derivative of the basis should be taken
 * @param   inarray         An array of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$.
 * @param   outarray        An array of size \f$N_{\mathrm{eof}}\f$
 *                          used to store the result.
 */
void ExpList::v_IProductWRTDerivBase(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int i;
 
    Array<OneD, NekDouble> e_outarray;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        (*m_exp)[i]->IProductWRTDerivBase(dir, inarray + m_phys_offset[i],
                                          e_outarray =
                                              outarray + m_coeff_offset[i]);
    }
}
 
/**
 * @brief Directional derivative along a given direction
 *
 */
void ExpList::IProductWRTDirectionalDerivBase(
    const Array<OneD, const NekDouble> &direction,
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int npts_e;
    int coordim = (*m_exp)[0]->GetGeom()->GetCoordim();
    int nq      = direction.size() / coordim;
 
    Array<OneD, NekDouble> e_outarray;
    Array<OneD, NekDouble> e_MFdiv;
 
    Array<OneD, NekDouble> locdir;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        npts_e = (*m_exp)[i]->GetTotPoints();
        locdir = Array<OneD, NekDouble>(npts_e * coordim);
 
        for (int k = 0; k < coordim; ++k)
        {
            Vmath::Vcopy(npts_e, &direction[k * nq + m_phys_offset[i]], 1,
                         &locdir[k * npts_e], 1);
        }
 
        (*m_exp)[i]->IProductWRTDirectionalDerivBase(
            locdir, inarray + m_phys_offset[i],
            e_outarray = outarray + m_coeff_offset[i]);
    }
}
 
/**
 * The operation is evaluated locally for every element by the function
 * StdRegions#StdExpansion#IProductWRTDerivBase.
 *
 * @param   inarray         An array of arrays of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$ in dir directions.
 * @param   outarray        An array of size \f$N_{\mathrm{eof}}\f$
 *                          used to store the result.
 */
void ExpList::v_IProductWRTDerivBase(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> tmp0, tmp1, tmp2;
    // assume coord dimension defines the size of Deriv Base
    int dim = GetCoordim(0);
 
    ASSERTL1(inarray.size() >= dim, "inarray is not of sufficient dimension");
 
    // initialise if required
    if (m_collectionsDoInit[Collections::eIProductWRTDerivBase])
    {
        for (int i = 0; i < m_collections.size(); ++i)
        {
            m_collections[i].Initialise(Collections::eIProductWRTDerivBase);
        }
        m_collectionsDoInit[Collections::eIProductWRTDerivBase] = false;
    }
 
    LibUtilities::Timer timer;
 
    LIKWID_MARKER_START("IProductWRTDerivBase_coll");
    timer.Start();
 
    switch (dim)
    {
        case 1:
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].ApplyOperator(
                    Collections::eIProductWRTDerivBase,
                    inarray[0] + m_coll_phys_offset[i],
                    tmp0 = outarray + m_coll_coeff_offset[i]);
            }
            break;
        case 2:
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].ApplyOperator(
                    Collections::eIProductWRTDerivBase,
                    inarray[0] + m_coll_phys_offset[i],
                    tmp0 = inarray[1] + m_coll_phys_offset[i],
                    tmp1 = outarray + m_coll_coeff_offset[i]);
            }
            break;
        case 3:
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].ApplyOperator(
                    Collections::eIProductWRTDerivBase,
                    inarray[0] + m_coll_phys_offset[i],
                    tmp0 = inarray[1] + m_coll_phys_offset[i],
                    tmp1 = inarray[2] + m_coll_phys_offset[i],
                    tmp2 = outarray + m_coll_coeff_offset[i]);
            }
            break;
        default:
            NEKERROR(ErrorUtil::efatal, "Dimension of inarray not correct");
            break;
    }
 
    timer.Stop();
    LIKWID_MARKER_STOP("IProductWRTDerivBase_coll");
 
    // Elapsed time
    timer.AccumulateRegion("Collections:IProductWRTDerivBase", 10);
}
/**
 * Given a function \f$f(\boldsymbol{x})\f$ evaluated at
 * the quadrature points, this function calculates the
 * derivatives \f$\frac{d}{dx_1}\f$, \f$\frac{d}{dx_2}\f$
 * and \f$\frac{d}{dx_3}\f$ of the function
 * \f$f(\boldsymbol{x})\f$ at the same quadrature
 * points. The local distribution of the quadrature points
 * allows an elemental evaluation of the derivative. This
 * is done by a call to the function
 * StdRegions#StdExpansion#PhysDeriv.
 *
 * @param   inarray         An array of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$.
 * @param   out_d0          The discrete evaluation of the
 *                          derivative\f$\frac{d}{dx_1}\f$ will
 *                          be stored in this array of size
 *                          \f$Q_{\mathrm{tot}}\f$.
 * @param   out_d1          The discrete evaluation of the
 *                          derivative\f$\frac{d}{dx_2}\f$ will be
 *                          stored in this array of size
 *                          \f$Q_{\mathrm{tot}}\f$. Note that if no
 *                          memory is allocated for \a out_d1, the
 *                          derivative \f$\frac{d}{dx_2}\f$ will not be
 *                          calculated.
 * @param   out_d2          The discrete evaluation of the
 *                          derivative\f$\frac{d}{dx_3}\f$ will be
 *                          stored in this array of size
 *                          \f$Q_{\mathrm{tot}}\f$. Note that if no
 *                          memory is allocated for \a out_d2, the
 *                          derivative \f$\frac{d}{dx_3}\f$ will not be
 *                          calculated.
 */
void ExpList::v_PhysDeriv(const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> &out_d0,
                          Array<OneD, NekDouble> &out_d1,
                          Array<OneD, NekDouble> &out_d2)
{
    Array<OneD, NekDouble> e_out_d0;
    Array<OneD, NekDouble> e_out_d1;
    Array<OneD, NekDouble> e_out_d2;
    int offset;
 
    // initialise if required
    if (m_collectionsDoInit[Collections::ePhysDeriv])
    {
        for (int i = 0; i < m_collections.size(); ++i)
        {
            m_collections[i].Initialise(Collections::ePhysDeriv);
        }
        m_collectionsDoInit[Collections::ePhysDeriv] = false;
    }
 
    LibUtilities::Timer timer;
    timer.Start();
    for (int i = 0; i < m_collections.size(); ++i)
    {
        offset   = m_coll_phys_offset[i];
        e_out_d0 = out_d0 + offset;
        e_out_d1 = out_d1 + offset;
        e_out_d2 = out_d2 + offset;
 
        m_collections[i].ApplyOperator(Collections::ePhysDeriv,
                                       inarray + offset, e_out_d0, e_out_d1,
                                       e_out_d2);
    }
    timer.Stop();
    // Elapsed time
    timer.AccumulateRegion("Collections:PhysDeriv", 10);
}
 
void ExpList::v_PhysDeriv(const int dir,
                          const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> &out_d)
{
    Direction edir = DirCartesianMap[dir];
    v_PhysDeriv(edir, inarray, out_d);
}
 
void ExpList::v_PhysDeriv(Direction edir,
                          const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> &out_d)
{
    int i;
    if (edir == MultiRegions::eS)
    {
        Array<OneD, NekDouble> e_out_ds;
        for (i = 0; i < (*m_exp).size(); ++i)
        {
            e_out_ds = out_d + m_phys_offset[i];
            (*m_exp)[i]->PhysDeriv_s(inarray + m_phys_offset[i], e_out_ds);
        }
    }
    else if (edir == MultiRegions::eN)
    {
        Array<OneD, NekDouble> e_out_dn;
        for (i = 0; i < (*m_exp).size(); i++)
        {
            e_out_dn = out_d + m_phys_offset[i];
            (*m_exp)[i]->PhysDeriv_n(inarray + m_phys_offset[i], e_out_dn);
        }
    }
    else
    {
 
        // initialise if required
        if (m_collectionsDoInit[Collections::ePhysDeriv])
        {
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].Initialise(Collections::ePhysDeriv);
            }
            m_collectionsDoInit[Collections::ePhysDeriv] = false;
        }
 
        // convert enum into int
        int intdir = (int)edir;
        Array<OneD, NekDouble> e_out_d;
        int offset;
        for (int i = 0; i < m_collections.size(); ++i)
        {
            offset  = m_coll_phys_offset[i];
            e_out_d = out_d + offset;
 
            m_collections[i].ApplyOperator(Collections::ePhysDeriv, intdir,
                                           inarray + offset, e_out_d);
        }
    }
}
 
/* Computes the curl of velocity = \nabla \times u
 * if m_expType == 2D, Q = [omg_z, (nothing done)]
 * if m_expType == 3D, Q = [omg_x, omg_y, omg_z]
 */
void ExpList::v_Curl(Array<OneD, Array<OneD, NekDouble>> &Vel,
                     Array<OneD, Array<OneD, NekDouble>> &Q)
{
    int nq = GetTotPoints();
    Array<OneD, NekDouble> Vx(nq);
    Array<OneD, NekDouble> Uy(nq);
    Array<OneD, NekDouble> Dummy(nq);
 
    switch (m_expType)
    {
        case e2D:
        {
            PhysDeriv(xDir, Vel[yDir], Vx);
            PhysDeriv(yDir, Vel[xDir], Uy);
 
            Vmath::Vsub(nq, Vx, 1, Uy, 1, Q[0], 1);
        }
        break;
 
        case e3D:
        {
            Array<OneD, NekDouble> Vz(nq);
            Array<OneD, NekDouble> Uz(nq);
            Array<OneD, NekDouble> Wx(nq);
            Array<OneD, NekDouble> Wy(nq);
 
            PhysDeriv(Vel[xDir], Dummy, Uy, Uz);
            PhysDeriv(Vel[yDir], Vx, Dummy, Vz);
            PhysDeriv(Vel[zDir], Wx, Wy, Dummy);
 
            Vmath::Vsub(nq, Wy, 1, Vz, 1, Q[0], 1);
            Vmath::Vsub(nq, Uz, 1, Wx, 1, Q[1], 1);
            Vmath::Vsub(nq, Vx, 1, Uy, 1, Q[2], 1);
        }
        break;
        default:
            ASSERTL0(0, "Dimension not supported by ExpList::Curl");
            break;
    }
}
 
/* Computes the curl of vorticity = \nabla \times \nabla \times u
 * if m_expType == 2D, Q = [dy omg_z, -dx omg_z, 0]
 *
 * if m_expType == 3D, Q = [dy omg_z - dz omg_y,
 *                          dz omg_x - dx omg_z,
 *                          dx omg_y - dy omg_x]
 *
 */
void ExpList::v_CurlCurl(Array<OneD, Array<OneD, NekDouble>> &Vel,
                         Array<OneD, Array<OneD, NekDouble>> &Q)
{
    int nq = GetTotPoints();
    Array<OneD, NekDouble> Vx(nq);
    Array<OneD, NekDouble> Uy(nq);
    Array<OneD, NekDouble> Dummy(nq);
 
    bool halfMode = false;
    if (GetExpType() == e3DH1D)
    {
        m_session->MatchSolverInfo("ModeType", "HalfMode", halfMode, false);
    }
 
    switch (m_expType)
    {
        case e2D:
        {
            PhysDeriv(xDir, Vel[yDir], Vx);
            PhysDeriv(yDir, Vel[xDir], Uy);
 
            Vmath::Vsub(nq, Vx, 1, Uy, 1, Dummy, 1);
 
            PhysDeriv(Dummy, Q[1], Q[0]);
 
            Vmath::Smul(nq, -1.0, Q[1], 1, Q[1], 1);
        }
        break;
 
        case e3D:
        case e3DH1D:
        case e3DH2D:
        {
            Array<OneD, NekDouble> Vz(nq);
            Array<OneD, NekDouble> Uz(nq);
            Array<OneD, NekDouble> Wx(nq);
            Array<OneD, NekDouble> Wy(nq);
 
            PhysDeriv(Vel[xDir], Dummy, Uy, Uz);
            PhysDeriv(Vel[yDir], Vx, Dummy, Vz);
            PhysDeriv(Vel[zDir], Wx, Wy, Dummy);
 
            Vmath::Vsub(nq, Wy, 1, Vz, 1, Q[0], 1);
            Vmath::Vsub(nq, Uz, 1, Wx, 1, Q[1], 1);
            Vmath::Vsub(nq, Vx, 1, Uy, 1, Q[2], 1);
 
            PhysDeriv(Q[0], Dummy, Uy, Uz);
            PhysDeriv(Q[1], Vx, Dummy, Vz);
            PhysDeriv(Q[2], Wx, Wy, Dummy);
 
            // For halfmode, need to change the sign of z derivatives
            if (halfMode)
            {
                Vmath::Neg(nq, Uz, 1);
                Vmath::Neg(nq, Vz, 1);
            }
 
            Vmath::Vsub(nq, Wy, 1, Vz, 1, Q[0], 1);
            Vmath::Vsub(nq, Uz, 1, Wx, 1, Q[1], 1);
            Vmath::Vsub(nq, Vx, 1, Uy, 1, Q[2], 1);
        }
        break;
        default:
            ASSERTL0(0, "Dimension not supported");
            break;
    }
}
 
void ExpList::v_PhysDirectionalDeriv(
    const Array<OneD, const NekDouble> &direction,
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int npts_e;
    int coordim = (*m_exp)[0]->GetGeom()->GetCoordim();
    int nq      = direction.size() / coordim;
 
    Array<OneD, NekDouble> e_outarray;
    Array<OneD, NekDouble> e_MFdiv;
    Array<OneD, NekDouble> locdir;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        npts_e = (*m_exp)[i]->GetTotPoints();
        locdir = Array<OneD, NekDouble>(npts_e * coordim);
 
        for (int k = 0; k < coordim; ++k)
        {
            Vmath::Vcopy(npts_e, &direction[k * nq + m_phys_offset[i]], 1,
                         &locdir[k * npts_e], 1);
        }
 
        (*m_exp)[i]->PhysDirectionalDeriv(inarray + m_phys_offset[i], locdir,
                                          e_outarray =
                                              outarray + m_phys_offset[i]);
    }
}
 
void ExpList::ExponentialFilter(Array<OneD, NekDouble> &array,
                                const NekDouble alpha, const NekDouble exponent,
                                const NekDouble cutoff)
{
    Array<OneD, NekDouble> e_array;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        (*m_exp)[i]->ExponentialFilter(e_array = array + m_phys_offset[i],
                                       alpha, exponent, cutoff);
    }
}
 
/**
 * The coefficients of the function to be acted upon
 * should be contained in the \param inarray. The
 * resulting coefficients are stored in \param outarray
 *
 * @param   inarray         An array of size \f$N_{\mathrm{eof}}\f$
 *                          containing the inner product.
 */
void ExpList::MultiplyByElmtInvMass(const Array<OneD, const NekDouble> &inarray,
                                    Array<OneD, NekDouble> &outarray)
{
    GlobalMatrixKey mkey(StdRegions::eInvMass);
    const DNekScalBlkMatSharedPtr &InvMass = GetBlockMatrix(mkey);
 
    // Inverse mass matrix
    NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
    if (inarray.get() == outarray.get())
    {
        NekVector<NekDouble> in(m_ncoeffs, inarray); // copy data
        out = (*InvMass) * in;
    }
    else
    {
        NekVector<NekDouble> in(m_ncoeffs, inarray, eWrapper);
        out = (*InvMass) * in;
    }
}
 
/**
 * Given a function \f$u(\boldsymbol{x})\f$ defined at the
 * quadrature points, this function determines the
 * transformed elemental coefficients \f$\hat{u}_n^e\f$
 * employing a discrete elemental Galerkin projection from
 * physical space to coefficient space. For each element,
 * the operation is evaluated locally by the function
 * StdRegions#StdExpansion#IproductWRTBase followed by a
 * call to #MultiRegions#MultiplyByElmtInvMass.
 *
 * @param   inarray         An array of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$.
 * @param   outarray        The resulting coefficients
 *                          \f$\hat{u}_n^e\f$ will be stored in this
 *                          array of size \f$N_{\mathrm{eof}}\f$.
 */
void ExpList::v_FwdTransLocalElmt(const Array<OneD, const NekDouble> &inarray,
                                  Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> f(m_ncoeffs);
 
    IProductWRTBase(inarray, f);
    MultiplyByElmtInvMass(f, outarray);
}
 
void ExpList::v_FwdTransBndConstrained(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int i;
 
    Array<OneD, NekDouble> e_outarray;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        (*m_exp)[i]->FwdTransBndConstrained(inarray + m_phys_offset[i],
                                            e_outarray =
                                                outarray + m_coeff_offset[i]);
    }
}
 
/**
 * This function smooth a field after some calculaitons which have
 * been done elementally.
 *
 * @param   field     An array containing the field in physical space
 *
 */
void ExpList::v_SmoothField(Array<OneD, NekDouble> &field)
{
    boost::ignore_unused(field);
    // Do nothing unless the method is implemented in the appropriate
    // class, i.e. ContField1D,ContField2D, etc.
 
    // So far it has been implemented just for ContField2D and
    // ContField3DHomogeneous1D
 
    // Block in case users try the smoothing with a modal expansion.
    // Maybe a different techique for the smoothing require
    // implementation for modal basis.
 
    ASSERTL0((*m_exp)[0]->GetBasisType(0) == LibUtilities::eGLL_Lagrange ||
                 (*m_exp)[0]->GetBasisType(0) == LibUtilities::eGauss_Lagrange,
             "Smoothing is currently not allowed unless you are using "
             "a nodal base for efficiency reasons. The implemented "
             "smoothing technique requires the mass matrix inversion "
             "which is trivial just for GLL_LAGRANGE_SEM and "
             "GAUSS_LAGRANGE_SEMexpansions.");
}
 
/**
 * This function assembles the block diagonal matrix
 * \f$\underline{\boldsymbol{M}}^e\f$, which is the
 * concatenation of the local matrices
 * \f$\boldsymbol{M}^e\f$ of the type \a mtype, that is
 *
 * \f[
 * \underline{\boldsymbol{M}}^e = \left[
 * \begin{array}{cccc}
 * \boldsymbol{M}^1 & 0 & \hspace{3mm}0 \hspace{3mm}& 0 \\
 *  0 & \boldsymbol{M}^2 & 0 & 0 \\
 *  0 &  0 & \ddots &  0 \\
 *  0 &  0 & 0 & \boldsymbol{M}^{N_{\mathrm{el}}} \end{array}\right].\f]
 *
 * @param   mtype           the type of matrix to be assembled
 * @param   scalar          an optional parameter
 * @param   constant        an optional parameter
 */
const DNekScalBlkMatSharedPtr ExpList::GenBlockMatrix(
    const GlobalMatrixKey &gkey)
{
    int i, cnt1;
    int n_exp = 0;
    DNekScalMatSharedPtr loc_mat;
    DNekScalBlkMatSharedPtr BlkMatrix;
    map<int, int> elmt_id;
    LibUtilities::ShapeType ShapeType = gkey.GetShapeType();
 
    if (ShapeType != LibUtilities::eNoShapeType)
    {
        for (i = 0; i < (*m_exp).size(); ++i)
        {
            if ((*m_exp)[i]->DetShapeType() == ShapeType)
            {
                elmt_id[n_exp++] = i;
            }
        }
    }
    else
    {
        n_exp = (*m_exp).size();
        for (i = 0; i < n_exp; ++i)
        {
            elmt_id[i] = i;
        }
    }
 
    Array<OneD, unsigned int> nrows(n_exp);
    Array<OneD, unsigned int> ncols(n_exp);
 
    switch (gkey.GetMatrixType())
    {
        case StdRegions::eBwdTrans:
        {
            // set up an array of integers for block matrix construction
            for (i = 0; i < n_exp; ++i)
            {
                nrows[i] = (*m_exp)[elmt_id.find(i)->second]->GetTotPoints();
                ncols[i] = (*m_exp)[elmt_id.find(i)->second]->GetNcoeffs();
            }
        }
        break;
        case StdRegions::eIProductWRTBase:
        {
            // set up an array of integers for block matrix construction
            for (i = 0; i < n_exp; ++i)
            {
                nrows[i] = (*m_exp)[elmt_id.find(i)->second]->GetNcoeffs();
                ncols[i] = (*m_exp)[elmt_id.find(i)->second]->GetTotPoints();
            }
        }
        break;
        case StdRegions::eMass:
        case StdRegions::eInvMass:
        case StdRegions::eHelmholtz:
        case StdRegions::eLaplacian:
        case StdRegions::eInvHybridDGHelmholtz:
        {
            // set up an array of integers for block matrix construction
            for (i = 0; i < n_exp; ++i)
            {
                nrows[i] = (*m_exp)[elmt_id.find(i)->second]->GetNcoeffs();
                ncols[i] = (*m_exp)[elmt_id.find(i)->second]->GetNcoeffs();
            }
        }
        break;
 
        case StdRegions::eHybridDGLamToU:
        {
            // set up an array of integers for block matrix construction
            for (i = 0; i < n_exp; ++i)
            {
                nrows[i] = (*m_exp)[elmt_id.find(i)->second]->GetNcoeffs();
                ncols[i] =
                    (*m_exp)[elmt_id.find(i)->second]->NumDGBndryCoeffs();
            }
        }
        break;
        case StdRegions::eHybridDGHelmBndLam:
        {
            // set up an array of integers for block matrix construction
            for (i = 0; i < n_exp; ++i)
            {
                nrows[i] =
                    (*m_exp)[elmt_id.find(i)->second]->NumDGBndryCoeffs();
                ncols[i] =
                    (*m_exp)[elmt_id.find(i)->second]->NumDGBndryCoeffs();
            }
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal,
                     "Global Matrix creation not defined for this "
                     "type of matrix");
        }
    }
 
    MatrixStorage blkmatStorage = eDIAGONAL;
    BlkMatrix = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(nrows, ncols,
                                                                 blkmatStorage);
 
    int nvarcoeffs = gkey.GetNVarCoeffs();
    int eid;
    Array<OneD, NekDouble> varcoeffs_wk;
 
    for (i = cnt1 = 0; i < n_exp; ++i)
    {
        // need to be initialised with zero size for non
        // variable coefficient case
        StdRegions::VarCoeffMap varcoeffs;
 
        eid = elmt_id[i];
        if (nvarcoeffs > 0)
        {
            varcoeffs = StdRegions::RestrictCoeffMap(
                gkey.GetVarCoeffs(), m_phys_offset[i],
                (*m_exp)[i]->GetTotPoints());
        }
 
        LocalRegions::MatrixKey matkey(
            gkey.GetMatrixType(), (*m_exp)[eid]->DetShapeType(), *(*m_exp)[eid],
            gkey.GetConstFactors(), varcoeffs);
 
        loc_mat = std::dynamic_pointer_cast<LocalRegions::Expansion>(
                      (*m_exp)[elmt_id.find(i)->second])
                      ->GetLocMatrix(matkey);
        BlkMatrix->SetBlock(i, i, loc_mat);
    }
 
    return BlkMatrix;
}
 
const DNekScalBlkMatSharedPtr &ExpList::GetBlockMatrix(
    const GlobalMatrixKey &gkey)
{
    auto matrixIter = m_blockMat->find(gkey);
 
    if (matrixIter == m_blockMat->end())
    {
        return ((*m_blockMat)[gkey] = GenBlockMatrix(gkey));
    }
    else
    {
        return matrixIter->second;
    }
}
 
// Routines for continous matrix solution
/**
 * This operation is equivalent to the evaluation of
 * \f$\underline{\boldsymbol{M}}^e\boldsymbol{\hat{u}}_l\f$, that is,
 * \f[ \left[
 * \begin{array}{cccc}
 * \boldsymbol{M}^1 & 0 & \hspace{3mm}0 \hspace{3mm}& 0 \\
 * 0 & \boldsymbol{M}^2 & 0 & 0 \\
 * 0 &  0 & \ddots &  0 \\
 * 0 &  0 & 0 & \boldsymbol{M}^{N_{\mathrm{el}}} \end{array} \right]
 *\left [ \begin{array}{c}
 * \boldsymbol{\hat{u}}^{1} \\
 * \boldsymbol{\hat{u}}^{2} \\
 * \vdots \\
 * \boldsymbol{\hat{u}}^{{{N_{\mathrm{el}}}}} \end{array} \right ]\f]
 * where \f$\boldsymbol{M}^e\f$ are the local matrices of type
 * specified by the key \a mkey. The decoupling of the local matrices
 * allows for a local evaluation of the operation. However, rather than
 * a local matrix-vector multiplication, the local operations are
 * evaluated as implemented in the function
 * StdRegions#StdExpansion#GeneralMatrixOp.
 *
 * @param   mkey            This key uniquely defines the type matrix
 *                          required for the operation.
 * @param   inarray         The vector \f$\boldsymbol{\hat{u}}_l\f$ of
 *                          size \f$N_{\mathrm{eof}}\f$.
 * @param   outarray        The resulting vector of size
 *                          \f$N_{\mathrm{eof}}\f$.
 */
void ExpList::GeneralMatrixOp(const GlobalMatrixKey &gkey,
                              const Array<OneD, const NekDouble> &inarray,
                              Array<OneD, NekDouble> &outarray)
{
    int nvarcoeffs = gkey.GetNVarCoeffs();
 
    if ((nvarcoeffs == 0) && (gkey.GetMatrixType() == StdRegions::eHelmholtz))
    {
        // initialise if required
        if (m_collections.size() &&
            m_collectionsDoInit[Collections::eHelmholtz])
        {
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].Initialise(Collections::eHelmholtz,
                                            gkey.GetConstFactors());
            }
            m_collectionsDoInit[Collections::eHelmholtz] = false;
        }
        else
        {
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].CheckFactors(Collections::eHelmholtz,
                                              gkey.GetConstFactors(),
                                              m_coll_phys_offset[i]);
            }
        }
 
        Array<OneD, NekDouble> tmp;
        for (int i = 0; i < m_collections.size(); ++i)
        {
            m_collections[i].ApplyOperator(
                Collections::eHelmholtz, inarray + m_coll_coeff_offset[i],
                tmp = outarray + m_coll_coeff_offset[i]);
        }
    }
    else
    {
        Array<OneD, NekDouble> tmp_outarray;
        for (int i = 0; i < (*m_exp).size(); ++i)
        {
            // need to be initialised with zero size for non
            // variable coefficient case
            StdRegions::VarCoeffMap varcoeffs;
 
            if (nvarcoeffs > 0)
            {
                varcoeffs = StdRegions::RestrictCoeffMap(
                    gkey.GetVarCoeffs(), m_phys_offset[i],
                    (*m_exp)[i]->GetTotPoints());
            }
 
            StdRegions::StdMatrixKey mkey(
                gkey.GetMatrixType(), (*m_exp)[i]->DetShapeType(),
                *((*m_exp)[i]), gkey.GetConstFactors(), varcoeffs);
 
            (*m_exp)[i]->GeneralMatrixOp(
                inarray + m_coeff_offset[i],
                tmp_outarray = outarray + m_coeff_offset[i], mkey);
        }
    }
}
 
/**
 * Retrieves local matrices from each expansion in the expansion list
 * and combines them together to generate a global matrix system.
 * @param   mkey        Matrix key for the matrix to be generated.
 * @param   locToGloMap Local to global mapping.
 * @returns Shared pointer to the generated global matrix.
 */
GlobalMatrixSharedPtr ExpList::GenGlobalMatrix(
    const GlobalMatrixKey &mkey, const AssemblyMapCGSharedPtr &locToGloMap)
{
    int i, j, n, gid1, gid2, cntdim1, cntdim2;
    NekDouble sign1, sign2;
    DNekScalMatSharedPtr loc_mat;
 
    unsigned int glob_rows = 0;
    unsigned int glob_cols = 0;
    unsigned int loc_rows  = 0;
    unsigned int loc_cols  = 0;
 
    bool assembleFirstDim  = false;
    bool assembleSecondDim = false;
 
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eBwdTrans:
        {
            glob_rows = m_npoints;
            glob_cols = locToGloMap->GetNumGlobalCoeffs();
 
            assembleFirstDim  = false;
            assembleSecondDim = true;
        }
        break;
        case StdRegions::eIProductWRTBase:
        {
            glob_rows = locToGloMap->GetNumGlobalCoeffs();
            glob_cols = m_npoints;
 
            assembleFirstDim  = true;
            assembleSecondDim = false;
        }
        break;
        case StdRegions::eMass:
        case StdRegions::eHelmholtz:
        case StdRegions::eLaplacian:
        case StdRegions::eHybridDGHelmBndLam:
        {
            glob_rows = locToGloMap->GetNumGlobalCoeffs();
            glob_cols = locToGloMap->GetNumGlobalCoeffs();
 
            assembleFirstDim  = true;
            assembleSecondDim = true;
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal,
                     "Global Matrix creation not defined for this "
                     "type of matrix");
        }
    }
 
    COOMatType spcoomat;
    CoordType coord;
 
    int nvarcoeffs = mkey.GetNVarCoeffs();
    int eid;
 
    // fill global matrix
    for (n = cntdim1 = cntdim2 = 0; n < (*m_exp).size(); ++n)
    {
        // need to be initialised with zero size for non
        // variable coefficient case
        StdRegions::VarCoeffMap varcoeffs;
 
        eid = n;
        if (nvarcoeffs > 0)
        {
            varcoeffs = StdRegions::RestrictCoeffMap(
                mkey.GetVarCoeffs(), m_phys_offset[eid],
                (*m_exp)[eid]->GetTotPoints());
        }
 
        LocalRegions::MatrixKey matkey(
            mkey.GetMatrixType(), (*m_exp)[eid]->DetShapeType(),
            *((*m_exp)[eid]), mkey.GetConstFactors(), varcoeffs);
 
        loc_mat =
            std::dynamic_pointer_cast<LocalRegions::Expansion>((*m_exp)[n])
                ->GetLocMatrix(matkey);
 
        loc_rows = loc_mat->GetRows();
        loc_cols = loc_mat->GetColumns();
 
        for (i = 0; i < loc_rows; ++i)
        {
            if (assembleFirstDim)
            {
                gid1  = locToGloMap->GetLocalToGlobalMap(cntdim1 + i);
                sign1 = locToGloMap->GetLocalToGlobalSign(cntdim1 + i);
            }
            else
            {
                gid1  = cntdim1 + i;
                sign1 = 1.0;
            }
 
            for (j = 0; j < loc_cols; ++j)
            {
                if (assembleSecondDim)
                {
                    gid2  = locToGloMap->GetLocalToGlobalMap(cntdim2 + j);
                    sign2 = locToGloMap->GetLocalToGlobalSign(cntdim2 + j);
                }
                else
                {
                    gid2  = cntdim2 + j;
                    sign2 = 1.0;
                }
 
                // sparse matrix fill
                coord = make_pair(gid1, gid2);
                if (spcoomat.count(coord) == 0)
                {
                    spcoomat[coord] = sign1 * sign2 * (*loc_mat)(i, j);
                }
                else
                {
                    spcoomat[coord] += sign1 * sign2 * (*loc_mat)(i, j);
                }
            }
        }
        cntdim1 += loc_rows;
        cntdim2 += loc_cols;
    }
 
    return MemoryManager<GlobalMatrix>::AllocateSharedPtr(m_session, glob_rows,
                                                          glob_cols, spcoomat);
}
 
DNekMatSharedPtr ExpList::GenGlobalMatrixFull(
    const GlobalLinSysKey &mkey, const AssemblyMapCGSharedPtr &locToGloMap)
{
    int i, j, n, gid1, gid2, loc_lda, eid;
    NekDouble sign1, sign2, value;
    DNekScalMatSharedPtr loc_mat;
 
    int totDofs   = locToGloMap->GetNumGlobalCoeffs();
    int NumDirBCs = locToGloMap->GetNumGlobalDirBndCoeffs();
 
    unsigned int rows = totDofs - NumDirBCs;
    unsigned int cols = totDofs - NumDirBCs;
    NekDouble zero    = 0.0;
 
    DNekMatSharedPtr Gmat;
    int bwidth = locToGloMap->GetFullSystemBandWidth();
 
    int nvarcoeffs = mkey.GetNVarCoeffs();
    MatrixStorage matStorage;
 
    map<int, RobinBCInfoSharedPtr> RobinBCInfo = GetRobinBCInfo();
 
    switch (mkey.GetMatrixType())
    {
            // case for all symmetric matices
        case StdRegions::eHelmholtz:
        case StdRegions::eLaplacian:
            if ((2 * (bwidth + 1)) < rows)
            {
                matStorage = ePOSITIVE_DEFINITE_SYMMETRIC_BANDED;
                Gmat       = MemoryManager<DNekMat>::AllocateSharedPtr(
                    rows, cols, zero, matStorage, bwidth, bwidth);
            }
            else
            {
                matStorage = ePOSITIVE_DEFINITE_SYMMETRIC;
                Gmat       = MemoryManager<DNekMat>::AllocateSharedPtr(
                    rows, cols, zero, matStorage);
            }
 
            break;
        default: // Assume general matrix - currently only set up
            // for full invert
            {
                matStorage = eFULL;
                Gmat       = MemoryManager<DNekMat>::AllocateSharedPtr(
                    rows, cols, zero, matStorage);
            }
    }
 
    // fill global symmetric matrix
    for (n = 0; n < (*m_exp).size(); ++n)
    {
        // need to be initialised with zero size for non
        // variable coefficient case
        StdRegions::VarCoeffMap varcoeffs;
 
        eid = n;
        if (nvarcoeffs > 0)
        {
            varcoeffs = StdRegions::RestrictCoeffMap(
                mkey.GetVarCoeffs(), m_phys_offset[eid],
                (*m_exp)[eid]->GetTotPoints());
        }
 
        LocalRegions::MatrixKey matkey(
            mkey.GetMatrixType(), (*m_exp)[eid]->DetShapeType(),
            *((*m_exp)[eid]), mkey.GetConstFactors(), varcoeffs);
 
        loc_mat =
            std::dynamic_pointer_cast<LocalRegions::Expansion>((*m_exp)[n])
                ->GetLocMatrix(matkey);
 
        if (RobinBCInfo.count(n) != 0) // add robin mass matrix
        {
            RobinBCInfoSharedPtr rBC;
 
            // declare local matrix from scaled matrix.
            int rows             = loc_mat->GetRows();
            int cols             = loc_mat->GetColumns();
            const NekDouble *dat = loc_mat->GetRawPtr();
            DNekMatSharedPtr new_mat =
                MemoryManager<DNekMat>::AllocateSharedPtr(rows, cols, dat);
            Blas::Dscal(rows * cols, loc_mat->Scale(), new_mat->GetRawPtr(), 1);
 
            // add local matrix contribution
            for (rBC = RobinBCInfo.find(n)->second; rBC; rBC = rBC->next)
            {
                (*m_exp)[n]->AddRobinMassMatrix(
                    rBC->m_robinID, rBC->m_robinPrimitiveCoeffs, new_mat);
            }
 
            NekDouble one = 1.0;
            // redeclare loc_mat to point to new_mat plus the scalar.
            loc_mat =
                MemoryManager<DNekScalMat>::AllocateSharedPtr(one, new_mat);
        }
 
        loc_lda = loc_mat->GetColumns();
 
        for (i = 0; i < loc_lda; ++i)
        {
            gid1 = locToGloMap->GetLocalToGlobalMap(m_coeff_offset[n] + i) -
                   NumDirBCs;
            sign1 = locToGloMap->GetLocalToGlobalSign(m_coeff_offset[n] + i);
            if (gid1 >= 0)
            {
                for (j = 0; j < loc_lda; ++j)
                {
                    gid2 = locToGloMap->GetLocalToGlobalMap(m_coeff_offset[n] +
                                                            j) -
                           NumDirBCs;
                    sign2 = locToGloMap->GetLocalToGlobalSign(
                        m_coeff_offset[n] + j);
                    if (gid2 >= 0)
                    {
                        // When global matrix is symmetric,
                        // only add the value for the upper
                        // triangular part in order to avoid
                        // entries to be entered twice
                        if ((matStorage == eFULL) || (gid2 >= gid1))
                        {
                            value = Gmat->GetValue(gid1, gid2) +
                                    sign1 * sign2 * (*loc_mat)(i, j);
                            Gmat->SetValue(gid1, gid2, value);
                        }
                    }
                }
            }
        }
    }
 
    return Gmat;
}
 
/**
 * Consider a linear system
 * \f$\boldsymbol{M\hat{u}}_g=\boldsymbol{f}\f$ to be solved. Dependent
 * on the solution method, this function constructs
 * - <b>The full linear system</b><BR>
 *   A call to the function #GenGlobalLinSysFullDirect
 * - <b>The statically condensed linear system</b><BR>
 *   A call to the function #GenGlobalLinSysStaticCond
 *
 * @param   mkey            A key which uniquely defines the global
 *                          matrix to be constructed.
 * @param   locToGloMap     Contains the mapping array and required
 *                          information for the transformation from
 *                          local to global degrees of freedom.
 * @return  (A shared pointer to) the global linear system in
 *          required format.
 */
GlobalLinSysSharedPtr ExpList::GenGlobalLinSys(
    const GlobalLinSysKey &mkey, const AssemblyMapCGSharedPtr &locToGloMap)
{
    GlobalLinSysSharedPtr returnlinsys;
    std::shared_ptr<ExpList> vExpList = GetSharedThisPtr();
 
    MultiRegions::GlobalSysSolnType vType = mkey.GetGlobalSysSolnType();
 
    if (vType >= eSIZE_GlobalSysSolnType)
    {
        NEKERROR(ErrorUtil::efatal, "Matrix solution type not defined");
    }
    std::string vSolnType = MultiRegions::GlobalSysSolnTypeMap[vType];
 
    return GetGlobalLinSysFactory().CreateInstance(vSolnType, mkey, vExpList,
                                                   locToGloMap);
}
 
GlobalLinSysSharedPtr ExpList::GenGlobalBndLinSys(
    const GlobalLinSysKey &mkey, const AssemblyMapSharedPtr &locToGloMap)
{
    std::shared_ptr<ExpList> vExpList                 = GetSharedThisPtr();
    const map<int, RobinBCInfoSharedPtr> vRobinBCInfo = GetRobinBCInfo();
 
    MultiRegions::GlobalSysSolnType vType = mkey.GetGlobalSysSolnType();
 
    if (vType >= eSIZE_GlobalSysSolnType)
    {
        NEKERROR(ErrorUtil::efatal, "Matrix solution type not defined");
    }
    std::string vSolnType = MultiRegions::GlobalSysSolnTypeMap[vType];
 
    return GetGlobalLinSysFactory().CreateInstance(vSolnType, mkey, vExpList,
                                                   locToGloMap);
}
 
/**
 * Given the elemental coefficients \f$\hat{u}_n^e\f$ of
 * an expansion, this function evaluates the spectral/hp
 * expansion \f$u^{\delta}(\boldsymbol{x})\f$ at the
 * quadrature points \f$\boldsymbol{x}_i\f$. The operation
 * is evaluated locally by the elemental function
 * StdRegions#StdExpansion#BwdTrans.
 *
 * @param   inarray         An array of size \f$N_{\mathrm{eof}}\f$
 *                          containing the local coefficients
 *                          \f$\hat{u}_n^e\f$.
 * @param   outarray        The resulting physical values at the
 *                          quadrature points
 *                          \f$u^{\delta}(\boldsymbol{x}_i)\f$
 *                          will be stored in this array of size
 *                          \f$Q_{\mathrm{tot}}\f$.
 */
 
void ExpList::v_BwdTrans(const Array<OneD, const NekDouble> &inarray,
                         Array<OneD, NekDouble> &outarray)
{
    LibUtilities::Timer timer;
 
    if (m_expType == e0D)
    {
        Vmath::Vcopy(m_ncoeffs, inarray, 1, outarray, 1);
    }
    else
    {
        // initialise if required
        if (m_collections.size() && m_collectionsDoInit[Collections::eBwdTrans])
        {
            for (int i = 0; i < m_collections.size(); ++i)
            {
                m_collections[i].Initialise(Collections::eBwdTrans);
            }
            m_collectionsDoInit[Collections::eBwdTrans] = false;
        }
 
        LIKWID_MARKER_START("v_BwdTrans");
        timer.Start();
 
        Array<OneD, NekDouble> tmp;
        for (int i = 0; i < m_collections.size(); ++i)
        {
            m_collections[i].ApplyOperator(
                Collections::eBwdTrans, inarray + m_coll_coeff_offset[i],
                tmp = outarray + m_coll_phys_offset[i]);
        }
 
        timer.Stop();
        LIKWID_MARKER_STOP("v_BwdTrans");
    }
 
    // Elapsed time
    timer.AccumulateRegion("Collections:BwdTrans", 10);
}
 
LocalRegions::ExpansionSharedPtr &ExpList::GetExp(
    const Array<OneD, const NekDouble> &gloCoord)
{
    return GetExp(GetExpIndex(gloCoord));
}
 
/**
 * @todo need a smarter search here that first just looks at bounding
 * vertices - suggest first seeing if point is within 10% of
 * region defined by vertices. The do point search.
 */
int ExpList::GetExpIndex(const Array<OneD, const NekDouble> &gloCoord,
                         NekDouble tol, bool returnNearestElmt, int cachedId,
                         NekDouble maxDistance)
{
    Array<OneD, NekDouble> Lcoords(gloCoord.size());
 
    return GetExpIndex(gloCoord, Lcoords, tol, returnNearestElmt, cachedId,
                       maxDistance);
}
 
int ExpList::GetExpIndex(const Array<OneD, const NekDouble> &gloCoords,
                         Array<OneD, NekDouble> &locCoords, NekDouble tol,
                         bool returnNearestElmt, int cachedId,
                         NekDouble maxDistance)
{
    if (GetNumElmts() == 0)
    {
        return -1;
    }
 
    if (m_elmtToExpId.size() == 0)
    {
        // Loop in reverse order so that in case where using a
        // Homogeneous expansion it sets geometry ids to first part of
        // m_exp list. Otherwise will set to second (complex) expansion
        for (int i = (*m_exp).size() - 1; i >= 0; --i)
        {
            m_elmtToExpId[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
        }
    }
 
    NekDouble nearpt     = 1e6;
    NekDouble nearpt_min = 1e6;
    int min_id           = -1;
    Array<OneD, NekDouble> savLocCoords(locCoords.size());
 
    if (cachedId >= 0 && cachedId < (*m_exp).size())
    {
        nearpt = 1e12;
        if ((*m_exp)[cachedId]->GetGeom()->ContainsPoint(gloCoords, locCoords,
                                                         tol, nearpt))
        {
            return cachedId;
        }
        else if (returnNearestElmt && (nearpt < nearpt_min))
        {
            // If it does not lie within, keep track of which element
            // is nearest.
            min_id     = cachedId;
            nearpt_min = nearpt;
            Vmath::Vcopy(locCoords.size(), locCoords, 1, savLocCoords, 1);
        }
    }
 
    NekDouble x = (gloCoords.size() > 0 ? gloCoords[0] : 0.0);
    NekDouble y = (gloCoords.size() > 1 ? gloCoords[1] : 0.0);
    NekDouble z = (gloCoords.size() > 2 ? gloCoords[2] : 0.0);
    SpatialDomains::PointGeomSharedPtr p =
        MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr(
            GetExp(0)->GetCoordim(), -1, x, y, z);
 
    // Get the list of elements whose bounding box contains the desired
    // point.
    std::vector<int> elmts = m_graph->GetElementsContainingPoint(p);
 
    // Check each element in turn to see if point lies within it.
    for (int i = 0; i < elmts.size(); ++i)
    {
        int id = m_elmtToExpId[elmts[i]];
        if (id == cachedId)
        {
            continue;
        }
        if ((*m_exp)[id]->GetGeom()->ContainsPoint(gloCoords, locCoords, tol,
                                                   nearpt))
        {
            return id;
        }
        else if (returnNearestElmt && (nearpt < nearpt_min))
        {
            // If it does not lie within, keep track of which element
            // is nearest.
            min_id     = id;
            nearpt_min = nearpt;
            Vmath::Vcopy(locCoords.size(), locCoords, 1, savLocCoords, 1);
        }
    }
 
    // If the calling function is with just the nearest element, return
    // that. Otherwise return -1 to indicate no matching elemenet found.
    if (returnNearestElmt && nearpt_min <= maxDistance)
    {
 
        std::string msg =
            "Failed to find point within element to "
            "tolerance of " +
            boost::lexical_cast<std::string>(tol) + " using local point (" +
            boost::lexical_cast<std::string>(locCoords[0]) + "," +
            boost::lexical_cast<std::string>(locCoords[1]) + "," +
            boost::lexical_cast<std::string>(locCoords[1]) +
            ") in element: " + boost::lexical_cast<std::string>(min_id);
        WARNINGL1(false, msg.c_str());
 
        Vmath::Vcopy(locCoords.size(), savLocCoords, 1, locCoords, 1);
        return min_id;
    }
    else
    {
        return -1;
    }
}
 
/**
 * Given some coordinates, output the expansion field value at that
 * point
 */
NekDouble ExpList::PhysEvaluate(const Array<OneD, const NekDouble> &coords,
                                const Array<OneD, const NekDouble> &phys)
{
    int dim = GetCoordim(0);
    ASSERTL0(dim == coords.size(), "Invalid coordinate dimension.");
 
    // Grab the element index corresponding to coords.
    Array<OneD, NekDouble> xi(dim);
    int elmtIdx = GetExpIndex(coords, xi);
    ASSERTL0(elmtIdx > 0, "Unable to find element containing point.");
 
    // Grab that element's physical storage.
    Array<OneD, NekDouble> elmtPhys = phys + m_phys_offset[elmtIdx];
 
    // Evaluate the element at the appropriate point.
    return (*m_exp)[elmtIdx]->StdPhysEvaluate(xi, elmtPhys);
}
 
/**
 * Configures geometric info, such as tangent direction, on each
 * expansion.
 * @param   graph2D         Mesh
 */
void ExpList::ApplyGeomInfo()
{
}
 
/**
 * @brief Reset geometry information, metrics, matrix managers and
 * geometry information.
 *
 * This routine clears all matrix managers and resets all geometry
 * information, which allows the geometry information to be dynamically
 * updated as the solver is run.
 */
void ExpList::v_Reset()
{
    // Reset matrix managers.
    LibUtilities::NekManager<LocalRegions::MatrixKey, DNekScalMat,
                             LocalRegions::MatrixKey::opLess>::ClearManager();
    LibUtilities::NekManager<LocalRegions::MatrixKey, DNekScalBlkMat,
                             LocalRegions::MatrixKey::opLess>::ClearManager();
 
    // Loop over all elements and reset geometry information.
    for (int i = 0; i < m_exp->size(); ++i)
    {
        (*m_exp)[i]->GetGeom()->Reset(m_graph->GetCurvedEdges(),
                                      m_graph->GetCurvedFaces());
    }
 
    // Loop over all elements and rebuild geometric factors.
    for (int i = 0; i < m_exp->size(); ++i)
    {
        (*m_exp)[i]->Reset();
    }
}
 
/**
 * Write Tecplot Files Header
 * @param   outfile Output file name.
 * @param   var                 variables names
 */
void ExpList::v_WriteTecplotHeader(std::ostream &outfile, std::string var)
{
    if (GetNumElmts() == 0)
    {
        return;
    }
 
    int coordim  = GetExp(0)->GetCoordim();
    char vars[3] = {'x', 'y', 'z'};
 
    if (m_expType == e3DH1D)
    {
        coordim += 1;
    }
    else if (m_expType == e3DH2D)
    {
        coordim += 2;
    }
 
    outfile << "Variables = x";
    for (int i = 1; i < coordim; ++i)
    {
        outfile << ", " << vars[i];
    }
 
    if (var.size() > 0)
    {
        outfile << ", " << var;
    }
 
    outfile << std::endl << std::endl;
}
 
/**
 * Write Tecplot Files Zone
 * @param   outfile    Output file name.
 * @param   expansion  Expansion that is considered
 */
void ExpList::v_WriteTecplotZone(std::ostream &outfile, int expansion)
{
    int i, j;
    int coordim   = GetCoordim(0);
    int nPoints   = GetTotPoints();
    int nBases    = (*m_exp)[0]->GetNumBases();
    int numBlocks = 0;
 
    Array<OneD, Array<OneD, NekDouble>> coords(3);
 
    if (expansion == -1)
    {
        nPoints = GetTotPoints();
 
        coords[0] = Array<OneD, NekDouble>(nPoints);
        coords[1] = Array<OneD, NekDouble>(nPoints);
        coords[2] = Array<OneD, NekDouble>(nPoints);
 
        GetCoords(coords[0], coords[1], coords[2]);
 
        for (i = 0; i < m_exp->size(); ++i)
        {
            int numInt = 1;
 
            for (j = 0; j < nBases; ++j)
            {
                numInt *= (*m_exp)[i]->GetNumPoints(j) - 1;
            }
 
            numBlocks += numInt;
        }
    }
    else
    {
        nPoints = (*m_exp)[expansion]->GetTotPoints();
 
        coords[0] = Array<OneD, NekDouble>(nPoints);
        coords[1] = Array<OneD, NekDouble>(nPoints);
        coords[2] = Array<OneD, NekDouble>(nPoints);
 
        (*m_exp)[expansion]->GetCoords(coords[0], coords[1], coords[2]);
 
        numBlocks = 1;
        for (j = 0; j < nBases; ++j)
        {
            numBlocks *= (*m_exp)[expansion]->GetNumPoints(j) - 1;
        }
    }
 
    if (m_expType == e3DH1D)
    {
        nBases += 1;
        coordim += 1;
        int nPlanes   = GetZIDs().size();
        NekDouble tmp = numBlocks * (nPlanes - 1.0) / nPlanes;
        numBlocks     = (int)tmp;
    }
    else if (m_expType == e3DH2D)
    {
        nBases += 2;
        coordim += 1;
    }
 
    outfile << "Zone, N=" << nPoints << ", E=" << numBlocks << ", F=FEBlock";
 
    switch (nBases)
    {
        case 2:
            outfile << ", ET=QUADRILATERAL" << std::endl;
            break;
        case 3:
            outfile << ", ET=BRICK" << std::endl;
            break;
        default:
            NEKERROR(ErrorUtil::efatal, "Not set up for this type of output");
            break;
    }
 
    // Write out coordinates
    for (j = 0; j < coordim; ++j)
    {
        for (i = 0; i < nPoints; ++i)
        {
            outfile << coords[j][i] << " ";
            if (i % 1000 == 0 && i)
            {
                outfile << std::endl;
            }
        }
        outfile << std::endl;
    }
}
 
void ExpList::v_WriteTecplotConnectivity(std::ostream &outfile, int expansion)
{
    int i, j, k, l;
    int nbase = (*m_exp)[0]->GetNumBases();
    int cnt   = 0;
 
    std::shared_ptr<LocalRegions::ExpansionVector> exp = m_exp;
 
    if (expansion != -1)
    {
        exp = std::shared_ptr<LocalRegions::ExpansionVector>(
            new LocalRegions::ExpansionVector(1));
        (*exp)[0] = (*m_exp)[expansion];
    }
 
    if (nbase == 2)
    {
        for (i = 0; i < (*exp).size(); ++i)
        {
            const int np0 = (*exp)[i]->GetNumPoints(0);
            const int np1 = (*exp)[i]->GetNumPoints(1);
 
            for (j = 1; j < np1; ++j)
            {
                for (k = 1; k < np0; ++k)
                {
                    outfile << cnt + (j - 1) * np0 + k << " ";
                    outfile << cnt + (j - 1) * np0 + k + 1 << " ";
                    outfile << cnt + j * np0 + k + 1 << " ";
                    outfile << cnt + j * np0 + k << endl;
                }
            }
 
            cnt += np0 * np1;
        }
    }
    else if (nbase == 3)
    {
        for (i = 0; i < (*exp).size(); ++i)
        {
            const int np0  = (*exp)[i]->GetNumPoints(0);
            const int np1  = (*exp)[i]->GetNumPoints(1);
            const int np2  = (*exp)[i]->GetNumPoints(2);
            const int np01 = np0 * np1;
 
            for (j = 1; j < np2; ++j)
            {
                for (k = 1; k < np1; ++k)
                {
                    for (l = 1; l < np0; ++l)
                    {
                        outfile << cnt + (j - 1) * np01 + (k - 1) * np0 + l
                                << " ";
                        outfile << cnt + (j - 1) * np01 + (k - 1) * np0 + l + 1
                                << " ";
                        outfile << cnt + (j - 1) * np01 + k * np0 + l + 1
                                << " ";
                        outfile << cnt + (j - 1) * np01 + k * np0 + l << " ";
                        outfile << cnt + j * np01 + (k - 1) * np0 + l << " ";
                        outfile << cnt + j * np01 + (k - 1) * np0 + l + 1
                                << " ";
                        outfile << cnt + j * np01 + k * np0 + l + 1 << " ";
                        outfile << cnt + j * np01 + k * np0 + l << endl;
                    }
                }
            }
            cnt += np0 * np1 * np2;
        }
    }
    else
    {
        NEKERROR(ErrorUtil::efatal, "Not set up for this dimension");
    }
}
 
/**
 * Write Tecplot Files Field
 * @param   outfile    Output file name.
 * @param   expansion  Expansion that is considered
 */
void ExpList::v_WriteTecplotField(std::ostream &outfile, int expansion)
{
    if (expansion == -1)
    {
        int totpoints = GetTotPoints();
        if (m_physState == false)
        {
            BwdTrans(m_coeffs, m_phys);
        }
 
        for (int i = 0; i < totpoints; ++i)
        {
            outfile << m_phys[i] << " ";
            if (i % 1000 == 0 && i)
            {
                outfile << std::endl;
            }
        }
        outfile << std::endl;
    }
    else
    {
        int nPoints = (*m_exp)[expansion]->GetTotPoints();
 
        for (int i = 0; i < nPoints; ++i)
        {
            outfile << m_phys[i + m_phys_offset[expansion]] << " ";
        }
 
        outfile << std::endl;
    }
}
 
void ExpList::WriteVtkHeader(std::ostream &outfile)
{
    outfile << "<?xml version=\"1.0\"?>" << endl;
    outfile << "<VTKFile type=\"UnstructuredGrid\" version=\"0.1\" "
            << "byte_order=\"LittleEndian\">" << endl;
    outfile << "  <UnstructuredGrid>" << endl;
}
 
void ExpList::WriteVtkFooter(std::ostream &outfile)
{
    outfile << "  </UnstructuredGrid>" << endl;
    outfile << "</VTKFile>" << endl;
}
 
void ExpList::v_WriteVtkPieceHeader(std::ostream &outfile, int expansion,
                                    int istrip)
{
    boost::ignore_unused(istrip);
    int i, j, k;
    int nbase = (*m_exp)[expansion]->GetNumBases();
    int ntot  = (*m_exp)[expansion]->GetTotPoints();
    int nquad[3];
 
    int ntotminus = 1;
    for (i = 0; i < nbase; ++i)
    {
        nquad[i] = (*m_exp)[expansion]->GetNumPoints(i);
        ntotminus *= (nquad[i] - 1);
    }
 
    Array<OneD, NekDouble> coords[3];
    coords[0] = Array<OneD, NekDouble>(ntot, 0.0);
    coords[1] = Array<OneD, NekDouble>(ntot, 0.0);
    coords[2] = Array<OneD, NekDouble>(ntot, 0.0);
    (*m_exp)[expansion]->GetCoords(coords[0], coords[1], coords[2]);
 
    outfile << "    <Piece NumberOfPoints=\"" << ntot << "\" NumberOfCells=\""
            << ntotminus << "\">" << endl;
    outfile << "      <Points>" << endl;
    outfile << "        <DataArray type=\"Float64\" "
            << "NumberOfComponents=\"3\" format=\"ascii\">" << endl;
    outfile << "          ";
    for (i = 0; i < ntot; ++i)
    {
        for (j = 0; j < 3; ++j)
        {
            outfile << setprecision(8) << scientific << (float)coords[j][i]
                    << " ";
        }
        outfile << endl;
    }
    outfile << endl;
    outfile << "        </DataArray>" << endl;
    outfile << "      </Points>" << endl;
    outfile << "      <Cells>" << endl;
    outfile << "        <DataArray type=\"Int32\" "
            << "Name=\"connectivity\" format=\"ascii\">" << endl;
 
    int ns = 0; // pow(2,dim) for later usage
    string ostr;
    switch (m_expType)
    {
        case e1D:
        {
            ns   = 2;
            ostr = "3 ";
            for (i = 0; i < nquad[0] - 1; ++i)
            {
                outfile << i << " " << i + 1 << endl;
            }
        }
        break;
        case e2D:
        {
            ns   = 4;
            ostr = "9 ";
            for (i = 0; i < nquad[0] - 1; ++i)
            {
                for (j = 0; j < nquad[1] - 1; ++j)
                {
                    outfile << j * nquad[0] + i << " " << j * nquad[0] + i + 1
                            << " " << (j + 1) * nquad[0] + i + 1 << " "
                            << (j + 1) * nquad[0] + i << endl;
                }
            }
        }
        break;
        case e3D:
        {
            ns   = 8;
            ostr = "12 ";
            for (i = 0; i < nquad[0] - 1; ++i)
            {
                for (j = 0; j < nquad[1] - 1; ++j)
                {
                    for (k = 0; k < nquad[2] - 1; ++k)
                    {
                        outfile
                            << k * nquad[0] * nquad[1] + j * nquad[0] + i << " "
                            << k * nquad[0] * nquad[1] + j * nquad[0] + i + 1
                            << " "
                            << k * nquad[0] * nquad[1] + (j + 1) * nquad[0] +
                                   i + 1
                            << " "
                            << k * nquad[0] * nquad[1] + (j + 1) * nquad[0] + i
                            << " "
                            << (k + 1) * nquad[0] * nquad[1] + j * nquad[0] + i
                            << " "
                            << (k + 1) * nquad[0] * nquad[1] + j * nquad[0] +
                                   i + 1
                            << " "
                            << (k + 1) * nquad[0] * nquad[1] +
                                   (j + 1) * nquad[0] + i + 1
                            << " "
                            << (k + 1) * nquad[0] * nquad[1] +
                                   (j + 1) * nquad[0] + i
                            << " " << endl;
                    }
                }
            }
        }
        break;
        default:
            break;
    }
 
    outfile << endl;
    outfile << "        </DataArray>" << endl;
    outfile << "        <DataArray type=\"Int32\" "
            << "Name=\"offsets\" format=\"ascii\">" << endl;
    for (i = 0; i < ntotminus; ++i)
    {
        outfile << i * ns + ns << " ";
    }
    outfile << endl;
    outfile << "        </DataArray>" << endl;
    outfile << "        <DataArray type=\"UInt8\" "
            << "Name=\"types\" format=\"ascii\">" << endl;
    for (i = 0; i < ntotminus; ++i)
    {
        outfile << ostr;
    }
    outfile << endl;
    outfile << "        </DataArray>" << endl;
    outfile << "      </Cells>" << endl;
    outfile << "      <PointData>" << endl;
}
 
void ExpList::WriteVtkPieceFooter(std::ostream &outfile, int expansion)
{
    boost::ignore_unused(expansion);
    outfile << "      </PointData>" << endl;
    outfile << "    </Piece>" << endl;
}
 
void ExpList::v_WriteVtkPieceData(std::ostream &outfile, int expansion,
                                  std::string var)
{
    int i;
    int nq = (*m_exp)[expansion]->GetTotPoints();
 
    // printing the fields of that zone
    outfile << "        <DataArray type=\"Float64\" Name=\"" << var << "\">"
            << endl;
    outfile << "          ";
 
    const Array<OneD, NekDouble> phys = m_phys + m_phys_offset[expansion];
 
    for (i = 0; i < nq; ++i)
    {
        outfile << (fabs(phys[i]) < NekConstants::kNekZeroTol ? 0 : phys[i])
                << " ";
    }
    outfile << endl;
    outfile << "        </DataArray>" << endl;
}
 
/**
 * Given a spectral/hp approximation
 * \f$u^{\delta}(\boldsymbol{x})\f$ evaluated at the quadrature points
 * (which should be contained in #m_phys), this function calculates the
 * \f$L_\infty\f$ error of this approximation with respect to an exact
 * solution. The local distribution of the quadrature points allows an
 * elemental evaluation of this operation through the functions
 * StdRegions#StdExpansion#Linf.
 *
 * The exact solution, also evaluated at the quadrature
 * points, should be contained in the variable #m_phys of
 * the ExpList object \a Sol.
 *
 * @param   soln            A 1D array, containing the discrete
 *                          evaluation of the exact solution at the
 *                          quadrature points in its array #m_phys.
 * @return  The \f$L_\infty\f$ error of the approximation.
 */
NekDouble ExpList::Linf(const Array<OneD, const NekDouble> &inarray,
                        const Array<OneD, const NekDouble> &soln)
{
    NekDouble err = 0.0;
 
    if (soln == NullNekDouble1DArray)
    {
        err = Vmath::Vmax(m_npoints, inarray, 1);
    }
    else
    {
        for (int i = 0; i < m_npoints; ++i)
        {
            err = max(err, abs(inarray[i] - soln[i]));
        }
    }
 
    m_comm->GetRowComm()->AllReduce(err, LibUtilities::ReduceMax);
 
    return err;
}
 
/**
 * Given a spectral/hp approximation \f$u^{\delta}(\boldsymbol{x})\f$
 * evaluated at the quadrature points (which should be contained in
 * #m_phys), this function calculates the \f$L_2\f$ error of this
 * approximation with respect to an exact solution. The local
 * distribution of the quadrature points allows an elemental evaluation
 * of this operation through the functions StdRegions#StdExpansion#L2.
 *
 * The exact solution, also evaluated at the quadrature points, should
 * be contained in the variable #m_phys of the ExpList object \a Sol.
 *
 * @param   Sol             An ExpList, containing the discrete
 *                          evaluation of the exact solution at the
 *                          quadrature points in its array #m_phys.
 * @return  The \f$L_2\f$ error of the approximation.
 */
NekDouble ExpList::v_L2(const Array<OneD, const NekDouble> &inarray,
                        const Array<OneD, const NekDouble> &soln)
{
    NekDouble err = 0.0, errl2;
    int i;
 
    if (soln == NullNekDouble1DArray)
    {
        for (i = 0; i < (*m_exp).size(); ++i)
        {
            errl2 = (*m_exp)[i]->L2(inarray + m_phys_offset[i]);
            err += errl2 * errl2;
        }
    }
    else
    {
        for (i = 0; i < (*m_exp).size(); ++i)
        {
            errl2 = (*m_exp)[i]->L2(inarray + m_phys_offset[i],
                                    soln + m_phys_offset[i]);
            err += errl2 * errl2;
        }
    }
 
    m_comm->GetRowComm()->AllReduce(err, LibUtilities::ReduceSum);
 
    return sqrt(err);
}
 
/**
 * The integration is evaluated locally, that is
 * \f[\int
 *    f(\boldsymbol{x})d\boldsymbol{x}=\sum_{e=1}^{{N_{\mathrm{el}}}}
 * \left\{\int_{\Omega_e}f(\boldsymbol{x})d\boldsymbol{x}\right\},  \f]
 * where the integration over the separate elements is done by the
 * function StdRegions#StdExpansion#Integral, which discretely
 * evaluates the integral using Gaussian quadrature.
 *
 * @param   inarray         An array of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$.
 * @return  The value of the discretely evaluated integral
 *          \f$\int f(\boldsymbol{x})d\boldsymbol{x}\f$.
 */
NekDouble ExpList::v_Integral(const Array<OneD, const NekDouble> &inarray)
{
    NekDouble sum = 0.0;
    int i         = 0;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        sum += (*m_exp)[i]->Integral(inarray + m_phys_offset[i]);
    }
    m_comm->GetRowComm()->AllReduce(sum, LibUtilities::ReduceSum);
 
    return sum;
}
 
NekDouble ExpList::v_VectorFlux(
    const Array<OneD, Array<OneD, NekDouble>> &inarray)
{
    NekDouble flux = 0.0;
    int i          = 0;
    int j;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        Array<OneD, Array<OneD, NekDouble>> tmp(inarray.size());
        for (j = 0; j < inarray.size(); ++j)
        {
            tmp[j] = Array<OneD, NekDouble>(inarray[j] + m_phys_offset[i]);
        }
        flux += (*m_exp)[i]->VectorFlux(tmp);
    }
 
    return flux;
}
 
Array<OneD, const NekDouble> ExpList::v_HomogeneousEnergy(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    Array<OneD, NekDouble> NoEnergy(1, 0.0);
    return NoEnergy;
}
 
LibUtilities::TranspositionSharedPtr ExpList::v_GetTransposition(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    LibUtilities::TranspositionSharedPtr trans;
    return trans;
}
 
NekDouble ExpList::v_GetHomoLen(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    NekDouble len = 0.0;
    return len;
}
 
void ExpList::v_SetHomoLen(const NekDouble lhom)
{
    boost::ignore_unused(lhom);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
Array<OneD, const unsigned int> ExpList::v_GetZIDs(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    Array<OneD, unsigned int> NoModes(1);
    return NoModes;
}
 
Array<OneD, const unsigned int> ExpList::v_GetYIDs(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    Array<OneD, unsigned int> NoModes(1);
    return NoModes;
}
 
void ExpList::v_ClearGlobalLinSysManager(void)
{
    NEKERROR(ErrorUtil::efatal,
             "ClearGlobalLinSysManager not implemented for ExpList.");
}
 
int ExpList::v_GetPoolCount(std::string poolName)
{
    boost::ignore_unused(poolName);
    NEKERROR(ErrorUtil::efatal, "GetPoolCount not implemented for ExpList.");
    return -1;
}
 
void ExpList::v_UnsetGlobalLinSys(GlobalLinSysKey key, bool clearLocalMatrices)
{
    boost::ignore_unused(key, clearLocalMatrices);
    NEKERROR(ErrorUtil::efatal,
             "UnsetGlobalLinSys not implemented for ExpList.");
}
 
LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys>
    &ExpList::v_GetGlobalLinSysManager(void)
{
    NEKERROR(ErrorUtil::efatal,
             "GetGlobalLinSysManager not implemented for ExpList.");
    return NullGlobalLinSysManager;
}
 
void ExpList::ExtractCoeffsFromFile(const std::string &fileName,
                                    LibUtilities::CommSharedPtr comm,
                                    const std::string &varName,
                                    Array<OneD, NekDouble> &coeffs)
{
    string varString = fileName.substr(0, fileName.find_last_of("."));
    int j, k, len = varString.length();
    varString = varString.substr(len - 1, len);
 
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef;
    std::vector<std::vector<NekDouble>> FieldData;
 
    std::string ft = LibUtilities::FieldIO::GetFileType(fileName, comm);
    LibUtilities::FieldIOSharedPtr f =
        LibUtilities::GetFieldIOFactory().CreateInstance(
            ft, comm, m_session->GetSharedFilesystem());
 
    f->Import(fileName, FieldDef, FieldData);
 
    bool found = false;
    for (j = 0; j < FieldDef.size(); ++j)
    {
        for (k = 0; k < FieldDef[j]->m_fields.size(); ++k)
        {
            if (FieldDef[j]->m_fields[k] == varName)
            {
                // Copy FieldData into locExpList
                ExtractDataToCoeffs(FieldDef[j], FieldData[j],
                                    FieldDef[j]->m_fields[k], coeffs);
                found = true;
            }
        }
    }
 
    ASSERTL0(found, "Could not find variable '" + varName +
                        "' in file boundary condition " + fileName);
}
 
/**
 * Given a spectral/hp approximation
 * \f$u^{\delta}(\boldsymbol{x})\f$ evaluated at the quadrature points
 * (which should be contained in #m_phys), this function calculates the
 * \f$H^1_2\f$ error of this approximation with respect to an exact
 * solution. The local distribution of the quadrature points allows an
 * elemental evaluation of this operation through the functions
 * StdRegions#StdExpansion#H1.
 *
 * The exact solution, also evaluated at the quadrature points, should
 * be contained in the variable #m_phys of the ExpList object \a Sol.
 *
 * @param   soln        An 1D array, containing the discrete evaluation
 *                      of the exact solution at the quadrature points.
 *
 * @return  The \f$H^1_2\f$ error of the approximation.
 */
NekDouble ExpList::H1(const Array<OneD, const NekDouble> &inarray,
                      const Array<OneD, const NekDouble> &soln)
{
    NekDouble err = 0.0, errh1;
    int i;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        errh1 = (*m_exp)[i]->H1(inarray + m_phys_offset[i],
                                soln + m_phys_offset[i]);
        err += errh1 * errh1;
    }
 
    m_comm->GetRowComm()->AllReduce(err, LibUtilities::ReduceSum);
 
    return sqrt(err);
}
 
void ExpList::GeneralGetFieldDefinitions(
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> &fielddef,
    int NumHomoDir, Array<OneD, LibUtilities::BasisSharedPtr> &HomoBasis,
    std::vector<NekDouble> &HomoLen, bool homoStrips,
    std::vector<unsigned int> &HomoSIDs, std::vector<unsigned int> &HomoZIDs,
    std::vector<unsigned int> &HomoYIDs)
{
    int startenum = (int)LibUtilities::eSegment;
    int endenum   = (int)LibUtilities::eHexahedron;
    int s         = 0;
    LibUtilities::ShapeType shape;
 
    ASSERTL1(NumHomoDir == HomoBasis.size(),
             "Homogeneous basis is not the same length as NumHomoDir");
    ASSERTL1(NumHomoDir == HomoLen.size(),
             "Homogeneous length vector is not the same length as NumHomDir");
 
    // count number of shapes
    switch ((*m_exp)[0]->GetShapeDimension())
    {
        case 1:
            startenum = (int)LibUtilities::eSegment;
            endenum   = (int)LibUtilities::eSegment;
            break;
        case 2:
            startenum = (int)LibUtilities::eTriangle;
            endenum   = (int)LibUtilities::eQuadrilateral;
            break;
        case 3:
            startenum = (int)LibUtilities::eTetrahedron;
            endenum   = (int)LibUtilities::eHexahedron;
            break;
    }
 
    for (s = startenum; s <= endenum; ++s)
    {
        std::vector<unsigned int> elementIDs;
        std::vector<LibUtilities::BasisType> basis;
        std::vector<unsigned int> numModes;
        std::vector<std::string> fields;
 
        bool first    = true;
        bool UniOrder = true;
        int n;
 
        shape = (LibUtilities::ShapeType)s;
 
        for (int i = 0; i < (*m_exp).size(); ++i)
        {
            if ((*m_exp)[i]->GetGeom()->GetShapeType() == shape)
            {
                elementIDs.push_back((*m_exp)[i]->GetGeom()->GetGlobalID());
                if (first)
                {
                    for (int j = 0; j < (*m_exp)[i]->GetNumBases(); ++j)
                    {
                        basis.push_back(
                            (*m_exp)[i]->GetBasis(j)->GetBasisType());
                        numModes.push_back(
                            (*m_exp)[i]->GetBasis(j)->GetNumModes());
                    }
 
                    // add homogeneous direction details if defined
                    for (n = 0; n < NumHomoDir; ++n)
                    {
                        basis.push_back(HomoBasis[n]->GetBasisType());
                        numModes.push_back(HomoBasis[n]->GetNumModes());
                    }
 
                    first = false;
                }
                else
                {
                    ASSERTL0(
                        (*m_exp)[i]->GetBasis(0)->GetBasisType() == basis[0],
                        "Routine is not set up for multiple bases definitions");
 
                    for (int j = 0; j < (*m_exp)[i]->GetNumBases(); ++j)
                    {
                        numModes.push_back(
                            (*m_exp)[i]->GetBasis(j)->GetNumModes());
                        if (numModes[j] !=
                            (*m_exp)[i]->GetBasis(j)->GetNumModes())
                        {
                            UniOrder = false;
                        }
                    }
                    // add homogeneous direction details if defined
                    for (n = 0; n < NumHomoDir; ++n)
                    {
                        numModes.push_back(HomoBasis[n]->GetNumModes());
                    }
                }
            }
        }
 
        if (elementIDs.size() > 0)
        {
            LibUtilities::FieldDefinitionsSharedPtr fdef =
                MemoryManager<LibUtilities::FieldDefinitions>::
                    AllocateSharedPtr(shape, elementIDs, basis, UniOrder,
                                      numModes, fields, NumHomoDir, HomoLen,
                                      homoStrips, HomoSIDs, HomoZIDs, HomoYIDs);
            fielddef.push_back(fdef);
        }
    }
}
 
//
// Virtual functions
//
std::vector<LibUtilities::FieldDefinitionsSharedPtr> ExpList::
    v_GetFieldDefinitions()
{
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> returnval;
    v_GetFieldDefinitions(returnval);
    return returnval;
}
 
void ExpList::v_GetFieldDefinitions(
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> &fielddef)
{
    GeneralGetFieldDefinitions(fielddef);
}
 
// Append the element data listed in elements
// fielddef->m_ElementIDs onto fielddata
void ExpList::v_AppendFieldData(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata)
{
    v_AppendFieldData(fielddef, fielddata, m_coeffs);
}
 
void ExpList::v_AppendFieldData(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata, Array<OneD, NekDouble> &coeffs)
{
    int i;
    // Determine mapping from element ids to location in
    // expansion list
    // Determine mapping from element ids to location in
    // expansion list
    map<int, int> ElmtID_to_ExpID;
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        ElmtID_to_ExpID[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
    }
 
    for (i = 0; i < fielddef->m_elementIDs.size(); ++i)
    {
        int eid     = ElmtID_to_ExpID[fielddef->m_elementIDs[i]];
        int datalen = (*m_exp)[eid]->GetNcoeffs();
        fielddata.insert(fielddata.end(), &coeffs[m_coeff_offset[eid]],
                         &coeffs[m_coeff_offset[eid]] + datalen);
    }
}
 
/// Extract the data in fielddata into the coeffs
void ExpList::ExtractDataToCoeffs(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata, std::string &field,
    Array<OneD, NekDouble> &coeffs, std::unordered_map<int, int> zIdToPlane)
{
    v_ExtractDataToCoeffs(fielddef, fielddata, field, coeffs, zIdToPlane);
}
 
void ExpList::ExtractCoeffsToCoeffs(
    const std::shared_ptr<ExpList> &fromExpList,
    const Array<OneD, const NekDouble> &fromCoeffs,
    Array<OneD, NekDouble> &toCoeffs)
{
    v_ExtractCoeffsToCoeffs(fromExpList, fromCoeffs, toCoeffs);
}
 
/**
 * @brief Extract data from raw field data into expansion list.
 *
 * @param fielddef   Field definitions.
 * @param fielddata  Data for associated field.
 * @param field      Field variable name.
 * @param coeffs     Resulting coefficient array.
 */
void ExpList::v_ExtractDataToCoeffs(
    LibUtilities::FieldDefinitionsSharedPtr &fielddef,
    std::vector<NekDouble> &fielddata, std::string &field,
    Array<OneD, NekDouble> &coeffs, std::unordered_map<int, int> zIdToPlane)
{
    boost::ignore_unused(zIdToPlane);
    int i, expId;
    int offset       = 0;
    int modes_offset = 0;
    int datalen      = fielddata.size() / fielddef->m_fields.size();
 
    // Find data location according to field definition
    for (i = 0; i < fielddef->m_fields.size(); ++i)
    {
        if (fielddef->m_fields[i] == field)
        {
            break;
        }
        offset += datalen;
    }
 
    ASSERTL0(i != fielddef->m_fields.size(),
             "Field (" + field + ") not found in file.");
 
    if (m_elmtToExpId.size() == 0)
    {
        // Loop in reverse order so that in case where using a
        // Homogeneous expansion it sets geometry ids to first part of
        // m_exp list. Otherwise will set to second (complex) expansion
        for (i = (*m_exp).size() - 1; i >= 0; --i)
        {
            m_elmtToExpId[(*m_exp)[i]->GetGeom()->GetGlobalID()] = i;
        }
    }
 
    for (i = 0; i < fielddef->m_elementIDs.size(); ++i)
    {
        // Reset modes_offset in the case where all expansions of
        // the same order.
        if (fielddef->m_uniOrder == true)
        {
            modes_offset = 0;
        }
 
        datalen = LibUtilities::GetNumberOfCoefficients(
            fielddef->m_shapeType, fielddef->m_numModes, modes_offset);
 
        const int elmtId = fielddef->m_elementIDs[i];
        auto eIt         = m_elmtToExpId.find(elmtId);
 
        if (eIt == m_elmtToExpId.end())
        {
            offset += datalen;
            modes_offset += (*m_exp)[0]->GetNumBases();
            continue;
        }
 
        expId = eIt->second;
 
        bool sameBasis = true;
        for (int j = 0; j < fielddef->m_basis.size(); ++j)
        {
            if (fielddef->m_basis[j] != (*m_exp)[expId]->GetBasisType(j))
            {
                sameBasis = false;
                break;
            }
        }
 
        if (datalen == (*m_exp)[expId]->GetNcoeffs() && sameBasis)
        {
            Vmath::Vcopy(datalen, &fielddata[offset], 1,
                         &coeffs[m_coeff_offset[expId]], 1);
        }
        else
        {
            (*m_exp)[expId]->ExtractDataToCoeffs(
                &fielddata[offset], fielddef->m_numModes, modes_offset,
                &coeffs[m_coeff_offset[expId]], fielddef->m_basis);
        }
 
        offset += datalen;
        modes_offset += (*m_exp)[0]->GetNumBases();
    }
 
    return;
}
 
void ExpList::v_ExtractCoeffsToCoeffs(
    const std::shared_ptr<ExpList> &fromExpList,
    const Array<OneD, const NekDouble> &fromCoeffs,
    Array<OneD, NekDouble> &toCoeffs)
{
    int i;
    int offset = 0;
 
    for (i = 0; i < (*m_exp).size(); ++i)
    {
        std::vector<unsigned int> nummodes;
        vector<LibUtilities::BasisType> basisTypes;
        for (int j = 0; j < fromExpList->GetExp(i)->GetNumBases(); ++j)
        {
            nummodes.push_back(fromExpList->GetExp(i)->GetBasisNumModes(j));
            basisTypes.push_back(fromExpList->GetExp(i)->GetBasisType(j));
        }
 
        (*m_exp)[i]->ExtractDataToCoeffs(&fromCoeffs[offset], nummodes, 0,
                                         &toCoeffs[m_coeff_offset[i]],
                                         basisTypes);
 
        offset += fromExpList->GetExp(i)->GetNcoeffs();
    }
}
 
/**
 * Get the weight value on boundaries
 */
void ExpList::GetBwdWeight(Array<OneD, NekDouble> &weightAver,
                           Array<OneD, NekDouble> &weightJump)
{
    size_t nTracePts = weightAver.size();
    // average for interior traces
    for (int i = 0; i < nTracePts; ++i)
    {
        weightAver[i] = 0.5;
        weightJump[i] = 1.0;
    }
    FillBwdWithBwdWeight(weightAver, weightJump);
}
 
void ExpList::v_GetMovingFrames(const SpatialDomains::GeomMMF MMFdir,
                                const Array<OneD, const NekDouble> &CircCentre,
                                Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    int npts;
 
    int MFdim = 3;
    int nq    = outarray[0].size() / MFdim;
 
    // Assume whole array is of same coordinate dimension
    int coordim = (*m_exp)[0]->GetGeom()->GetCoordim();
 
    Array<OneD, Array<OneD, NekDouble>> MFloc(MFdim * coordim);
    // Process each expansion.
    for (int i = 0; i < m_exp->size(); ++i)
    {
        npts = (*m_exp)[i]->GetTotPoints();
 
        for (int j = 0; j < MFdim * coordim; ++j)
        {
            MFloc[j] = Array<OneD, NekDouble>(npts, 0.0);
        }
 
        // MF from LOCALREGIONS
        (*m_exp)[i]->GetMetricInfo()->GetMovingFrames(
            (*m_exp)[i]->GetPointsKeys(), MMFdir, CircCentre, MFloc);
 
        // Get the physical data offset for this expansion.
        for (int j = 0; j < MFdim; ++j)
        {
            for (int k = 0; k < coordim; ++k)
            {
                Vmath::Vcopy(npts, &MFloc[j * coordim + k][0], 1,
                             &outarray[j][k * nq + m_phys_offset[i]], 1);
            }
        }
    }
}
 
/**
 * @brief Generate vector v such that v[i] = scalar1 if i is in the
 * element < ElementID. Otherwise, v[i] = scalar2.
 *
 */
void ExpList::GenerateElementVector(const int ElementID,
                                    const NekDouble scalar1,
                                    const NekDouble scalar2,
                                    Array<OneD, NekDouble> &outarray)
{
    int npoints_e;
    NekDouble coeff;
 
    Array<OneD, NekDouble> outarray_e;
 
    for (int i = 0; i < (*m_exp).size(); ++i)
    {
        npoints_e = (*m_exp)[i]->GetTotPoints();
 
        if (i <= ElementID)
        {
            coeff = scalar1;
        }
        else
        {
            coeff = scalar2;
        }
 
        outarray_e = Array<OneD, NekDouble>(npoints_e, coeff);
        Vmath::Vcopy(npoints_e, &outarray_e[0], 1, &outarray[m_phys_offset[i]],
                     1);
    }
}
 
const Array<OneD, const std::shared_ptr<ExpList>>
    &ExpList::v_GetBndCondExpansions(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static Array<OneD, const std::shared_ptr<ExpList>> result;
    return result;
}
 
std::shared_ptr<ExpList> &ExpList::v_UpdateBndCondExpansion(int i)
{
    boost::ignore_unused(i);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static std::shared_ptr<ExpList> result;
    return result;
}
 
/**
 * Upwind the left and right states given by the Arrays Fwd and Bwd
 * using the vector quantity Vec and ouput the upwinded value in the
 * array upwind.
 *
 * @param   Vec         Velocity field.
 * @param   Fwd         Left state.
 * @param   Bwd         Right state.
 * @param   Upwind      Output vector.
 */
void ExpList::v_Upwind(const Array<OneD, const Array<OneD, NekDouble>> &Vec,
                       const Array<OneD, const NekDouble> &Fwd,
                       const Array<OneD, const NekDouble> &Bwd,
                       Array<OneD, NekDouble> &Upwind)
{
    switch (m_expType)
    {
        case e1D:
        {
            int i, j, k, e_npoints, offset;
            Array<OneD, NekDouble> normals;
            NekDouble Vn;
 
            // Assume whole array is of same coordimate dimension
            int coordim = GetCoordim(0);
 
            ASSERTL1(Vec.size() >= coordim,
                     "Input vector does not have sufficient dimensions to "
                     "match coordim");
 
            // Process each expansion
            for (i = 0; i < m_exp->size(); ++i)
            {
                // Get the number of points in the expansion and the normals.
                e_npoints = (*m_exp)[i]->GetNumPoints(0);
                normals   = (*m_exp)[i]->GetPhysNormals();
 
                // Get the physical data offset of the expansion in m_phys.
                offset = m_phys_offset[i];
 
                // Compute each data point.
                for (j = 0; j < e_npoints; ++j)
                {
                    // Calculate normal velocity.
                    Vn = 0.0;
                    for (k = 0; k < coordim; ++k)
                    {
                        Vn += Vec[k][offset + j] * normals[k * e_npoints + j];
                    }
 
                    // Upwind based on direction of normal velocity.
                    if (Vn > 0.0)
                    {
                        Upwind[offset + j] = Fwd[offset + j];
                    }
                    else
                    {
                        Upwind[offset + j] = Bwd[offset + j];
                    }
                }
            }
        }
        break;
        default:
            NEKERROR(ErrorUtil::efatal,
                     "This method is not defined or valid for this class type");
            break;
    }
}
 
/**
 * One-dimensional upwind.
 * \see    ExpList::Upwind(
 *           const Array<OneD, const Array<OneD, NekDouble> >,
 *           const Array<OneD, const NekDouble>,
 *           const Array<OneD, const NekDouble>,
 *                 Array<OneD, NekDouble>, int)
 *
 * @param   Vn          Velocity field.
 * @param   Fwd         Left state.
 * @param   Bwd         Right state.
 * @param   Upwind      Output vector.
 */
void ExpList::v_Upwind(const Array<OneD, const NekDouble> &Vn,
                       const Array<OneD, const NekDouble> &Fwd,
                       const Array<OneD, const NekDouble> &Bwd,
                       Array<OneD, NekDouble> &Upwind)
{
    ASSERTL1(Vn.size() >= m_npoints, "Vn is not of sufficient length");
    ASSERTL1(Fwd.size() >= m_npoints, "Fwd is not of sufficient length");
    ASSERTL1(Bwd.size() >= m_npoints, "Bwd is not of sufficient length");
    ASSERTL1(Upwind.size() >= m_npoints, "Upwind is not of sufficient length");
 
    // Process each point in the expansion.
    for (int j = 0; j < m_npoints; ++j)
    {
        // Upwind based on one-dimensional velocity.
        if (Vn[j] > 0.0)
        {
            Upwind[j] = Fwd[j];
        }
        else
        {
            Upwind[j] = Bwd[j];
        }
    }
}
 
std::shared_ptr<ExpList> &ExpList::v_GetTrace()
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static std::shared_ptr<ExpList> returnVal;
    return returnVal;
}
 
std::shared_ptr<AssemblyMapDG> &ExpList::v_GetTraceMap()
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static std::shared_ptr<AssemblyMapDG> result;
    return result;
}
 
const Array<OneD, const int> &ExpList::v_GetTraceBndMap()
{
    return GetTraceMap()->GetBndCondIDToGlobalTraceID();
}
 
std::vector<bool> &ExpList::v_GetLeftAdjacentTraces()
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static std::vector<bool> result;
    return result;
}
 
/**
 * @brief Helper function to re-align face to a given orientation.
 */
void AlignFace(const StdRegions::Orientation orient, const int nquad1,
               const int nquad2, const Array<OneD, const NekDouble> &in,
               Array<OneD, NekDouble> &out)
{
    // Copy transpose.
    if (orient == StdRegions::eDir1FwdDir2_Dir2FwdDir1 ||
        orient == StdRegions::eDir1BwdDir2_Dir2FwdDir1 ||
        orient == StdRegions::eDir1FwdDir2_Dir2BwdDir1 ||
        orient == StdRegions::eDir1BwdDir2_Dir2BwdDir1)
    {
        for (int i = 0; i < nquad2; ++i)
        {
            for (int j = 0; j < nquad1; ++j)
            {
                out[i * nquad1 + j] = in[j * nquad2 + i];
            }
        }
    }
    else
    {
        for (int i = 0; i < nquad2; ++i)
        {
            for (int j = 0; j < nquad1; ++j)
            {
                out[i * nquad1 + j] = in[i * nquad1 + j];
            }
        }
    }
 
    if (orient == StdRegions::eDir1BwdDir1_Dir2FwdDir2 ||
        orient == StdRegions::eDir1BwdDir1_Dir2BwdDir2 ||
        orient == StdRegions::eDir1BwdDir2_Dir2FwdDir1 ||
        orient == StdRegions::eDir1BwdDir2_Dir2BwdDir1)
    {
        // Reverse x direction
        for (int i = 0; i < nquad2; ++i)
        {
            for (int j = 0; j < nquad1 / 2; ++j)
            {
                swap(out[i * nquad1 + j], out[i * nquad1 + nquad1 - j - 1]);
            }
        }
    }
 
    if (orient == StdRegions::eDir1FwdDir1_Dir2BwdDir2 ||
        orient == StdRegions::eDir1BwdDir1_Dir2BwdDir2 ||
        orient == StdRegions::eDir1FwdDir2_Dir2BwdDir1 ||
        orient == StdRegions::eDir1BwdDir2_Dir2BwdDir1)
    {
        // Reverse y direction
        for (int j = 0; j < nquad1; ++j)
        {
            for (int i = 0; i < nquad2 / 2; ++i)
            {
                swap(out[i * nquad1 + j], out[(nquad2 - i - 1) * nquad1 + j]);
            }
        }
    }
}
 
/**
 * For each local element, copy the normals stored in the element list
 * into the array \a normals.
 * @param   normals     Multidimensional array in which to copy normals
 *                      to. Must have dimension equal to or larger than
 *                      the spatial dimension of the elements.
 */
void ExpList::v_GetNormals(Array<OneD, Array<OneD, NekDouble>> &normals)
{
    int i, j, k, e_npoints, offset;
    Array<OneD, Array<OneD, NekDouble>> locnormals;
 
    // Assume whole array is of same coordinate dimension
    int coordim = GetCoordim(0);
 
    ASSERTL1(normals.size() >= coordim,
             "Output vector does not have sufficient dimensions to "
             "match coordim");
 
    switch (m_expType)
    {
        case e0D:
        {
            // Process each expansion.
            for (i = 0; i < m_exp->size(); ++i)
            {
                LocalRegions::ExpansionSharedPtr loc_exp = (*m_exp)[i];
 
                LocalRegions::ExpansionSharedPtr loc_elmt =
                    loc_exp->GetLeftAdjacentElementExp();
 
                // Get the number of points and normals for this expansion.
                e_npoints  = 1;
                locnormals = loc_elmt->GetTraceNormal(
                    loc_exp->GetLeftAdjacentElementTrace());
 
                // Get the physical data offset for this expansion.
                offset = m_phys_offset[i];
 
                // Process each point in the expansion.
                for (j = 0; j < e_npoints; ++j)
                {
                    // Process each spatial dimension and copy the
                    // values into the output array.
                    for (k = 0; k < coordim; ++k)
                    {
                        normals[k][offset] = locnormals[k][0];
                    }
                }
            }
        }
        break;
        case e1D:
        {
            SpatialDomains::Geometry1DSharedPtr segGeom;
            Array<OneD, Array<OneD, NekDouble>> locnormals2;
            Array<OneD, Array<OneD, NekDouble>> Norms;
 
            for (i = 0; i < m_exp->size(); ++i)
            {
                LocalRegions::ExpansionSharedPtr loc_exp = (*m_exp)[i];
 
                LocalRegions::ExpansionSharedPtr loc_elmt =
                    loc_exp->GetLeftAdjacentElementExp();
 
                int edgeNumber = loc_exp->GetLeftAdjacentElementTrace();
 
                // Get the number of points and normals for this expansion.
                e_npoints = (*m_exp)[i]->GetNumPoints(0);
 
                locnormals     = loc_elmt->GetTraceNormal(edgeNumber);
                int e_nmodes   = loc_exp->GetBasis(0)->GetNumModes();
                int loc_nmodes = loc_elmt->GetBasis(0)->GetNumModes();
 
                if (e_nmodes != loc_nmodes)
                {
                    if (loc_exp->GetRightAdjacentElementTrace() >= 0)
                    {
                        LocalRegions::ExpansionSharedPtr loc_elmt =
                            loc_exp->GetRightAdjacentElementExp();
 
                        int EdgeNumber =
                            loc_exp->GetRightAdjacentElementTrace();
 
                        // Serial case: right element is connected so we can
                        // just grab that normal.
                        locnormals = loc_elmt->GetTraceNormal(EdgeNumber);
 
                        offset = m_phys_offset[i];
 
                        // Process each point in the expansion.
                        for (j = 0; j < e_npoints; ++j)
                        {
                            // Process each spatial dimension and
                            // copy the values into the output
                            // array.
                            for (k = 0; k < coordim; ++k)
                            {
                                normals[k][offset + j] = -locnormals[k][j];
                            }
                        }
                    }
                    else
                    {
                        // Parallel case: need to interpolate normal.
                        Array<OneD, Array<OneD, NekDouble>> normal(coordim);
 
                        for (int p = 0; p < coordim; ++p)
                        {
                            normal[p] = Array<OneD, NekDouble>(e_npoints, 0.0);
                            LibUtilities::PointsKey to_key =
                                loc_exp->GetBasis(0)->GetPointsKey();
                            LibUtilities::PointsKey from_key =
                                loc_elmt->GetBasis(0)->GetPointsKey();
                            LibUtilities::Interp1D(from_key, locnormals[p],
                                                   to_key, normal[p]);
                        }
 
                        offset = m_phys_offset[i];
 
                        // Process each point in the expansion.
                        for (j = 0; j < e_npoints; ++j)
                        {
                            // Process each spatial dimension and copy the
                            // values into the output array.
                            for (k = 0; k < coordim; ++k)
                            {
                                normals[k][offset + j] = normal[k][j];
                            }
                        }
                    }
                }
                else
                {
                    // Get the physical data offset for this expansion.
                    offset = m_phys_offset[i];
 
                    // Process each point in the expansion.
                    for (j = 0; j < e_npoints; ++j)
                    {
                        // Process each spatial dimension and copy the values
                        // into the output array.
                        for (k = 0; k < coordim; ++k)
                        {
                            normals[k][offset + j] = locnormals[k][j];
                        }
                    }
                }
            }
        }
        break;
        case e2D:
        {
            Array<OneD, NekDouble> tmp;
 
            // Process each expansion.
            for (i = 0; i < m_exp->size(); ++i)
            {
                LocalRegions::ExpansionSharedPtr traceExp = (*m_exp)[i];
                LocalRegions::ExpansionSharedPtr exp3D =
                    traceExp->GetLeftAdjacentElementExp();
 
                // Get the number of points and normals for this expansion.
                int faceNum = traceExp->GetLeftAdjacentElementTrace();
                int offset  = m_phys_offset[i];
 
                const Array<OneD, const Array<OneD, NekDouble>> &locNormals =
                    exp3D->GetTraceNormal(faceNum);
 
                // Project normals from 3D element onto the same
                // orientation as the trace expansion.
                StdRegions::Orientation orient = exp3D->GetTraceOrient(faceNum);
 
                int fromid0, fromid1;
 
                if (orient < StdRegions::eDir1FwdDir2_Dir2FwdDir1)
                {
                    fromid0 = 0;
                    fromid1 = 1;
                }
                else
                {
                    fromid0 = 1;
                    fromid1 = 0;
                }
 
                LibUtilities::BasisKey faceBasis0 =
                    exp3D->GetTraceBasisKey(faceNum, fromid0);
                LibUtilities::BasisKey faceBasis1 =
                    exp3D->GetTraceBasisKey(faceNum, fromid1);
                LibUtilities::BasisKey traceBasis0 =
                    traceExp->GetBasis(0)->GetBasisKey();
                LibUtilities::BasisKey traceBasis1 =
                    traceExp->GetBasis(1)->GetBasisKey();
 
                const int faceNq0 = faceBasis0.GetNumPoints();
                const int faceNq1 = faceBasis1.GetNumPoints();
 
                Array<OneD, int> faceids;
                exp3D->ReOrientTracePhysMap(orient, faceids, faceNq0, faceNq1);
 
                Array<OneD, NekDouble> traceNormals(faceNq0 * faceNq1);
 
                for (j = 0; j < coordim; ++j)
                {
                    Vmath::Scatr(faceNq0 * faceNq1, locNormals[j], faceids,
                                 traceNormals);
 
                    LibUtilities::Interp2D(
                        faceBasis0.GetPointsKey(), faceBasis1.GetPointsKey(),
                        traceNormals, traceBasis0.GetPointsKey(),
                        traceBasis1.GetPointsKey(), tmp = normals[j] + offset);
                }
            }
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal,
                     "This method is not defined or valid for this class type");
        }
    }
}
 
void ExpList::GetElmtNormalLength(Array<OneD, NekDouble> &lengthsFwd,
                                  Array<OneD, NekDouble> &lengthsBwd)
{
    int e_npoints;
 
    Array<OneD, NekDouble> locLeng;
    Array<OneD, Array<OneD, NekDouble>> lengintp(2);
    Array<OneD, Array<OneD, NekDouble>> lengAdd(2);
    Array<OneD, int> LRbndnumbs(2);
    Array<OneD, Array<OneD, NekDouble>> lengLR(2);
    lengLR[0] = lengthsFwd;
    lengLR[1] = lengthsBwd;
    Array<OneD, LocalRegions::ExpansionSharedPtr> LRelmts(2);
    LocalRegions::ExpansionSharedPtr loc_elmt;
    LocalRegions::ExpansionSharedPtr loc_exp;
    int e_npoints0 = -1;
    if (m_expType == e1D)
    {
        for (int i = 0; i < m_exp->size(); ++i)
        {
            loc_exp    = (*m_exp)[i];
            int offset = m_phys_offset[i];
 
            int e_nmodes = loc_exp->GetBasis(0)->GetNumModes();
            e_npoints    = (*m_exp)[i]->GetNumPoints(0);
            if (e_npoints0 < e_npoints)
            {
                for (int nlr = 0; nlr < 2; nlr++)
                {
                    lengintp[nlr] = Array<OneD, NekDouble>(e_npoints, 0.0);
                }
                e_npoints0 = e_npoints;
            }
 
            LRelmts[0] = loc_exp->GetLeftAdjacentElementExp();
            LRelmts[1] = loc_exp->GetRightAdjacentElementExp();
 
            LRbndnumbs[0] = loc_exp->GetLeftAdjacentElementTrace();
            LRbndnumbs[1] = loc_exp->GetRightAdjacentElementTrace();
            for (int nlr = 0; nlr < 2; ++nlr)
            {
                Vmath::Zero(e_npoints0, lengintp[nlr], 1);
                lengAdd[nlr]  = lengintp[nlr];
                int bndNumber = LRbndnumbs[nlr];
                loc_elmt      = LRelmts[nlr];
                if (bndNumber >= 0)
                {
                    locLeng = loc_elmt->GetElmtBndNormDirElmtLen(bndNumber);
                    lengAdd[nlr] = locLeng;
 
                    int loc_nmodes = loc_elmt->GetBasis(0)->GetNumModes();
                    if (e_nmodes != loc_nmodes)
                    {
                        // Parallel case: need to interpolate.
                        LibUtilities::PointsKey to_key =
                            loc_exp->GetBasis(0)->GetPointsKey();
                        LibUtilities::PointsKey from_key =
                            loc_elmt->GetBasis(0)->GetPointsKey();
                        LibUtilities::Interp1D(from_key, locLeng, to_key,
                                               lengintp[nlr]);
                        lengAdd[nlr] = lengintp[nlr];
                    }
                }
 
                for (int j = 0; j < e_npoints; ++j)
                {
                    lengLR[nlr][offset + j] = lengAdd[nlr][j];
                }
            }
        }
    }
    else if (m_expType == e2D)
    {
        for (int i = 0; i < m_exp->size(); ++i)
        {
            loc_exp    = (*m_exp)[i];
            int offset = m_phys_offset[i];
 
            LibUtilities::BasisKey traceBasis0 =
                loc_exp->GetBasis(0)->GetBasisKey();
            LibUtilities::BasisKey traceBasis1 =
                loc_exp->GetBasis(1)->GetBasisKey();
            const int TraceNq0 = traceBasis0.GetNumPoints();
            const int TraceNq1 = traceBasis1.GetNumPoints();
            e_npoints          = TraceNq0 * TraceNq1;
            if (e_npoints0 < e_npoints)
            {
                for (int nlr = 0; nlr < 2; nlr++)
                {
                    lengintp[nlr] = Array<OneD, NekDouble>(e_npoints, 0.0);
                }
                e_npoints0 = e_npoints;
            }
 
            LRelmts[0] = loc_exp->GetLeftAdjacentElementExp();
            LRelmts[1] = loc_exp->GetRightAdjacentElementExp();
 
            LRbndnumbs[0] = loc_exp->GetLeftAdjacentElementTrace();
            LRbndnumbs[1] = loc_exp->GetRightAdjacentElementTrace();
            for (int nlr = 0; nlr < 2; ++nlr)
            {
                Vmath::Zero(e_npoints0, lengintp[nlr], 1);
                int bndNumber = LRbndnumbs[nlr];
                loc_elmt      = LRelmts[nlr];
                if (bndNumber >= 0)
                {
                    locLeng = loc_elmt->GetElmtBndNormDirElmtLen(bndNumber);
                    // Project normals from 3D element onto the
                    // same orientation as the trace expansion.
                    StdRegions::Orientation orient =
                        loc_elmt->GetTraceOrient(bndNumber);
 
                    int fromid0, fromid1;
                    if (orient < StdRegions::eDir1FwdDir2_Dir2FwdDir1)
                    {
                        fromid0 = 0;
                        fromid1 = 1;
                    }
                    else
                    {
                        fromid0 = 1;
                        fromid1 = 0;
                    }
 
                    LibUtilities::BasisKey faceBasis0 =
                        loc_elmt->GetTraceBasisKey(bndNumber, fromid0);
                    LibUtilities::BasisKey faceBasis1 =
                        loc_elmt->GetTraceBasisKey(bndNumber, fromid1);
                    const int faceNq0 = faceBasis0.GetNumPoints();
                    const int faceNq1 = faceBasis1.GetNumPoints();
                    Array<OneD, NekDouble> alignedLeng(faceNq0 * faceNq1);
 
                    AlignFace(orient, faceNq0, faceNq1, locLeng, alignedLeng);
                    LibUtilities::Interp2D(
                        faceBasis0.GetPointsKey(), faceBasis1.GetPointsKey(),
                        alignedLeng, traceBasis0.GetPointsKey(),
                        traceBasis1.GetPointsKey(), lengintp[nlr]);
                }
 
                for (int j = 0; j < e_npoints; ++j)
                {
                    lengLR[nlr][offset + j] = lengintp[nlr][j];
                }
            }
        }
    }
}
 
void ExpList::v_AddTraceIntegral(const Array<OneD, const NekDouble> &Fx,
                                 const Array<OneD, const NekDouble> &Fy,
                                 Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(Fx, Fy, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_AddTraceIntegral(const Array<OneD, const NekDouble> &Fn,
                                 Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(Fn, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_AddFwdBwdTraceIntegral(const Array<OneD, const NekDouble> &Fwd,
                                       const Array<OneD, const NekDouble> &Bwd,
                                       Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(Fwd, Bwd, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_GetFwdBwdTracePhys(Array<OneD, NekDouble> &Fwd,
                                   Array<OneD, NekDouble> &Bwd)
{
    boost::ignore_unused(Fwd, Bwd);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_GetFwdBwdTracePhys(const Array<OneD, const NekDouble> &field,
                                   Array<OneD, NekDouble> &Fwd,
                                   Array<OneD, NekDouble> &Bwd, bool FillBnd,
                                   bool PutFwdInBwdOnBCs, bool DoExchange)
{
    boost::ignore_unused(field, Fwd, Bwd, FillBnd, PutFwdInBwdOnBCs,
                         DoExchange);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_FillBwdWithBoundCond(const Array<OneD, NekDouble> &Fwd,
                                     Array<OneD, NekDouble> &Bwd,
                                     bool PutFwdInBwdOnBCs)
{
    boost::ignore_unused(Fwd, Bwd, PutFwdInBwdOnBCs);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_AddTraceQuadPhysToField(const Array<OneD, const NekDouble> &Fwd,
                                        const Array<OneD, const NekDouble> &Bwd,
                                        Array<OneD, NekDouble> &field)
{
    boost::ignore_unused(field, Fwd, Bwd);
    NEKERROR(ErrorUtil::efatal,
             "v_AddTraceQuadPhysToField is not defined for this class type");
}
 
void ExpList::v_AddTraceQuadPhysToOffDiag(
    const Array<OneD, const NekDouble> &Fwd,
    const Array<OneD, const NekDouble> &Bwd, Array<OneD, NekDouble> &field)
{
    boost::ignore_unused(field, Fwd, Bwd);
    NEKERROR(ErrorUtil::efatal,
             "v_AddTraceQuadPhysToOffDiag is not defined for this class");
}
 
void ExpList::v_GetLocTraceFromTracePts(const Array<OneD, const NekDouble> &Fwd,
                                        const Array<OneD, const NekDouble> &Bwd,
                                        Array<OneD, NekDouble> &locTraceFwd,
                                        Array<OneD, NekDouble> &locTraceBwd)
{
    boost::ignore_unused(Fwd, Bwd, locTraceFwd, locTraceBwd);
    NEKERROR(ErrorUtil::efatal,
             "v_GetLocTraceFromTracePts is not defined for this class");
}
 
const Array<OneD, const NekDouble> &ExpList::v_GetBndCondBwdWeight()
{
    NEKERROR(ErrorUtil::efatal,
             "v_GetBndCondBwdWeight is not defined for this class type");
    static Array<OneD, NekDouble> tmp;
    return tmp;
}
 
void ExpList::v_SetBndCondBwdWeight(const int index, const NekDouble value)
{
    boost::ignore_unused(index, value);
    NEKERROR(ErrorUtil::efatal,
             "v_setBndCondBwdWeight is not defined for this class type");
}
 
const vector<bool> &ExpList::v_GetLeftAdjacentFaces(void) const
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static vector<bool> tmp;
    return tmp;
}
 
void ExpList::v_ExtractTracePhys(Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_ExtractTracePhys(const Array<OneD, const NekDouble> &inarray,
                                 Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(inarray, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_MultiplyByInvMassMatrix(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(inarray, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
GlobalLinSysKey ExpList::v_HelmSolve(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdRegions::ConstFactorMap &factors,
    const StdRegions::VarCoeffMap &varcoeff,
    const MultiRegions::VarFactorsMap &varfactors,
    const Array<OneD, const NekDouble> &dirForcing, const bool PhysSpaceForcing)
{
    boost::ignore_unused(inarray, outarray, factors, varcoeff, varfactors,
                         dirForcing, PhysSpaceForcing);
    NEKERROR(ErrorUtil::efatal, "HelmSolve not implemented.");
    return NullGlobalLinSysKey;
}
 
GlobalLinSysKey ExpList::v_LinearAdvectionDiffusionReactionSolve(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdRegions::ConstFactorMap &factors,
    const StdRegions::VarCoeffMap &varcoeff,
    const MultiRegions::VarFactorsMap &varfactors,
    const Array<OneD, const NekDouble> &dirForcing, const bool PhysSpaceForcing)
{
    boost::ignore_unused(inarray, outarray, factors, varcoeff, varfactors,
                         dirForcing, PhysSpaceForcing);
    NEKERROR(ErrorUtil::efatal,
             "LinearAdvectionDiffusionReactionSolve not implemented.");
    return NullGlobalLinSysKey;
}
 
void ExpList::v_LinearAdvectionReactionSolve(
    const Array<OneD, Array<OneD, NekDouble>> &velocity,
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const NekDouble lambda,
    const Array<OneD, const NekDouble> &dirForcing)
{
    boost::ignore_unused(velocity, inarray, outarray, lambda, dirForcing);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_HomogeneousFwdTrans(const int npts,
                                    const Array<OneD, const NekDouble> &inarray,
                                    Array<OneD, NekDouble> &outarray,
                                    bool Shuff, bool UnShuff)
{
    boost::ignore_unused(npts, inarray, outarray, Shuff, UnShuff);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_HomogeneousBwdTrans(const int npts,
                                    const Array<OneD, const NekDouble> &inarray,
                                    Array<OneD, NekDouble> &outarray,
                                    bool Shuff, bool UnShuff)
{
    boost::ignore_unused(npts, inarray, outarray, Shuff, UnShuff);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_DealiasedProd(const int npts,
                              const Array<OneD, NekDouble> &inarray1,
                              const Array<OneD, NekDouble> &inarray2,
                              Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(npts, inarray1, inarray2, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_DealiasedDotProd(
    const int npts, const Array<OneD, Array<OneD, NekDouble>> &inarray1,
    const Array<OneD, Array<OneD, NekDouble>> &inarray2,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    boost::ignore_unused(npts, inarray1, inarray2, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_GetBCValues(Array<OneD, NekDouble> &BndVals,
                            const Array<OneD, NekDouble> &TotField, int BndID)
{
    boost::ignore_unused(BndVals, TotField, BndID);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_NormVectorIProductWRTBase(Array<OneD, const NekDouble> &V1,
                                          Array<OneD, const NekDouble> &V2,
                                          Array<OneD, NekDouble> &outarray,
                                          int BndID)
{
    boost::ignore_unused(V1, V2, outarray, BndID);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_NormVectorIProductWRTBase(
    Array<OneD, Array<OneD, NekDouble>> &V, Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> tmp;
    switch (GetCoordim(0))
    {
        case 1:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                (*m_exp)[i]->NormVectorIProductWRTBase(
                    V[0] + GetPhys_Offset(i),
                    tmp = outarray + GetCoeff_Offset(i));
            }
        }
        break;
        case 2:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                (*m_exp)[i]->NormVectorIProductWRTBase(
                    V[0] + GetPhys_Offset(i), V[1] + GetPhys_Offset(i),
                    tmp = outarray + GetCoeff_Offset(i));
            }
        }
        break;
        case 3:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                (*m_exp)[i]->NormVectorIProductWRTBase(
                    V[0] + GetPhys_Offset(i), V[1] + GetPhys_Offset(i),
                    V[2] + GetPhys_Offset(i),
                    tmp = outarray + GetCoeff_Offset(i));
            }
        }
        break;
        default:
            NEKERROR(ErrorUtil::efatal, "Dimension not supported");
            break;
    }
}
 
void ExpList::v_ImposeDirichletConditions(Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
/**
 */
void ExpList::v_FillBndCondFromField(const Array<OneD, NekDouble> coeffs)
{
    boost::ignore_unused(coeffs);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
/**
 */
void ExpList::v_FillBndCondFromField(const int nreg,
                                     const Array<OneD, NekDouble> coeffs)
{
    boost::ignore_unused(nreg, coeffs);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_LocalToGlobal(bool useComm)
{
    boost::ignore_unused(useComm);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_LocalToGlobal(const Array<OneD, const NekDouble> &inarray,
                              Array<OneD, NekDouble> &outarray, bool useComm)
{
    boost::ignore_unused(inarray, outarray, useComm);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_GlobalToLocal(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_GlobalToLocal(const Array<OneD, const NekDouble> &inarray,
                              Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(inarray, outarray);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_FwdTrans(const Array<OneD, const NekDouble> &inarray,
                         Array<OneD, NekDouble> &outarray)
{
    v_FwdTransLocalElmt(inarray, outarray);
}
 
/**
 * The operation is evaluated locally for every element by the function
 * StdRegions#StdExpansion#IProductWRTBase.
 *
 * @param   inarray         An array of size \f$Q_{\mathrm{tot}}\f$
 *                          containing the values of the function
 *                          \f$f(\boldsymbol{x})\f$ at the quadrature
 *                          points \f$\boldsymbol{x}_i\f$.
 * @param   outarray        An array of size \f$N_{\mathrm{eof}}\f$
 *                          used to store the result.
 */
void ExpList::v_IProductWRTBase(const Array<OneD, const NekDouble> &inarray,
                                Array<OneD, NekDouble> &outarray)
{
    // initialise if required
    if (m_collectionsDoInit[Collections::eIProductWRTBase])
    {
        for (int i = 0; i < m_collections.size(); ++i)
        {
            m_collections[i].Initialise(Collections::eIProductWRTBase);
        }
        m_collectionsDoInit[Collections::eIProductWRTBase] = false;
    }
 
    Array<OneD, NekDouble> tmp;
    for (int i = 0; i < m_collections.size(); ++i)
    {
 
        m_collections[i].ApplyOperator(Collections::eIProductWRTBase,
                                       inarray + m_coll_phys_offset[i],
                                       tmp = outarray + m_coll_coeff_offset[i]);
    }
}
 
/**
 * The operation is evaluated locally by the elemental
 * function StdRegions#StdExpansion#GetCoords.
 *
 * @param   coord_0         After calculation, the \f$x_1\f$ coordinate
 *                          will be stored in this array.
 * @param   coord_1         After calculation, the \f$x_2\f$ coordinate
 *                          will be stored in this array.
 * @param   coord_2         After calculation, the \f$x_3\f$ coordinate
 *                          will be stored in this array.
 */
void ExpList::v_GetCoords(Array<OneD, NekDouble> &coord_0,
                          Array<OneD, NekDouble> &coord_1,
                          Array<OneD, NekDouble> &coord_2)
{
    if (GetNumElmts() == 0)
    {
        return;
    }
 
    int i;
    Array<OneD, NekDouble> e_coord_0;
    Array<OneD, NekDouble> e_coord_1;
    Array<OneD, NekDouble> e_coord_2;
 
    switch (GetExp(0)->GetCoordim())
    {
        case 1:
            for (i = 0; i < (*m_exp).size(); ++i)
            {
                e_coord_0 = coord_0 + m_phys_offset[i];
                (*m_exp)[i]->GetCoords(e_coord_0);
            }
            break;
        case 2:
            ASSERTL0(coord_1.size() != 0, "output coord_1 is not defined");
 
            for (i = 0; i < (*m_exp).size(); ++i)
            {
                e_coord_0 = coord_0 + m_phys_offset[i];
                e_coord_1 = coord_1 + m_phys_offset[i];
                (*m_exp)[i]->GetCoords(e_coord_0, e_coord_1);
            }
            break;
        case 3:
            ASSERTL0(coord_1.size() != 0, "output coord_1 is not defined");
            ASSERTL0(coord_2.size() != 0, "output coord_2 is not defined");
 
            for (i = 0; i < (*m_exp).size(); ++i)
            {
                e_coord_0 = coord_0 + m_phys_offset[i];
                e_coord_1 = coord_1 + m_phys_offset[i];
                e_coord_2 = coord_2 + m_phys_offset[i];
                (*m_exp)[i]->GetCoords(e_coord_0, e_coord_1, e_coord_2);
            }
            break;
    }
}
 
void ExpList::v_GetCoords(const int eid, Array<OneD, NekDouble> &xc0,
                          Array<OneD, NekDouble> &xc1,
                          Array<OneD, NekDouble> &xc2)
{
    (*m_exp)[eid]->GetCoords(xc0, xc1, xc2);
}
 
/**
 * @brief: Set up a normal along the trace elements between
 * two elements at elemental level
 *
 */
void ExpList::v_SetUpPhysNormals()
{
    for (int i = 0; i < m_exp->size(); ++i)
    {
        for (int j = 0; j < (*m_exp)[i]->GetNtraces(); ++j)
        {
            (*m_exp)[i]->ComputeTraceNormal(j);
        }
    }
}
 
/**
 */
void ExpList::v_GetBndElmtExpansion(int i, std::shared_ptr<ExpList> &result,
                                    const bool DeclareCoeffPhysArrays)
{
    boost::ignore_unused(i, result, DeclareCoeffPhysArrays);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
/**
 */
void ExpList::v_ExtractElmtToBndPhys(const int i,
                                     const Array<OneD, NekDouble> &element,
                                     Array<OneD, NekDouble> &boundary)
{
    int n, cnt;
    Array<OneD, NekDouble> tmp1, tmp2;
    LocalRegions::ExpansionSharedPtr elmt;
 
    Array<OneD, int> ElmtID, EdgeID;
    GetBoundaryToElmtMap(ElmtID, EdgeID);
 
    // Initialise result
    boundary =
        Array<OneD, NekDouble>(GetBndCondExpansions()[i]->GetTotPoints(), 0.0);
 
    // Skip other boundary regions
    for (cnt = n = 0; n < i; ++n)
    {
        cnt += GetBndCondExpansions()[n]->GetExpSize();
    }
 
    int offsetBnd;
    int offsetElmt = 0;
    for (n = 0; n < GetBndCondExpansions()[i]->GetExpSize(); ++n)
    {
        offsetBnd = GetBndCondExpansions()[i]->GetPhys_Offset(n);
 
        elmt = GetExp(ElmtID[cnt + n]);
        elmt->GetTracePhysVals(
            EdgeID[cnt + n], GetBndCondExpansions()[i]->GetExp(n),
            tmp1 = element + offsetElmt, tmp2 = boundary + offsetBnd);
 
        offsetElmt += elmt->GetTotPoints();
    }
}
 
/**
 */
void ExpList::v_ExtractPhysToBndElmt(const int i,
                                     const Array<OneD, const NekDouble> &phys,
                                     Array<OneD, NekDouble> &bndElmt)
{
    int n, cnt, nq;
 
    Array<OneD, int> ElmtID, EdgeID;
    GetBoundaryToElmtMap(ElmtID, EdgeID);
 
    // Skip other boundary regions
    for (cnt = n = 0; n < i; ++n)
    {
        cnt += GetBndCondExpansions()[n]->GetExpSize();
    }
 
    // Count number of points
    int npoints = 0;
    for (n = 0; n < GetBndCondExpansions()[i]->GetExpSize(); ++n)
    {
        npoints += GetExp(ElmtID[cnt + n])->GetTotPoints();
    }
 
    // Initialise result
    bndElmt = Array<OneD, NekDouble>(npoints, 0.0);
 
    // Extract data
    int offsetPhys;
    int offsetElmt = 0;
    for (n = 0; n < GetBndCondExpansions()[i]->GetExpSize(); ++n)
    {
        nq         = GetExp(ElmtID[cnt + n])->GetTotPoints();
        offsetPhys = GetPhys_Offset(ElmtID[cnt + n]);
        Vmath::Vcopy(nq, &phys[offsetPhys], 1, &bndElmt[offsetElmt], 1);
        offsetElmt += nq;
    }
}
 
/**
 */
void ExpList::v_ExtractPhysToBnd(int i,
                                 const Array<OneD, const NekDouble> &phys,
                                 Array<OneD, NekDouble> &bnd)
{
    int n, cnt;
    Array<OneD, NekDouble> tmp1;
    LocalRegions::ExpansionSharedPtr elmt;
 
    Array<OneD, int> ElmtID, EdgeID;
    GetBoundaryToElmtMap(ElmtID, EdgeID);
 
    // Initialise result
    bnd =
        Array<OneD, NekDouble>(GetBndCondExpansions()[i]->GetTotPoints(), 0.0);
 
    // Skip other boundary regions
    for (cnt = n = 0; n < i; ++n)
    {
        cnt += GetBndCondExpansions()[n]->GetExpSize();
    }
 
    int offsetBnd;
    int offsetPhys;
    for (n = 0; n < GetBndCondExpansions()[i]->GetExpSize(); ++n)
    {
        offsetPhys = GetPhys_Offset(ElmtID[cnt + n]);
        offsetBnd  = GetBndCondExpansions()[i]->GetPhys_Offset(n);
 
        elmt = GetExp(ElmtID[cnt + n]);
        elmt->GetTracePhysVals(EdgeID[cnt + n],
                               GetBndCondExpansions()[i]->GetExp(n),
                               phys + offsetPhys, tmp1 = bnd + offsetBnd);
    }
}
 
/**
 */
void ExpList::v_GetBoundaryNormals(int i,
                                   Array<OneD, Array<OneD, NekDouble>> &normals)
{
    int j, n, cnt, nq;
    int coordim = GetCoordim(0);
    Array<OneD, NekDouble> tmp;
    LocalRegions::ExpansionSharedPtr elmt;
 
    Array<OneD, int> ElmtID, EdgeID;
    GetBoundaryToElmtMap(ElmtID, EdgeID);
 
    // Initialise result
    normals = Array<OneD, Array<OneD, NekDouble>>(coordim);
    for (j = 0; j < coordim; ++j)
    {
        normals[j] = Array<OneD, NekDouble>(
            GetBndCondExpansions()[i]->GetTotPoints(), 0.0);
    }
 
    // Skip other boundary regions
    for (cnt = n = 0; n < i; ++n)
    {
        cnt += GetBndCondExpansions()[n]->GetExpSize();
    }
 
    int offset;
    for (n = 0; n < GetBndCondExpansions()[i]->GetExpSize(); ++n)
    {
        offset = GetBndCondExpansions()[i]->GetPhys_Offset(n);
        nq     = GetBndCondExpansions()[i]->GetExp(n)->GetTotPoints();
 
        elmt = GetExp(ElmtID[cnt + n]);
        const Array<OneD, const Array<OneD, NekDouble>> normalsElmt =
            elmt->GetTraceNormal(EdgeID[cnt + n]);
        // Copy to result
        for (j = 0; j < coordim; ++j)
        {
            Vmath::Vcopy(nq, normalsElmt[j], 1, tmp = normals[j] + offset, 1);
        }
    }
}
 
/**
 */
void ExpList::v_GetBoundaryToElmtMap(Array<OneD, int> &ElmtID,
                                     Array<OneD, int> &EdgeID)
{
    boost::ignore_unused(ElmtID, EdgeID);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
void ExpList::v_FillBwdWithBwdWeight(Array<OneD, NekDouble> &weightave,
                                     Array<OneD, NekDouble> &weightjmp)
{
    boost::ignore_unused(weightave, weightjmp);
    NEKERROR(ErrorUtil::efatal, "v_FillBwdWithBwdWeight not defined");
}
 
void ExpList::v_PeriodicBwdCopy(const Array<OneD, const NekDouble> &Fwd,
                                Array<OneD, NekDouble> &Bwd)
{
    boost::ignore_unused(Fwd, Bwd);
    NEKERROR(ErrorUtil::efatal, "v_PeriodicBwdCopy not defined");
}
 
/**
 */
const Array<OneD, const SpatialDomains::BoundaryConditionShPtr>
    &ExpList::v_GetBndConditions(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static Array<OneD, const SpatialDomains::BoundaryConditionShPtr> result;
    return result;
}
 
/**
 */
Array<OneD, SpatialDomains::BoundaryConditionShPtr>
    &ExpList::v_UpdateBndConditions()
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static Array<OneD, SpatialDomains::BoundaryConditionShPtr> result;
    return result;
}
 
/**
 */
void ExpList::v_EvaluateBoundaryConditions(const NekDouble time,
                                           const std::string varName,
                                           const NekDouble x2_in,
                                           const NekDouble x3_in)
{
    boost::ignore_unused(time, varName, x2_in, x3_in);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
/**
 */
map<int, RobinBCInfoSharedPtr> ExpList::v_GetRobinBCInfo(void)
{
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    static map<int, RobinBCInfoSharedPtr> result;
    return result;
}
 
/**
 */
void ExpList::v_GetPeriodicEntities(PeriodicMap &periodicVerts,
                                    PeriodicMap &periodicEdges,
                                    PeriodicMap &periodicFaces)
{
    boost::ignore_unused(periodicVerts, periodicEdges, periodicFaces);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
}
 
SpatialDomains::BoundaryConditionShPtr ExpList::GetBoundaryCondition(
    const SpatialDomains::BoundaryConditionCollection &collection,
    unsigned int regionId, const std::string &variable)
{
    auto collectionIter = collection.find(regionId);
    ASSERTL1(collectionIter != collection.end(),
             "Unable to locate collection " +
                 boost::lexical_cast<string>(regionId));
 
    const SpatialDomains::BoundaryConditionMapShPtr bndCondMap =
        (*collectionIter).second;
    auto conditionMapIter = bndCondMap->find(variable);
    ASSERTL1(conditionMapIter != bndCondMap->end(),
             "Unable to locate condition map.");
 
    const SpatialDomains::BoundaryConditionShPtr boundaryCondition =
        (*conditionMapIter).second;
 
    return boundaryCondition;
}
 
ExpListSharedPtr &ExpList::v_GetPlane(int n)
{
    boost::ignore_unused(n);
    NEKERROR(ErrorUtil::efatal,
             "This method is not defined or valid for this class type");
    return NullExpListSharedPtr;
}
 
/**
 * @brief Construct collections of elements containing a single element
 * type and polynomial order from the list of expansions.
 */
void ExpList::CreateCollections(Collections::ImplementationType ImpType)
{
    map<LibUtilities::ShapeType,
        vector<std::pair<LocalRegions::ExpansionSharedPtr, int>>>
        collections;
 
    // Set up initialisation flags
    m_collectionsDoInit =
        std::vector<bool>(Collections::SIZE_OperatorType, true);
 
    // Figure out optimisation parameters if provided in
    // session file or default given
    Collections::CollectionOptimisation colOpt(
        m_session, (*m_exp)[0]->GetShapeDimension(), ImpType);
 
    // turn on autotuning if explicitly specified in xml file
    // or command line option is set but only do optimisation
    // for volumetric elements (not boundary condition)
    bool autotuning = colOpt.IsUsingAutotuning();
    if ((autotuning == false) && (ImpType == Collections::eNoImpType))
    {
        // turn on autotuning if writeoptfile specified
        // if m_graph available
        if (m_session->GetUpdateOptFile() && m_graph)
        {
            // only turn on autotuning for volumetric elements
            // where Mesh Dimension is equal to the Shape
            // Dimension of element.
            if (m_graph->GetMeshDimension() == (*m_exp)[0]->GetShapeDimension())
            {
                autotuning = true;
            }
        }
    }
    bool verbose = (m_session->DefinesCmdLineArgument("verbose")) &&
                   (m_session->GetComm()->GetRank() == 0);
    // the maximum size is either explicitly specified, or set to very large
    // value which will not affect the actual collection size
    int collmax =
        (colOpt.GetMaxCollectionSize() > 0 ? colOpt.GetMaxCollectionSize()
                                           : 2 * m_exp->size());
 
    // clear vectors in case previously called
    m_collections.clear();
    m_coll_coeff_offset.clear();
    m_coll_phys_offset.clear();
 
    /*-------------------------------------------------------------------------
      Dividing m_exp into sub groups (collections): original exp order is kept.
      Use 3 basiskey + deformed flag to determine if two exp belong to the same
      collection or not.
    -------------------------------------------------------------------------*/
    vector<StdRegions::StdExpansionSharedPtr> collExp;
    // initialize the basisKeys to NullBasisKey
    std::vector<LibUtilities::BasisKey> prevbasisKeys(
        3, LibUtilities::NullBasisKey);
    std::vector<LibUtilities::BasisKey> thisbasisKeys(
        3, LibUtilities::NullBasisKey);
    // initialize the deformed flag to false
    bool prevDef = false;
    // collcnt is the number of elements in current collection
    int collcnt = 0;
    // collsize is the maximum size among all collections
    int collsize = 0;
 
    for (int i = 0; i < (*m_exp).size(); i++)
    {
        LocalRegions::ExpansionSharedPtr exp = (*m_exp)[i];
        Collections::OperatorImpMap impTypes = colOpt.GetOperatorImpMap(exp);
 
        // fetch basiskeys of current element
        for (int d = 0; d < exp->GetNumBases(); d++)
        {
            thisbasisKeys[d] = exp->GetBasis(d)->GetBasisKey();
        }
        // fetch deformed flag of current element
        bool Deformed =
            (exp->GetMetricInfo()->GetGtype() == SpatialDomains::eDeformed);
 
        // Check if this element is the same type as the previous one or
        // if we have reached the maximum collection size
        if (thisbasisKeys != prevbasisKeys || prevDef != Deformed ||
            collcnt >= collmax)
        {
            // if previous one is not empty (i==0), create new collection
            // according to the previous collExp and push it back.
            if (i > 0)
            {
                Collections::Collection tmp(collExp, impTypes);
                m_collections.push_back(tmp);
 
                // if no Imp Type provided and No
                // setting in xml file. reset
                // impTypes using timings
                if (autotuning)
                {
                    // if current collection is larger than previous one
                    // update impTypes; otherwise, use previous impTypes
                    if (collExp.size() > collsize)
                    {
                        impTypes =
                            colOpt.SetWithTimings(collExp, impTypes, verbose);
                        collsize = collExp.size();
                    }
                }
 
                // start new geom list
                collExp.clear();
            }
 
            // set up initial offset of this collection
            m_coll_coeff_offset.push_back(m_coeff_offset[i]);
            m_coll_phys_offset.push_back(m_phys_offset[i]);
            // insert exp and reset count to 1
            collExp.push_back(exp);
            collcnt = 1;
            // update previous info
            prevbasisKeys = thisbasisKeys;
            prevDef       = Deformed;
        }
        else // The current exp is the same as the previous one
        {
            // insert exp and increment count
            collExp.push_back(exp);
            collcnt++;
            // No need to update previous info
        }
 
        // check if we have reached the end of m_exp
        if (i == (*m_exp).size() - 1)
        {
            // Then create and push back the last collection
            Collections::Collection tmp(collExp, impTypes);
            m_collections.push_back(tmp);
 
            // if no Imp Type provided and No
            // setting in xml file. reset
            // impTypes using timings
            if (autotuning)
            {
                if (collExp.size() > collsize)
                {
                    impTypes =
                        colOpt.SetWithTimings(collExp, impTypes, verbose);
                    collsize = collExp.size();
                }
            }
            collExp.clear();
        }
    }
 
    // update optimisation file
    if ((m_session->GetUpdateOptFile()) && (ImpType == Collections::eNoImpType))
    {
        colOpt.UpdateOptFile(m_session->GetSessionName(), m_comm);
        // turn off writeoptfile option so only first
        // instance is timed
        m_session->SetUpdateOptFile(false);
    }
}
 
void ExpList::ClearGlobalLinSysManager(void)
{
    v_ClearGlobalLinSysManager();
}
 
/**
 * Added for access to the pool count by external code (e.g. UnitTests)
 * which can't access the static pool across compilation units on
 * Windows builds.
 */
int ExpList::GetPoolCount(std::string poolName)
{
    return v_GetPoolCount(poolName);
}
 
void ExpList::UnsetGlobalLinSys(GlobalLinSysKey key, bool clearLocalMatrices)
{
    v_UnsetGlobalLinSys(key, clearLocalMatrices);
}
 
LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys>
    &ExpList::GetGlobalLinSysManager(void)
{
    return v_GetGlobalLinSysManager();
}
 
void ExpList::v_PhysInterp1DScaled(const NekDouble scale,
                                   const Array<OneD, NekDouble> &inarray,
                                   Array<OneD, NekDouble> &outarray)
{
    int cnt, cnt1;
 
    cnt = cnt1 = 0;
 
    switch (m_expType)
    {
        case e2D:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                // get new points key
                int pt0  = (*m_exp)[i]->GetNumPoints(0);
                int pt1  = (*m_exp)[i]->GetNumPoints(1);
                int npt0 = (int)pt0 * scale;
                int npt1 = (int)pt1 * scale;
 
                LibUtilities::PointsKey newPointsKey0(
                    npt0, (*m_exp)[i]->GetPointsType(0));
                LibUtilities::PointsKey newPointsKey1(
                    npt1, (*m_exp)[i]->GetPointsType(1));
 
                // Interpolate points;
                LibUtilities::Interp2D((*m_exp)[i]->GetBasis(0)->GetPointsKey(),
                                       (*m_exp)[i]->GetBasis(1)->GetPointsKey(),
                                       &inarray[cnt], newPointsKey0,
                                       newPointsKey1, &outarray[cnt1]);
 
                cnt += pt0 * pt1;
                cnt1 += npt0 * npt1;
            }
        }
        break;
        case e3D:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                // get new points key
                int pt0  = (*m_exp)[i]->GetNumPoints(0);
                int pt1  = (*m_exp)[i]->GetNumPoints(1);
                int pt2  = (*m_exp)[i]->GetNumPoints(2);
                int npt0 = (int)pt0 * scale;
                int npt1 = (int)pt1 * scale;
                int npt2 = (int)pt2 * scale;
 
                LibUtilities::PointsKey newPointsKey0(
                    npt0, (*m_exp)[i]->GetPointsType(0));
                LibUtilities::PointsKey newPointsKey1(
                    npt1, (*m_exp)[i]->GetPointsType(1));
                LibUtilities::PointsKey newPointsKey2(
                    npt2, (*m_exp)[i]->GetPointsType(2));
 
                // Interpolate points;
                LibUtilities::Interp3D((*m_exp)[i]->GetBasis(0)->GetPointsKey(),
                                       (*m_exp)[i]->GetBasis(1)->GetPointsKey(),
                                       (*m_exp)[i]->GetBasis(2)->GetPointsKey(),
                                       &inarray[cnt], newPointsKey0,
                                       newPointsKey1, newPointsKey2,
                                       &outarray[cnt1]);
 
                cnt += pt0 * pt1 * pt2;
                cnt1 += npt0 * npt1 * npt2;
            }
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal, "This expansion is not set");
        }
        break;
    }
}
 
void ExpList::v_AddTraceIntegralToOffDiag(
    const Array<OneD, const NekDouble> &FwdFlux,
    const Array<OneD, const NekDouble> &BwdFlux,
    Array<OneD, NekDouble> &outarray)
{
    boost::ignore_unused(FwdFlux, BwdFlux, outarray);
    NEKERROR(ErrorUtil::efatal, "AddTraceIntegralToOffDiag not defined");
}
 
void ExpList::GetMatIpwrtDeriveBase(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray, const int nDirctn,
    Array<OneD, DNekMatSharedPtr> &mtxPerVar)
{
    int nTotElmt  = (*m_exp).size();
    int nElmtPnt  = (*m_exp)[0]->GetTotPoints();
    int nElmtCoef = (*m_exp)[0]->GetNcoeffs();
 
    Array<OneD, NekDouble> tmpCoef(nElmtCoef, 0.0);
    Array<OneD, NekDouble> tmpPhys(nElmtPnt, 0.0);
 
    for (int nelmt = 0; nelmt < nTotElmt; nelmt++)
    {
        nElmtCoef = (*m_exp)[nelmt]->GetNcoeffs();
        nElmtPnt  = (*m_exp)[nelmt]->GetTotPoints();
 
        if (tmpPhys.size() != nElmtPnt || tmpCoef.size() != nElmtCoef)
        {
            tmpPhys = Array<OneD, NekDouble>(nElmtPnt, 0.0);
            tmpCoef = Array<OneD, NekDouble>(nElmtCoef, 0.0);
        }
 
        for (int ncl = 0; ncl < nElmtPnt; ncl++)
        {
            tmpPhys[ncl] = inarray[nelmt][ncl];
 
            (*m_exp)[nelmt]->IProductWRTDerivBase(nDirctn, tmpPhys, tmpCoef);
 
            for (int nrw = 0; nrw < nElmtCoef; nrw++)
            {
                (*mtxPerVar[nelmt])(nrw, ncl) = tmpCoef[nrw];
            }
            // to maintain all the other columes are zero.
            tmpPhys[ncl] = 0.0;
        }
    }
}
 
void ExpList::GetMatIpwrtDeriveBase(const TensorOfArray3D<NekDouble> &inarray,
                                    Array<OneD, DNekMatSharedPtr> &mtxPerVar)
{
    int nTotElmt = (*m_exp).size();
 
    int nspacedim = m_graph->GetSpaceDimension();
    Array<OneD, Array<OneD, NekDouble>> projectedpnts(nspacedim);
    Array<OneD, Array<OneD, NekDouble>> tmppnts(nspacedim);
    Array<OneD, DNekMatSharedPtr> ArrayStdMat(nspacedim);
    Array<OneD, Array<OneD, NekDouble>> ArrayStdMat_data(nspacedim);
 
    Array<OneD, NekDouble> clmnArray, clmnStdMatArray;
 
    LibUtilities::ShapeType ElmtTypePrevious = LibUtilities::eNoShapeType;
    int nElmtPntPrevious                     = 0;
    int nElmtCoefPrevious                    = 0;
 
    int nElmtPnt, nElmtCoef;
    for (int nelmt = 0; nelmt < nTotElmt; nelmt++)
    {
        nElmtCoef                           = (*m_exp)[nelmt]->GetNcoeffs();
        nElmtPnt                            = (*m_exp)[nelmt]->GetTotPoints();
        LibUtilities::ShapeType ElmtTypeNow = (*m_exp)[nelmt]->DetShapeType();
 
        if (nElmtPntPrevious != nElmtPnt || nElmtCoefPrevious != nElmtCoef ||
            (ElmtTypeNow != ElmtTypePrevious))
        {
            if (nElmtPntPrevious != nElmtPnt)
            {
                for (int ndir = 0; ndir < nspacedim; ndir++)
                {
                    projectedpnts[ndir] = Array<OneD, NekDouble>(nElmtPnt, 0.0);
                    tmppnts[ndir]       = Array<OneD, NekDouble>(nElmtPnt, 0.0);
                }
            }
            StdRegions::StdExpansionSharedPtr stdExp;
            stdExp = (*m_exp)[nelmt]->GetStdExp();
            StdRegions::StdMatrixKey matkey(StdRegions::eDerivBase0,
                                            stdExp->DetShapeType(), *stdExp);
 
            ArrayStdMat[0]      = stdExp->GetStdMatrix(matkey);
            ArrayStdMat_data[0] = ArrayStdMat[0]->GetPtr();
 
            if (nspacedim > 1)
            {
                StdRegions::StdMatrixKey matkey(
                    StdRegions::eDerivBase1, stdExp->DetShapeType(), *stdExp);
 
                ArrayStdMat[1]      = stdExp->GetStdMatrix(matkey);
                ArrayStdMat_data[1] = ArrayStdMat[1]->GetPtr();
 
                if (nspacedim > 2)
                {
                    StdRegions::StdMatrixKey matkey(StdRegions::eDerivBase2,
                                                    stdExp->DetShapeType(),
                                                    *stdExp);
 
                    ArrayStdMat[2]      = stdExp->GetStdMatrix(matkey);
                    ArrayStdMat_data[2] = ArrayStdMat[2]->GetPtr();
                }
            }
 
            ElmtTypePrevious  = ElmtTypeNow;
            nElmtPntPrevious  = nElmtPnt;
            nElmtCoefPrevious = nElmtCoef;
        }
        else
        {
            for (int ndir = 0; ndir < nspacedim; ndir++)
            {
                Vmath::Zero(nElmtPnt, projectedpnts[ndir], 1);
            }
        }
 
        for (int ndir = 0; ndir < nspacedim; ndir++)
        {
            (*m_exp)[nelmt]->AlignVectorToCollapsedDir(
                ndir, inarray[ndir][nelmt], tmppnts);
            for (int n = 0; n < nspacedim; n++)
            {
                Vmath::Vadd(nElmtPnt, tmppnts[n], 1, projectedpnts[n], 1,
                            projectedpnts[n], 1);
            }
        }
 
        for (int ndir = 0; ndir < nspacedim; ndir++)
        {
            // weight with metric
            (*m_exp)[nelmt]->MultiplyByQuadratureMetric(projectedpnts[ndir],
                                                        projectedpnts[ndir]);
            Array<OneD, NekDouble> MatDataArray = mtxPerVar[nelmt]->GetPtr();
 
            for (int np = 0; np < nElmtPnt; np++)
            {
                NekDouble factor = projectedpnts[ndir][np];
                clmnArray        = MatDataArray + np * nElmtCoef;
                clmnStdMatArray  = ArrayStdMat_data[ndir] + np * nElmtCoef;
                Vmath::Svtvp(nElmtCoef, factor, clmnStdMatArray, 1, clmnArray,
                             1, clmnArray, 1);
            }
        }
    }
}
 
// TODO: Reduce cost by getting Bwd Matrix directly
void ExpList::GetDiagMatIpwrtBase(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, DNekMatSharedPtr> &mtxPerVar)
{
    LibUtilities::ShapeType ElmtTypePrevious = LibUtilities::eNoShapeType;
    int nElmtPntPrevious                     = 0;
    int nElmtCoefPrevious                    = 0;
    int nTotElmt                             = (*m_exp).size();
    int nElmtPnt                             = (*m_exp)[0]->GetTotPoints();
    int nElmtCoef                            = (*m_exp)[0]->GetNcoeffs();
 
    Array<OneD, NekDouble> tmpPhys;
    Array<OneD, NekDouble> clmnArray, clmnStdMatArray;
    Array<OneD, NekDouble> stdMat_data;
 
    for (int nelmt = 0; nelmt < nTotElmt; nelmt++)
    {
        nElmtCoef                           = (*m_exp)[nelmt]->GetNcoeffs();
        nElmtPnt                            = (*m_exp)[nelmt]->GetTotPoints();
        LibUtilities::ShapeType ElmtTypeNow = (*m_exp)[nelmt]->DetShapeType();
 
        if (nElmtPntPrevious != nElmtPnt || nElmtCoefPrevious != nElmtCoef ||
            (ElmtTypeNow != ElmtTypePrevious))
        {
            StdRegions::StdExpansionSharedPtr stdExp;
            stdExp = (*m_exp)[nelmt]->GetStdExp();
            StdRegions::StdMatrixKey matkey(StdRegions::eBwdMat,
                                            stdExp->DetShapeType(), *stdExp);
 
            DNekMatSharedPtr BwdMat = stdExp->GetStdMatrix(matkey);
            stdMat_data             = BwdMat->GetPtr();
 
            if (nElmtPntPrevious != nElmtPnt)
            {
                tmpPhys = Array<OneD, NekDouble>(nElmtPnt, 0.0);
            }
 
            ElmtTypePrevious  = ElmtTypeNow;
            nElmtPntPrevious  = nElmtPnt;
            nElmtCoefPrevious = nElmtCoef;
        }
 
        (*m_exp)[nelmt]->MultiplyByQuadratureMetric(
            inarray[nelmt],
            tmpPhys); // weight with metric
 
        Array<OneD, NekDouble> MatDataArray = mtxPerVar[nelmt]->GetPtr();
 
        for (int np = 0; np < nElmtPnt; np++)
        {
            NekDouble factor = tmpPhys[np];
            clmnArray        = MatDataArray + np * nElmtCoef;
            clmnStdMatArray  = stdMat_data + np * nElmtCoef;
            Vmath::Smul(nElmtCoef, factor, clmnStdMatArray, 1, clmnArray, 1);
        }
    }
}
 
/**
 * @brief inverse process of v_GetFwdBwdTracePhys. Given Trace integration of
 * Fwd and Bwd Jacobian, with dimension NtotalTrace*TraceCoef*TracePhys. return
 * Elemental Jacobian matrix with dimension
 * NtotalElement*ElementCoef*ElementPhys.
 *
 *
 * @param field is a NekDouble array which contains the 2D data
 *              from which we wish to extract the backward and
 *              forward orientated trace/edge arrays.
 * @param Fwd   The resulting forwards space.
 * @param Bwd   The resulting backwards space.
 */
void ExpList::AddTraceJacToElmtJac(
    const Array<OneD, const DNekMatSharedPtr> &FwdMat,
    const Array<OneD, const DNekMatSharedPtr> &BwdMat,
    Array<OneD, DNekMatSharedPtr> &fieldMat)
{
    MultiRegions::ExpListSharedPtr tracelist = GetTrace();
    std::shared_ptr<LocalRegions::ExpansionVector> traceExp =
        tracelist->GetExp();
    int ntotTrace = (*traceExp).size();
    int nTracePnt, nTraceCoef;
 
    std::shared_ptr<LocalRegions::ExpansionVector> fieldExp = GetExp();
    int nElmtCoef;
 
    const MultiRegions::LocTraceToTraceMapSharedPtr locTraceToTraceMap =
        GetLocTraceToTraceMap();
    const Array<OneD, const Array<OneD, int>> LRAdjExpid =
        locTraceToTraceMap->GetLeftRightAdjacentExpId();
    const Array<OneD, const Array<OneD, bool>> LRAdjflag =
        locTraceToTraceMap->GetLeftRightAdjacentExpFlag();
 
    const Array<OneD, const Array<OneD, Array<OneD, int>>> elmtLRMap =
        locTraceToTraceMap->GetTraceCoeffToLeftRightExpCoeffMap();
    const Array<OneD, const Array<OneD, Array<OneD, int>>> elmtLRSign =
        locTraceToTraceMap->GetTraceCoeffToLeftRightExpCoeffSign();
    DNekMatSharedPtr ElmtMat;
    Array<OneD, NekDouble> ElmtMat_data;
    // int nclAdjExp;
    int nrwAdjExp;
    int MatIndex, nPnts;
    NekDouble sign = 1.0;
 
    int nTracePntsTtl   = tracelist->GetTotPoints();
    int nlocTracePts    = locTraceToTraceMap->GetNLocTracePts();
    int nlocTracePtsFwd = locTraceToTraceMap->GetNFwdLocTracePts();
    int nlocTracePtsBwd = nlocTracePts - nlocTracePtsFwd;
 
    Array<OneD, int> nlocTracePtsLR(2);
    nlocTracePtsLR[0] = nlocTracePtsFwd;
    nlocTracePtsLR[1] = nlocTracePtsBwd;
 
    size_t nFwdBwdNonZero = 0;
    Array<OneD, int> tmpIndex{2, -1};
    for (int i = 0; i < 2; ++i)
    {
        if (nlocTracePtsLR[i] > 0)
        {
            tmpIndex[nFwdBwdNonZero] = i;
            nFwdBwdNonZero++;
        }
    }
 
    Array<OneD, int> nlocTracePtsNonZeroIndex{nFwdBwdNonZero};
    for (int i = 0; i < nFwdBwdNonZero; ++i)
    {
        nlocTracePtsNonZeroIndex[i] = tmpIndex[i];
    }
 
    Array<OneD, NekDouble> TraceFwdPhy(nTracePntsTtl);
    Array<OneD, NekDouble> TraceBwdPhy(nTracePntsTtl);
    Array<OneD, Array<OneD, NekDouble>> tmplocTrace(2);
    for (int k = 0; k < 2; ++k)
    {
        tmplocTrace[k] = NullNekDouble1DArray;
    }
 
    for (int k = 0; k < nFwdBwdNonZero; ++k)
    {
        size_t i       = nlocTracePtsNonZeroIndex[k];
        tmplocTrace[i] = Array<OneD, NekDouble>(nlocTracePtsLR[i]);
    }
 
    int nNumbElmt = fieldMat.size();
    Array<OneD, Array<OneD, NekDouble>> ElmtMatDataArray(nNumbElmt);
    Array<OneD, int> ElmtCoefArray(nNumbElmt);
    for (int i = 0; i < nNumbElmt; i++)
    {
        ElmtMatDataArray[i] = fieldMat[i]->GetPtr();
        ElmtCoefArray[i]    = GetNcoeffs(i);
    }
 
    int nTraceCoefMax = 0;
    int nTraceCoefMin = std::numeric_limits<int>::max();
    Array<OneD, int> TraceCoefArray(ntotTrace);
    Array<OneD, int> TracePntArray(ntotTrace);
    Array<OneD, int> TraceOffArray(ntotTrace);
    Array<OneD, Array<OneD, NekDouble>> FwdMatData(ntotTrace);
    Array<OneD, Array<OneD, NekDouble>> BwdMatData(ntotTrace);
    for (int nt = 0; nt < ntotTrace; nt++)
    {
        nTraceCoef         = (*traceExp)[nt]->GetNcoeffs();
        nTracePnt          = tracelist->GetTotPoints(nt);
        int noffset        = tracelist->GetPhys_Offset(nt);
        TraceCoefArray[nt] = nTraceCoef;
        TracePntArray[nt]  = nTracePnt;
        TraceOffArray[nt]  = noffset;
        FwdMatData[nt]     = FwdMat[nt]->GetPtr();
        BwdMatData[nt]     = BwdMat[nt]->GetPtr();
        if (nTraceCoef > nTraceCoefMax)
        {
            nTraceCoefMax = nTraceCoef;
        }
        if (nTraceCoef < nTraceCoefMin)
        {
            nTraceCoefMin = nTraceCoef;
        }
    }
    WARNINGL1(nTraceCoefMax == nTraceCoefMin,
              "nTraceCoefMax!=nTraceCoefMin: Effeciency may be low ");
 
    int traceID, nfieldPnts, ElmtId, noffset;
    const Array<OneD, const Array<OneD, int>> LocTracephysToTraceIDMap =
        locTraceToTraceMap->GetLocTracephysToTraceIDMap();
    const Array<OneD, const int> fieldToLocTraceMap =
        locTraceToTraceMap->GetLocTraceToFieldMap();
    Array<OneD, Array<OneD, int>> fieldToLocTraceMapLR(2);
    noffset = 0;
    for (int k = 0; k < nFwdBwdNonZero; ++k)
    {
        size_t i                = nlocTracePtsNonZeroIndex[k];
        fieldToLocTraceMapLR[i] = Array<OneD, int>(nlocTracePtsLR[i]);
        Vmath::Vcopy(nlocTracePtsLR[i], &fieldToLocTraceMap[0] + noffset, 1,
                     &fieldToLocTraceMapLR[i][0], 1);
        noffset += nlocTracePtsLR[i];
    }
 
    Array<OneD, Array<OneD, int>> MatIndexArray(2);
    for (int k = 0; k < nFwdBwdNonZero; ++k)
    {
        size_t nlr         = nlocTracePtsNonZeroIndex[k];
        MatIndexArray[nlr] = Array<OneD, int>(nlocTracePtsLR[nlr]);
        for (int nloc = 0; nloc < nlocTracePtsLR[nlr]; nloc++)
        {
            traceID    = LocTracephysToTraceIDMap[nlr][nloc];
            nTraceCoef = TraceCoefArray[traceID];
            ElmtId     = LRAdjExpid[nlr][traceID];
            noffset    = GetPhys_Offset(ElmtId);
            nElmtCoef  = ElmtCoefArray[ElmtId];
            nfieldPnts = fieldToLocTraceMapLR[nlr][nloc];
            nPnts      = nfieldPnts - noffset;
 
            MatIndexArray[nlr][nloc] = nPnts * nElmtCoef;
        }
    }
 
    for (int nc = 0; nc < nTraceCoefMin; nc++)
    {
        for (int nt = 0; nt < ntotTrace; nt++)
        {
            nTraceCoef = TraceCoefArray[nt];
            nTracePnt  = TracePntArray[nt];
            noffset    = TraceOffArray[nt];
            Vmath::Vcopy(nTracePnt, &FwdMatData[nt][nc], nTraceCoef,
                         &TraceFwdPhy[noffset], 1);
            Vmath::Vcopy(nTracePnt, &BwdMatData[nt][nc], nTraceCoef,
                         &TraceBwdPhy[noffset], 1);
        }
 
        for (int k = 0; k < nFwdBwdNonZero; ++k)
        {
            size_t i = nlocTracePtsNonZeroIndex[k];
            Vmath::Zero(nlocTracePtsLR[i], tmplocTrace[i], 1);
        }
 
        GetLocTraceFromTracePts(TraceFwdPhy, TraceBwdPhy, tmplocTrace[0],
                                tmplocTrace[1]);
 
        for (int k = 0; k < nFwdBwdNonZero; ++k)
        {
            size_t nlr = nlocTracePtsNonZeroIndex[k];
            for (int nloc = 0; nloc < nlocTracePtsLR[nlr]; nloc++)
            {
                traceID    = LocTracephysToTraceIDMap[nlr][nloc];
                nTraceCoef = TraceCoefArray[traceID];
                ElmtId     = LRAdjExpid[nlr][traceID];
                nrwAdjExp  = elmtLRMap[nlr][traceID][nc];
                sign       = elmtLRSign[nlr][traceID][nc];
                MatIndex   = MatIndexArray[nlr][nloc] + nrwAdjExp;
 
                ElmtMatDataArray[ElmtId][MatIndex] -=
                    sign * tmplocTrace[nlr][nloc];
            }
        }
    }
 
    for (int nc = nTraceCoefMin; nc < nTraceCoefMax; nc++)
    {
        for (int nt = 0; nt < ntotTrace; nt++)
        {
            nTraceCoef = TraceCoefArray[nt];
            nTracePnt  = TracePntArray[nt];
            noffset    = TraceOffArray[nt];
            if (nc < nTraceCoef)
            {
                Vmath::Vcopy(nTracePnt, &FwdMatData[nt][nc], nTraceCoef,
                             &TraceFwdPhy[noffset], 1);
                Vmath::Vcopy(nTracePnt, &BwdMatData[nt][nc], nTraceCoef,
                             &TraceBwdPhy[noffset], 1);
            }
            else
            {
                Vmath::Zero(nTracePnt, &TraceFwdPhy[noffset], 1);
                Vmath::Zero(nTracePnt, &TraceBwdPhy[noffset], 1);
            }
        }
 
        for (int k = 0; k < nFwdBwdNonZero; ++k)
        {
            size_t i = nlocTracePtsNonZeroIndex[k];
            Vmath::Zero(nlocTracePtsLR[i], tmplocTrace[i], 1);
        }
        GetLocTraceFromTracePts(TraceFwdPhy, TraceBwdPhy, tmplocTrace[0],
                                tmplocTrace[1]);
 
        for (int k = 0; k < nFwdBwdNonZero; ++k)
        {
            size_t nlr = nlocTracePtsNonZeroIndex[k];
            for (int nloc = 0; nloc < nlocTracePtsLR[nlr]; nloc++)
            {
                traceID    = LocTracephysToTraceIDMap[nlr][nloc];
                nTraceCoef = TraceCoefArray[traceID];
                if (nc < nTraceCoef)
                {
                    ElmtId    = LRAdjExpid[nlr][traceID];
                    nrwAdjExp = elmtLRMap[nlr][traceID][nc];
                    sign      = -elmtLRSign[nlr][traceID][nc];
                    MatIndex  = MatIndexArray[nlr][nloc] + nrwAdjExp;
 
                    ElmtMatDataArray[ElmtId][MatIndex] +=
                        sign * tmplocTrace[nlr][nloc];
                }
            }
        }
    }
}
 
void ExpList::AddRightIPTPhysDerivBase(
    const int dir, const Array<OneD, const DNekMatSharedPtr> ElmtJacQuad,
    Array<OneD, DNekMatSharedPtr> ElmtJacCoef)
{
    int nelmt;
    int nelmtcoef, nelmtpnts, nelmtcoef0, nelmtpnts0;
 
    nelmtcoef = GetNcoeffs(0);
    nelmtpnts = GetTotPoints(0);
 
    Array<OneD, NekDouble> innarray(nelmtpnts, 0.0);
    Array<OneD, NekDouble> outarray(nelmtcoef, 0.0);
 
    Array<OneD, NekDouble> MatQ_data;
    Array<OneD, NekDouble> MatC_data;
 
    DNekMatSharedPtr tmpMatQ, tmpMatC;
 
    nelmtcoef0 = nelmtcoef;
    nelmtpnts0 = nelmtpnts;
 
    for (nelmt = 0; nelmt < (*m_exp).size(); ++nelmt)
    {
        nelmtcoef = GetNcoeffs(nelmt);
        nelmtpnts = GetTotPoints(nelmt);
 
        tmpMatQ = ElmtJacQuad[nelmt];
        tmpMatC = ElmtJacCoef[nelmt];
 
        MatQ_data = tmpMatQ->GetPtr();
        MatC_data = tmpMatC->GetPtr();
 
        if (nelmtcoef != nelmtcoef0)
        {
            outarray   = Array<OneD, NekDouble>(nelmtcoef, 0.0);
            nelmtcoef0 = nelmtcoef;
        }
 
        if (nelmtpnts != nelmtpnts0)
        {
            innarray   = Array<OneD, NekDouble>(nelmtpnts, 0.0);
            nelmtpnts0 = nelmtpnts;
        }
 
        for (int np = 0; np < nelmtcoef; np++)
        {
            Vmath::Vcopy(nelmtpnts, &MatQ_data[0] + np, nelmtcoef, &innarray[0],
                         1);
            (*m_exp)[nelmt]->DivideByQuadratureMetric(innarray, innarray);
            (*m_exp)[nelmt]->IProductWRTDerivBase(dir, innarray, outarray);
 
            Vmath::Vadd(nelmtcoef, &outarray[0], 1, &MatC_data[0] + np,
                        nelmtcoef, &MatC_data[0] + np, nelmtcoef);
        }
    }
}
 
void ExpList::AddRightIPTBaseMatrix(
    const Array<OneD, const DNekMatSharedPtr> ElmtJacQuad,
    Array<OneD, DNekMatSharedPtr> ElmtJacCoef)
{
    int nelmt;
    int nelmtcoef, nelmtpnts, nelmtcoef0, nelmtpnts0;
 
    nelmtcoef = GetNcoeffs(0);
    nelmtpnts = GetTotPoints(0);
 
    Array<OneD, NekDouble> innarray(nelmtpnts, 0.0);
    Array<OneD, NekDouble> outarray(nelmtcoef, 0.0);
 
    Array<OneD, NekDouble> MatQ_data;
    Array<OneD, NekDouble> MatC_data;
 
    DNekMatSharedPtr tmpMatQ, tmpMatC;
 
    nelmtcoef0 = nelmtcoef;
    nelmtpnts0 = nelmtpnts;
 
    for (nelmt = 0; nelmt < (*m_exp).size(); ++nelmt)
    {
        nelmtcoef = GetNcoeffs(nelmt);
        nelmtpnts = GetTotPoints(nelmt);
 
        tmpMatQ = ElmtJacQuad[nelmt];
        tmpMatC = ElmtJacCoef[nelmt];
 
        MatQ_data = tmpMatQ->GetPtr();
        MatC_data = tmpMatC->GetPtr();
 
        if (nelmtcoef != nelmtcoef0)
        {
            outarray   = Array<OneD, NekDouble>(nelmtcoef, 0.0);
            nelmtcoef0 = nelmtcoef;
        }
 
        if (nelmtpnts != nelmtpnts0)
        {
            innarray   = Array<OneD, NekDouble>(nelmtpnts, 0.0);
            nelmtpnts0 = nelmtpnts;
        }
 
        for (int np = 0; np < nelmtcoef; np++)
        {
            Vmath::Vcopy(nelmtpnts, &MatQ_data[0] + np, nelmtcoef, &innarray[0],
                         1);
            (*m_exp)[nelmt]->DivideByQuadratureMetric(innarray, innarray);
            (*m_exp)[nelmt]->IProductWRTBase(innarray, outarray);
 
            Vmath::Vadd(nelmtcoef, &outarray[0], 1, &MatC_data[0] + np,
                        nelmtcoef, &MatC_data[0] + np, nelmtcoef);
        }
    }
}
 
void ExpList::v_PhysGalerkinProjection1DScaled(
    const NekDouble scale, const Array<OneD, NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    int cnt, cnt1;
 
    cnt = cnt1 = 0;
 
    switch (m_expType)
    {
        case e2D:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                // get new points key
                int pt0  = (*m_exp)[i]->GetNumPoints(0);
                int pt1  = (*m_exp)[i]->GetNumPoints(1);
                int npt0 = (int)pt0 * scale;
                int npt1 = (int)pt1 * scale;
 
                LibUtilities::PointsKey newPointsKey0(
                    npt0, (*m_exp)[i]->GetPointsType(0));
                LibUtilities::PointsKey newPointsKey1(
                    npt1, (*m_exp)[i]->GetPointsType(1));
 
                // Project points;
                LibUtilities::PhysGalerkinProject2D(
                    newPointsKey0, newPointsKey1, &inarray[cnt],
                    (*m_exp)[i]->GetBasis(0)->GetPointsKey(),
                    (*m_exp)[i]->GetBasis(1)->GetPointsKey(), &outarray[cnt1]);
 
                cnt += npt0 * npt1;
                cnt1 += pt0 * pt1;
            }
        }
        break;
        case e3D:
        {
            for (int i = 0; i < GetExpSize(); ++i)
            {
                // get new points key
                int pt0  = (*m_exp)[i]->GetNumPoints(0);
                int pt1  = (*m_exp)[i]->GetNumPoints(1);
                int pt2  = (*m_exp)[i]->GetNumPoints(2);
                int npt0 = (int)pt0 * scale;
                int npt1 = (int)pt1 * scale;
                int npt2 = (int)pt2 * scale;
 
                LibUtilities::PointsKey newPointsKey0(
                    npt0, (*m_exp)[i]->GetPointsType(0));
                LibUtilities::PointsKey newPointsKey1(
                    npt1, (*m_exp)[i]->GetPointsType(1));
                LibUtilities::PointsKey newPointsKey2(
                    npt2, (*m_exp)[i]->GetPointsType(2));
 
                // Project points;
                LibUtilities::PhysGalerkinProject3D(
                    newPointsKey0, newPointsKey1, newPointsKey2, &inarray[cnt],
                    (*m_exp)[i]->GetBasis(0)->GetPointsKey(),
                    (*m_exp)[i]->GetBasis(1)->GetPointsKey(),
                    (*m_exp)[i]->GetBasis(2)->GetPointsKey(), &outarray[cnt1]);
 
                cnt += npt0 * npt1 * npt2;
                cnt1 += pt0 * pt1 * pt2;
            }
        }
        break;
        default:
        {
            NEKERROR(ErrorUtil::efatal, "not setup for this expansion");
        }
        break;
    }
}
 
const LocTraceToTraceMapSharedPtr &ExpList::v_GetLocTraceToTraceMap() const
{
    NEKERROR(ErrorUtil::efatal, "v_GetLocTraceToTraceMap not coded");
    return NullLocTraceToTraceMapSharedPtr;
}
 
} // namespace MultiRegions
} // namespace Nektar