PreconditionerLowEnergy.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: PreconditionerLowEnergy.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,
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// 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.
//
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// 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
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// DEALINGS IN THE SOFTWARE.
//
// Description: PreconditionerLowEnergy definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LocalRegions/MatrixKey.h>
#include <MultiRegions/GlobalLinSys.h>
#include <MultiRegions/GlobalLinSysIterativeStaticCond.h>
#include <MultiRegions/GlobalMatrixKey.h>
#include <MultiRegions/PreconditionerLowEnergy.h>
#include <cmath>
 
using namespace std;
 
namespace Nektar
{
using namespace LibUtilities;
 
namespace MultiRegions
{
/**
 * Registers the class with the Factory.
 */
string PreconditionerLowEnergy::className =
    GetPreconFactory().RegisterCreatorFunction("LowEnergyBlock",
                                               PreconditionerLowEnergy::create,
                                               "LowEnergy Preconditioning");
 
/**
 * @class PreconditionerLowEnergy
 *
 * This class implements low energy preconditioning for the conjugate
 * gradient matrix solver.
 */
 
PreconditionerLowEnergy::PreconditionerLowEnergy(
    const std::shared_ptr<GlobalLinSys> &plinsys,
    const AssemblyMapSharedPtr &pLocToGloMap)
    : Preconditioner(plinsys, pLocToGloMap)
{
}
 
void PreconditionerLowEnergy::v_InitObject()
{
    GlobalSysSolnType solvertype = m_locToGloMap.lock()->GetGlobalSysSolnType();
 
    ASSERTL0(solvertype == eIterativeStaticCond ||
                 solvertype == ePETScStaticCond,
             "Solver type not valid");
 
    std::shared_ptr<MultiRegions::ExpList> expList =
        ((m_linsys.lock())->GetLocMat()).lock();
 
    LocalRegions::ExpansionSharedPtr locExpansion;
 
    locExpansion = expList->GetExp(0);
 
    int nDim = locExpansion->GetShapeDimension();
 
    ASSERTL0(nDim == 3, "Preconditioner type only valid in 3D");
 
    // Set up block transformation matrix
    SetupBlockTransformationMatrix();
 
    // Sets up variable p mask
    CreateVariablePMask();
}
 
/**
 * \brief Construct the low energy preconditioner from
 * \f$\mathbf{S}_{2}\f$
 *
 * \f[\mathbf{M}^{-1}=\left[\begin{array}{ccc}
 *  Diag[(\mathbf{S_{2}})_{vv}] & & \\ & (\mathbf{S}_{2})_{eb} & \\ & &
 *  (\mathbf{S}_{2})_{fb} \end{array}\right] \f]
 *
 * where \f$\mathbf{R}\f$ is the transformation matrix and
 * \f$\mathbf{S}_{2}\f$ the Schur complement of the modified basis,
 * given by
 *
 * \f[\mathbf{S}_{2}=\mathbf{R}\mathbf{S}_{1}\mathbf{R}^{T}\f]
 *
 * where \f$\mathbf{S}_{1}\f$ is the local schur complement matrix for
 * each element.
 */
void PreconditionerLowEnergy::v_BuildPreconditioner()
{
    std::shared_ptr<MultiRegions::ExpList> expList =
        ((m_linsys.lock())->GetLocMat()).lock();
    LocalRegions::Expansion3DSharedPtr locExpansion;
    GlobalLinSysKey linSysKey = (m_linsys.lock())->GetKey();
 
    LibUtilities::CommSharedPtr vComm = expList->GetComm()->GetSpaceComm();
 
    int i, j, k;
    int nVerts, nEdges, nFaces;
    int eid, fid, n, cnt, nmodes, nedgemodes, nfacemodes;
    int nedgemodesloc;
    NekDouble zero = 0.0;
 
    int vMap1, vMap2, sign1, sign2;
    int m, v, eMap1, eMap2, fMap1, fMap2;
    int offset, globalrow, globalcol, nCoeffs;
 
    // Periodic information
    PeriodicMap periodicVerts;
    PeriodicMap periodicEdges;
    PeriodicMap periodicFaces;
    expList->GetPeriodicEntities(periodicVerts, periodicEdges, periodicFaces);
 
    // matrix storage
    MatrixStorage storage       = eFULL;
    MatrixStorage vertstorage   = eDIAGONAL;
    MatrixStorage blkmatStorage = eDIAGONAL;
 
    // local element static condensed matrices
    DNekScalBlkMatSharedPtr loc_mat;
    DNekScalMatSharedPtr bnd_mat;
 
    DNekMatSharedPtr pRSRT;
 
    DNekMat RS;
    DNekMat RSRT;
 
    auto asmMap = m_locToGloMap.lock();
 
    int nDirBnd      = asmMap->GetNumGlobalDirBndCoeffs();
    int nNonDirVerts = asmMap->GetNumNonDirVertexModes();
 
    // Vertex, edge and face preconditioner matrices
    DNekMatSharedPtr VertBlk = MemoryManager<DNekMat>::AllocateSharedPtr(
        nNonDirVerts, nNonDirVerts, zero, vertstorage);
 
    Array<OneD, NekDouble> vertArray(nNonDirVerts, 0.0);
    Array<OneD, long> VertBlockToUniversalMap(nNonDirVerts, -1);
 
    // maps for different element types
    int n_exp          = expList->GetNumElmts();
    int nNonDirEdgeIDs = asmMap->GetNumNonDirEdges();
    int nNonDirFaceIDs = asmMap->GetNumNonDirFaces();
 
    set<int> edgeDirMap;
    set<int> faceDirMap;
    map<int, int> uniqueEdgeMap;
    map<int, int> uniqueFaceMap;
 
    // this should be of size total number of local edges + faces
    Array<OneD, int> modeoffset(1 + nNonDirEdgeIDs + nNonDirFaceIDs, 0);
    Array<OneD, int> globaloffset(1 + nNonDirEdgeIDs + nNonDirFaceIDs, 0);
 
    const Array<OneD, const ExpListSharedPtr> &bndCondExp =
        expList->GetBndCondExpansions();
    LocalRegions::Expansion2DSharedPtr bndCondFaceExp;
    const Array<OneD, const SpatialDomains::BoundaryConditionShPtr>
        &bndConditions = expList->GetBndConditions();
 
    int meshVertId;
    int meshEdgeId;
    int meshFaceId;
 
    const Array<OneD, const int> &extradiredges = asmMap->GetExtraDirEdges();
    for (i = 0; i < extradiredges.size(); ++i)
    {
        meshEdgeId = extradiredges[i];
        edgeDirMap.insert(meshEdgeId);
    }
 
    // Determine which boundary edges and faces have dirichlet values
    for (i = 0; i < bndCondExp.size(); i++)
    {
        cnt = 0;
        for (j = 0; j < bndCondExp[i]->GetNumElmts(); j++)
        {
            bndCondFaceExp =
                std::dynamic_pointer_cast<LocalRegions::Expansion2D>(
                    bndCondExp[i]->GetExp(j));
            if (bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eDirichlet)
            {
                for (k = 0; k < bndCondFaceExp->GetNtraces(); k++)
                {
                    meshEdgeId = bndCondFaceExp->GetGeom()->GetEid(k);
                    if (edgeDirMap.count(meshEdgeId) == 0)
                    {
                        edgeDirMap.insert(meshEdgeId);
                    }
                }
                meshFaceId = bndCondFaceExp->GetGeom()->GetGlobalID();
                faceDirMap.insert(meshFaceId);
            }
        }
    }
 
    int dof               = 0;
    int maxFaceDof        = 0;
    int maxEdgeDof        = 0;
    int nlocalNonDirEdges = 0;
    int nlocalNonDirFaces = 0;
    int ntotalentries     = 0;
 
    map<int, int> EdgeSize;
    map<int, int> FaceSize;
    map<int, pair<int, int>> FaceModes;
 
    /// -  Count  edges, face and add up min edges and min face sizes
    for (n = 0; n < n_exp; ++n)
    {
        locExpansion = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
 
        nEdges = locExpansion->GetNedges();
        for (j = 0; j < nEdges; ++j)
        {
            int nEdgeInteriorCoeffs = locExpansion->GetEdgeNcoeffs(j) - 2;
            meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()
                             ->GetGeom3D()
                             ->GetEid(j);
            if (EdgeSize.count(meshEdgeId) == 0)
            {
                EdgeSize[meshEdgeId] = nEdgeInteriorCoeffs;
            }
            else
            {
                EdgeSize[meshEdgeId] =
                    min(EdgeSize[meshEdgeId], nEdgeInteriorCoeffs);
            }
        }
 
        nFaces = locExpansion->GetNtraces();
        for (j = 0; j < nFaces; ++j)
        {
            int nFaceInteriorCoeffs = locExpansion->GetTraceIntNcoeffs(j);
            meshFaceId              = locExpansion->GetGeom3D()->GetFid(j);
 
            if (FaceSize.count(meshFaceId) == 0)
            {
                FaceSize[meshFaceId] = nFaceInteriorCoeffs;
 
                int m0, m1;
                locExpansion->GetTraceNumModes(j, m0, m1,
                                               locExpansion->GetTraceOrient(j));
                FaceModes[meshFaceId] = pair<int, int>(m0, m1);
            }
            else
            {
                if (nFaceInteriorCoeffs < FaceSize[meshFaceId])
                {
                    FaceSize[meshFaceId] = nFaceInteriorCoeffs;
                    int m0, m1;
                    locExpansion->GetTraceNumModes(
                        j, m0, m1, locExpansion->GetTraceOrient(j));
                    FaceModes[meshFaceId] = pair<int, int>(m0, m1);
                }
            }
        }
    }
 
    bool verbose = expList->GetSession()->DefinesCmdLineArgument("verbose");
 
    // For parallel runs need to check have minimum of edges and faces over
    // partition boundaries
    if (vComm->GetSize() > 1)
    {
        int EdgeSizeLen = EdgeSize.size();
        int FaceSizeLen = FaceSize.size();
        Array<OneD, long> FacetMap(EdgeSizeLen + FaceSizeLen, -1);
        Array<OneD, NekDouble> FacetLen(EdgeSizeLen + FaceSizeLen, -1);
 
        map<int, int>::iterator it;
 
        cnt       = 0;
        int maxid = 0;
        for (it = EdgeSize.begin(); it != EdgeSize.end(); ++it, ++cnt)
        {
            FacetMap[cnt] = it->first;
            maxid         = max(it->first, maxid);
            FacetLen[cnt] = it->second;
        }
        maxid++;
 
        vComm->AllReduce(maxid, ReduceMax);
 
        for (it = FaceSize.begin(); it != FaceSize.end(); ++it, ++cnt)
        {
            FacetMap[cnt] = it->first + maxid;
            FacetLen[cnt] = it->second;
        }
 
        // Exchange vertex data over different processes
        Gs::gs_data *tmp = Gs::Init(FacetMap, vComm, verbose);
        Gs::Gather(FacetLen, Gs::gs_min, tmp);
        Gs::Free(tmp);
 
        cnt = 0;
        for (it = EdgeSize.begin(); it != EdgeSize.end(); ++it, ++cnt)
        {
            it->second = (int)FacetLen[cnt];
        }
 
        for (it = FaceSize.begin(); it != FaceSize.end(); ++it, ++cnt)
        {
            it->second = (int)FacetLen[cnt];
        }
    }
 
    // Loop over all the elements in the domain and compute total edge
    // DOF and set up unique ordering.
    map<int, int> nblks;
    int matrixlocation = 0;
 
    // First do periodic edges
    for (auto &pIt : periodicEdges)
    {
        meshEdgeId = pIt.first;
 
        if (edgeDirMap.count(meshEdgeId) == 0)
        {
            dof = EdgeSize[meshEdgeId];
            if (uniqueEdgeMap.count(meshEdgeId) == 0 && dof > 0)
            {
                bool SetUpNewEdge = true;
 
                for (i = 0; i < pIt.second.size(); ++i)
                {
                    if (!pIt.second[i].isLocal)
                    {
                        continue;
                    }
 
                    int meshEdgeId2 = pIt.second[i].id;
                    if (edgeDirMap.count(meshEdgeId2) == 0)
                    {
                        if (uniqueEdgeMap.count(meshEdgeId2) != 0)
                        {
                            // set unique map to same location
                            uniqueEdgeMap[meshEdgeId] =
                                uniqueEdgeMap[meshEdgeId2];
                            SetUpNewEdge = false;
                        }
                    }
                    else
                    {
                        edgeDirMap.insert(meshEdgeId);
                        SetUpNewEdge = false;
                    }
                }
 
                if (SetUpNewEdge)
                {
                    uniqueEdgeMap[meshEdgeId] = matrixlocation;
                    globaloffset[matrixlocation] += ntotalentries;
                    modeoffset[matrixlocation] = dof * dof;
                    ntotalentries += dof * dof;
                    nblks[matrixlocation++] = dof;
                }
            }
        }
    }
 
    for (cnt = n = 0; n < n_exp; ++n)
    {
        locExpansion = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
 
        for (j = 0; j < locExpansion->GetNedges(); ++j)
        {
            meshEdgeId = locExpansion->GetGeom()->GetEid(j);
            dof        = EdgeSize[meshEdgeId];
            maxEdgeDof = (dof > maxEdgeDof ? dof : maxEdgeDof);
 
            if (edgeDirMap.count(meshEdgeId) == 0)
            {
                if (uniqueEdgeMap.count(meshEdgeId) == 0 && dof > 0)
 
                {
                    uniqueEdgeMap[meshEdgeId] = matrixlocation;
 
                    globaloffset[matrixlocation] += ntotalentries;
                    modeoffset[matrixlocation] = dof * dof;
                    ntotalentries += dof * dof;
                    nblks[matrixlocation++] = dof;
                }
                nlocalNonDirEdges += dof * dof;
            }
        }
    }
 
    // Loop over all the elements in the domain and compute max face
    // DOF. Reduce across all processes to get universal maximum.
    // - Periodic faces
    for (auto &pIt : periodicFaces)
    {
        meshFaceId = pIt.first;
 
        if (faceDirMap.count(meshFaceId) == 0)
        {
            dof = FaceSize[meshFaceId];
 
            if (uniqueFaceMap.count(meshFaceId) == 0 && dof > 0)
            {
                bool SetUpNewFace = true;
 
                if (pIt.second[0].isLocal)
                {
                    int meshFaceId2 = pIt.second[0].id;
 
                    if (faceDirMap.count(meshFaceId2) == 0)
                    {
                        if (uniqueFaceMap.count(meshFaceId2) != 0)
                        {
                            // set unique map to same location
                            uniqueFaceMap[meshFaceId] =
                                uniqueFaceMap[meshFaceId2];
                            SetUpNewFace = false;
                        }
                    }
                    else // set face to be a Dirichlet face
                    {
                        faceDirMap.insert(meshFaceId);
                        SetUpNewFace = false;
                    }
                }
 
                if (SetUpNewFace)
                {
                    uniqueFaceMap[meshFaceId] = matrixlocation;
 
                    modeoffset[matrixlocation] = dof * dof;
                    globaloffset[matrixlocation] += ntotalentries;
                    ntotalentries += dof * dof;
                    nblks[matrixlocation++] = dof;
                }
            }
        }
    }
 
    for (cnt = n = 0; n < n_exp; ++n)
    {
        locExpansion = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
 
        for (j = 0; j < locExpansion->GetNtraces(); ++j)
        {
            meshFaceId = locExpansion->GetGeom()->GetFid(j);
 
            dof        = FaceSize[meshFaceId];
            maxFaceDof = (dof > maxFaceDof ? dof : maxFaceDof);
 
            if (faceDirMap.count(meshFaceId) == 0)
            {
                if (uniqueFaceMap.count(meshFaceId) == 0 && dof > 0)
                {
                    uniqueFaceMap[meshFaceId]  = matrixlocation;
                    modeoffset[matrixlocation] = dof * dof;
                    globaloffset[matrixlocation] += ntotalentries;
                    ntotalentries += dof * dof;
                    nblks[matrixlocation++] = dof;
                }
                nlocalNonDirFaces += dof * dof;
            }
        }
    }
 
    vComm->AllReduce(maxEdgeDof, ReduceMax);
    vComm->AllReduce(maxFaceDof, ReduceMax);
 
    // Allocate arrays for block to universal map (number of expansions * p^2)
    Array<OneD, long> BlockToUniversalMap(ntotalentries, -1);
    Array<OneD, int> localToGlobalMatrixMap(
        nlocalNonDirEdges + nlocalNonDirFaces, -1);
 
    // Allocate arrays to store matrices (number of expansions * p^2)
    Array<OneD, NekDouble> BlockArray(nlocalNonDirEdges + nlocalNonDirFaces,
                                      0.0);
 
    int matrixoffset = 0;
    int vGlobal;
    int uniEdgeOffset = 0;
 
    // Need to obtain a fixed offset for the universal number
    // of the faces which come after the edge numbering
    for (n = 0; n < n_exp; ++n)
    {
        for (j = 0; j < locExpansion->GetNedges(); ++j)
        {
            meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()
                             ->GetGeom3D()
                             ->GetEid(j);
 
            uniEdgeOffset = max(meshEdgeId, uniEdgeOffset);
        }
    }
    uniEdgeOffset++;
 
    vComm->AllReduce(uniEdgeOffset, ReduceMax);
    uniEdgeOffset = uniEdgeOffset * maxEdgeDof * maxEdgeDof;
 
    for (n = 0; n < n_exp; ++n)
    {
        locExpansion = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
 
        // loop over the edges of the expansion
        for (j = 0; j < locExpansion->GetNedges(); ++j)
        {
            // get mesh edge id
            meshEdgeId = locExpansion->GetGeom()->GetEid(j);
 
            nedgemodes = EdgeSize[meshEdgeId];
 
            if (edgeDirMap.count(meshEdgeId) == 0 && nedgemodes > 0)
            {
                // Determine the Global edge offset
                int edgeOffset = globaloffset[uniqueEdgeMap[meshEdgeId]];
 
                // Determine a universal map offset
                int uniOffset = meshEdgeId;
                auto pIt      = periodicEdges.find(meshEdgeId);
                if (pIt != periodicEdges.end())
                {
                    for (int l = 0; l < pIt->second.size(); ++l)
                    {
                        uniOffset = min(uniOffset, pIt->second[l].id);
                    }
                }
                uniOffset = uniOffset * maxEdgeDof * maxEdgeDof;
 
                for (k = 0; k < nedgemodes * nedgemodes; ++k)
                {
                    vGlobal                                  = edgeOffset + k;
                    localToGlobalMatrixMap[matrixoffset + k] = vGlobal;
                    BlockToUniversalMap[vGlobal] = uniOffset + k + 1;
                }
                matrixoffset += nedgemodes * nedgemodes;
            }
        }
 
        Array<OneD, unsigned int> faceInteriorMap;
        Array<OneD, int> faceInteriorSign;
        // loop over the faces of the expansion
        for (j = 0; j < locExpansion->GetNtraces(); ++j)
        {
            // get mesh face id
            meshFaceId = locExpansion->GetGeom()->GetFid(j);
 
            nfacemodes = FaceSize[meshFaceId];
 
            // Check if face has dirichlet values
            if (faceDirMap.count(meshFaceId) == 0 && nfacemodes > 0)
            {
                // Determine the Global edge offset
                int faceOffset = globaloffset[uniqueFaceMap[meshFaceId]];
                // Determine a universal map offset
                int uniOffset = meshFaceId;
                // use minimum face edge when periodic
                auto pIt = periodicFaces.find(meshFaceId);
                if (pIt != periodicFaces.end())
                {
                    uniOffset = min(uniOffset, pIt->second[0].id);
                }
                uniOffset = uniOffset * maxFaceDof * maxFaceDof;
 
                for (k = 0; k < nfacemodes * nfacemodes; ++k)
                {
                    vGlobal = faceOffset + k;
 
                    localToGlobalMatrixMap[matrixoffset + k] = vGlobal;
 
                    BlockToUniversalMap[vGlobal] =
                        uniOffset + uniEdgeOffset + k + 1;
                }
                matrixoffset += nfacemodes * nfacemodes;
            }
        }
    }
 
    matrixoffset = 0;
 
    map<int, int>::iterator it;
    Array<OneD, unsigned int> n_blks(nblks.size() + 1);
    n_blks[0] = nNonDirVerts;
    for (i = 1, it = nblks.begin(); it != nblks.end(); ++it)
    {
        n_blks[i++] = it->second;
    }
 
    m_BlkMat = MemoryManager<DNekBlkMat>::AllocateSharedPtr(n_blks, n_blks,
                                                            blkmatStorage);
 
    // Here we loop over the expansion and build the block low energy
    // preconditioner as well as the block versions of the transformation
    // matrices.
    for (cnt = n = 0; n < n_exp; ++n)
    {
        locExpansion = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
        nCoeffs      = locExpansion->NumBndryCoeffs();
 
        // Get correct transformation matrix for element type
        DNekMat &R = (*m_RBlk->GetBlock(n, n));
 
        pRSRT = MemoryManager<DNekMat>::AllocateSharedPtr(nCoeffs, nCoeffs,
                                                          zero, storage);
        RSRT  = (*pRSRT);
 
        nVerts = locExpansion->GetGeom()->GetNumVerts();
        nEdges = locExpansion->GetGeom()->GetNumEdges();
        nFaces = locExpansion->GetGeom()->GetNumFaces();
 
        // Get statically condensed matrix
        loc_mat = (m_linsys.lock())->GetStaticCondBlock(n);
 
        // Extract boundary block (elemental S1)
        bnd_mat = loc_mat->GetBlock(0, 0);
 
        // offset by number of rows
        offset = bnd_mat->GetRows();
 
        DNekScalMat &S = (*bnd_mat);
 
        DNekMat Sloc(nCoeffs, nCoeffs);
 
        // For variable p we need to just use the active modes
        NekDouble val;
 
        for (int i = 0; i < nCoeffs; ++i)
        {
            for (int j = 0; j < nCoeffs; ++j)
            {
                val = S(i, j) * m_variablePmask[cnt + i] *
                      m_variablePmask[cnt + j];
                Sloc.SetValue(i, j, val);
            }
        }
 
        // Calculate R*S*trans(R)
        RSRT = R * Sloc * Transpose(R);
 
        // loop over vertices of the element and return the vertex map
        // for each vertex
        for (v = 0; v < nVerts; ++v)
        {
            vMap1 = locExpansion->GetVertexMap(v);
 
            // Get vertex map
            globalrow = asmMap->GetLocalToGlobalBndMap(cnt + vMap1) - nDirBnd;
 
            if (globalrow >= 0)
            {
                for (m = 0; m < nVerts; ++m)
                {
                    vMap2 = locExpansion->GetVertexMap(m);
 
                    // global matrix location (without offset due to
                    // dirichlet values)
                    globalcol =
                        asmMap->GetLocalToGlobalBndMap(cnt + vMap2) - nDirBnd;
 
                    // offset for dirichlet conditions
                    if (globalcol == globalrow)
                    {
                        // modal connectivity between elements
                        sign1 = asmMap->GetLocalToGlobalBndSign(cnt + vMap1);
                        sign2 = asmMap->GetLocalToGlobalBndSign(cnt + vMap2);
 
                        vertArray[globalrow] +=
                            sign1 * sign2 * RSRT(vMap1, vMap2);
 
                        meshVertId = locExpansion->GetGeom()->GetVid(v);
 
                        auto pIt = periodicVerts.find(meshVertId);
                        if (pIt != periodicVerts.end())
                        {
                            for (k = 0; k < pIt->second.size(); ++k)
                            {
                                meshVertId = min(meshVertId, pIt->second[k].id);
                            }
                        }
 
                        VertBlockToUniversalMap[globalrow] = meshVertId + 1;
                    }
                }
            }
        }
 
        // loop over edges of the element and return the edge map
        for (eid = 0; eid < nEdges; ++eid)
        {
            meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()
                             ->GetGeom3D()
                             ->GetEid(eid);
 
            nedgemodes = EdgeSize[meshEdgeId];
            if (nedgemodes)
            {
                nedgemodesloc = locExpansion->GetEdgeNcoeffs(eid) - 2;
                DNekMatSharedPtr m_locMat =
                    MemoryManager<DNekMat>::AllocateSharedPtr(
                        nedgemodes, nedgemodes, zero, storage);
 
                Array<OneD, unsigned int> edgemodearray =
                    locExpansion->GetEdgeInverseBoundaryMap(eid);
 
                if (edgeDirMap.count(meshEdgeId) == 0)
                {
                    for (v = 0; v < nedgemodesloc; ++v)
                    {
                        eMap1 = edgemodearray[v];
                        sign1 = asmMap->GetLocalToGlobalBndSign(cnt + eMap1);
 
                        if (sign1 == 0)
                        {
                            continue;
                        }
 
                        for (m = 0; m < nedgemodesloc; ++m)
                        {
                            eMap2 = edgemodearray[m];
 
                            // modal connectivity between elements
                            sign2 =
                                asmMap->GetLocalToGlobalBndSign(cnt + eMap2);
 
                            NekDouble globalEdgeValue =
                                sign1 * sign2 * RSRT(eMap1, eMap2);
 
                            if (sign2 != 0)
                            {
                                // if(eMap1 == eMap2)
                                BlockArray[matrixoffset + v * nedgemodes + m] =
                                    globalEdgeValue;
                            }
                        }
                    }
                    matrixoffset += nedgemodes * nedgemodes;
                }
            }
        }
 
        // loop over faces of the element and return the face map
        for (fid = 0; fid < nFaces; ++fid)
        {
            meshFaceId = locExpansion->as<LocalRegions::Expansion3D>()
                             ->GetGeom3D()
                             ->GetFid(fid);
 
            nfacemodes = FaceSize[meshFaceId];
            if (nfacemodes > 0)
            {
                DNekMatSharedPtr m_locMat =
                    MemoryManager<DNekMat>::AllocateSharedPtr(
                        nfacemodes, nfacemodes, zero, storage);
 
                if (faceDirMap.count(meshFaceId) == 0)
                {
                    Array<OneD, unsigned int> facemodearray;
                    StdRegions::Orientation faceOrient =
                        locExpansion->GetTraceOrient(fid);
 
                    auto pIt = periodicFaces.find(meshFaceId);
                    if (pIt != periodicFaces.end())
                    {
                        if (meshFaceId == min(meshFaceId, pIt->second[0].id))
                        {
                            faceOrient = DeterminePeriodicFaceOrient(
                                faceOrient, pIt->second[0].orient);
                        }
                    }
 
                    facemodearray = locExpansion->GetTraceInverseBoundaryMap(
                        fid, faceOrient, FaceModes[meshFaceId].first,
                        FaceModes[meshFaceId].second);
 
                    for (v = 0; v < nfacemodes; ++v)
                    {
                        fMap1 = facemodearray[v];
 
                        sign1 = asmMap->GetLocalToGlobalBndSign(cnt + fMap1);
 
                        ASSERTL1(sign1 != 0,
                                 "Something is wrong since we "
                                 "shoudl only be extracting modes for "
                                 "lowest order expansion");
 
                        for (m = 0; m < nfacemodes; ++m)
                        {
                            fMap2 = facemodearray[m];
 
                            // modal connectivity between elements
                            sign2 =
                                asmMap->GetLocalToGlobalBndSign(cnt + fMap2);
 
                            ASSERTL1(sign2 != 0,
                                     "Something is wrong since "
                                     "we shoudl only be extracting modes for "
                                     "lowest order expansion");
 
                            // Get the face-face value from the
                            // low energy matrix (S2)
                            NekDouble globalFaceValue =
                                sign1 * sign2 * RSRT(fMap1, fMap2);
 
                            // local face value to global face value
                            // if(fMap1 == fMap2)
                            BlockArray[matrixoffset + v * nfacemodes + m] =
                                globalFaceValue;
                        }
                    }
                    matrixoffset += nfacemodes * nfacemodes;
                }
            }
        }
 
        // offset for the expansion
        cnt += nCoeffs;
    }
 
    // Exchange vertex data over different processes
    Gs::gs_data *tmp = Gs::Init(VertBlockToUniversalMap, vComm, verbose);
    Gs::Gather(vertArray, Gs::gs_add, tmp);
    Gs::Free(tmp);
 
    Array<OneD, NekDouble> GlobalBlock(ntotalentries, 0.0);
    if (ntotalentries)
    {
        // Assemble edge matrices of each process
        Vmath::Assmb(BlockArray.size(), BlockArray, localToGlobalMatrixMap,
                     GlobalBlock);
    }
 
    // Exchange edge & face data over different processes
    Gs::gs_data *tmp1 = Gs::Init(BlockToUniversalMap, vComm, verbose);
    Gs::Gather(GlobalBlock, Gs::gs_add, tmp1);
    Gs::Free(tmp1);
 
    // Populate vertex block
    for (int i = 0; i < nNonDirVerts; ++i)
    {
        VertBlk->SetValue(i, i, 1.0 / vertArray[i]);
    }
 
    // Set the first block to be the diagonal of the vertex space
    m_BlkMat->SetBlock(0, 0, VertBlk);
 
    // Build the edge and face matrices from the vector
    DNekMatSharedPtr gmat;
 
    offset = 0;
    // -1 since we ignore vert block
    for (int loc = 0; loc < n_blks.size() - 1; ++loc)
    {
        nmodes = n_blks[1 + loc];
        gmat   = MemoryManager<DNekMat>::AllocateSharedPtr(nmodes, nmodes, zero,
                                                           storage);
 
        for (v = 0; v < nmodes; ++v)
        {
            for (m = 0; m < nmodes; ++m)
            {
                NekDouble Value = GlobalBlock[offset + v * nmodes + m];
                gmat->SetValue(v, m, Value);
            }
        }
        m_BlkMat->SetBlock(1 + loc, 1 + loc, gmat);
        offset += modeoffset[loc];
    }
 
    // invert blocks.
    int totblks = m_BlkMat->GetNumberOfBlockRows();
    for (i = 1; i < totblks; ++i)
    {
        unsigned int nmodes = m_BlkMat->GetNumberOfRowsInBlockRow(i);
        if (nmodes)
        {
            DNekMatSharedPtr tmp_mat =
                MemoryManager<DNekMat>::AllocateSharedPtr(nmodes, nmodes, zero,
                                                          storage);
 
            tmp_mat = m_BlkMat->GetBlock(i, i);
            tmp_mat->Invert();
 
            m_BlkMat->SetBlock(i, i, tmp_mat);
        }
    }
}
 
/**
 * Apply the low energy preconditioner during the conjugate gradient
 * routine
 */
void PreconditionerLowEnergy::v_DoPreconditioner(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput,
    const bool &isLocal)
 
{
    ASSERTL0(isLocal == false, "PreconditionerLowEnergy is only currently "
                               "set up for Global iteratives sovles");
    int nDir      = m_locToGloMap.lock()->GetNumGlobalDirBndCoeffs();
    int nGlobal   = m_locToGloMap.lock()->GetNumGlobalBndCoeffs();
    int nNonDir   = nGlobal - nDir;
    DNekBlkMat &M = (*m_BlkMat);
 
    NekVector<NekDouble> r(nNonDir, pInput, eWrapper);
 
    NekVector<NekDouble> z(nNonDir, pOutput, eWrapper);
 
    z = M * r;
}
 
/**
 * Set a block transformation matrices for each element type. These are
 * needed in routines that transform the schur complement matrix to and
 * from the low energy basis.
 */
void PreconditionerLowEnergy::SetupBlockTransformationMatrix(void)
{
    std::shared_ptr<MultiRegions::ExpList> expList =
        ((m_linsys.lock())->GetLocMat()).lock();
    LocalRegions::Expansion3DSharedPtr locExp;
    LocalRegions::Expansion3DSharedPtr locExpSav;
    map<int, int> EdgeSize;
 
    int n;
 
    std::map<ShapeType, DNekScalMatSharedPtr> maxRmat;
    map<ShapeType, LocalRegions::Expansion3DSharedPtr> maxElmt;
    map<ShapeType, Array<OneD, unsigned int>> vertMapMaxR;
    map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> edgeMapMaxR;
 
    // Sets up reference element and builds transformation matrix for
    // maximum polynomial order meshes
    SetUpReferenceElements(maxRmat, maxElmt, vertMapMaxR, edgeMapMaxR);
 
    const Array<OneD, const unsigned int> &nbdry_size =
        m_locToGloMap.lock()->GetNumLocalBndCoeffsPerPatch();
 
    int n_exp = expList->GetNumElmts();
 
    MatrixStorage blkmatStorage = eDIAGONAL;
 
    // Variants of R matrices required for low energy preconditioning
    m_RBlk = MemoryManager<DNekBlkMat>::AllocateSharedPtr(
        nbdry_size, nbdry_size, blkmatStorage);
    m_InvRBlk = MemoryManager<DNekBlkMat>::AllocateSharedPtr(
        nbdry_size, nbdry_size, blkmatStorage);
 
    DNekMatSharedPtr rmat, invrmat;
 
    int offset = 0;
 
    // Set up transformation matrices whilst checking to see if
    // consecutive matrices are the same and if so reuse the
    // matrices and store how many consecutive offsets there
    // are
    for (n = 0; n < n_exp; ++n)
    {
        locExp = expList->GetExp(n)->as<LocalRegions::Expansion3D>();
 
        ShapeType eltype = locExp->DetShapeType();
 
        int nbndcoeffs = locExp->NumBndryCoeffs();
 
        if (m_sameBlock.size() == 0)
        {
            rmat = ExtractLocMat(locExp, maxRmat[eltype], maxElmt[eltype],
                                 vertMapMaxR[eltype], edgeMapMaxR[eltype]);
            // Block R matrix
            m_RBlk->SetBlock(n, n, rmat);
 
            invrmat = MemoryManager<DNekMat>::AllocateSharedPtr(*rmat);
            invrmat->Invert();
 
            // Block inverse R matrix
            m_InvRBlk->SetBlock(n, n, invrmat);
 
            m_sameBlock.push_back(pair<int, int>(1, nbndcoeffs));
            locExpSav = locExp;
        }
        else
        {
            bool reuse = true;
 
            // check to see if same as previous matrix and
            // reuse if we can
            for (int i = 0; i < 3; ++i)
            {
                if (locExpSav->GetBasis(i) != locExp->GetBasis(i))
                {
                    reuse = false;
                    break;
                }
            }
 
            if (reuse)
            {
                m_RBlk->SetBlock(n, n, rmat);
                m_InvRBlk->SetBlock(n, n, invrmat);
 
                m_sameBlock[offset] =
                    (pair<int, int>(m_sameBlock[offset].first + 1, nbndcoeffs));
            }
            else
            {
                rmat = ExtractLocMat(locExp, maxRmat[eltype], maxElmt[eltype],
                                     vertMapMaxR[eltype], edgeMapMaxR[eltype]);
 
                // Block R matrix
                m_RBlk->SetBlock(n, n, rmat);
 
                invrmat = MemoryManager<DNekMat>::AllocateSharedPtr(*rmat);
                invrmat->Invert();
                // Block inverse R matrix
                m_InvRBlk->SetBlock(n, n, invrmat);
 
                m_sameBlock.push_back(pair<int, int>(1, nbndcoeffs));
                offset++;
                locExpSav = locExp;
            }
        }
    }
}
 
/**
 * \brief Transform the basis  vector to low energy space
 *
 * As the conjugate gradient system is solved for the low energy basis,
 * the solution vector \f$\mathbf{x}\f$ must be transformed to the low
 * energy basis i.e. \f$\overline{\mathbf{x}}=\mathbf{R}\mathbf{x}\f$.
 */
void PreconditionerLowEnergy::v_DoTransformBasisToLowEnergy(
    Array<OneD, NekDouble> &pInOut)
{
    int nLocBndDofs = m_locToGloMap.lock()->GetNumLocalBndCoeffs();
 
    // Block transformation matrix
    DNekBlkMat &R = *m_RBlk;
 
    Array<OneD, NekDouble> pLocalIn(nLocBndDofs, pInOut.get());
 
    // Apply mask in case of variable P
    Vmath::Vmul(nLocBndDofs, pLocalIn, 1, m_variablePmask, 1, pLocalIn, 1);
 
    // Multiply by the block transformation matrix
    int cnt  = 0;
    int cnt1 = 0;
    for (int i = 0; i < m_sameBlock.size(); ++i)
    {
        int nexp       = m_sameBlock[i].first;
        int nbndcoeffs = m_sameBlock[i].second;
        Blas::Dgemm('N', 'N', nbndcoeffs, nexp, nbndcoeffs, 1.0,
                    &(R.GetBlock(cnt1, cnt1)->GetPtr()[0]), nbndcoeffs,
                    pLocalIn.get() + cnt, nbndcoeffs, 0.0, pInOut.get() + cnt,
                    nbndcoeffs);
        cnt += nbndcoeffs * nexp;
        cnt1 += nexp;
    }
}
 
/**
 * \brief transform the solution coeffiicents from low energy
 * back to the original coefficient space.
 *
 * After the conjugate gradient routine the output vector is in the low
 * energy basis and must be trasnformed back to the original basis in
 * order to get the correct solution out. the solution vector
 * i.e. \f$\mathbf{x}=\mathbf{R^{T}}\mathbf{\overline{x}}\f$.
 */
void PreconditionerLowEnergy::v_DoTransformCoeffsFromLowEnergy(
    Array<OneD, NekDouble> &pInOut)
{
    int nLocBndDofs = m_locToGloMap.lock()->GetNumLocalBndCoeffs();
 
    ASSERTL1(pInOut.size() >= nLocBndDofs,
             "Output array is not greater than the nLocBndDofs");
 
    // Block transposed transformation matrix
    DNekBlkMat &R = *m_RBlk;
 
    Array<OneD, NekDouble> pLocalIn(nLocBndDofs, pInOut.get());
 
    // Multiply by the transpose of block transformation matrix
    int cnt  = 0;
    int cnt1 = 0;
    for (int i = 0; i < m_sameBlock.size(); ++i)
    {
        int nexp       = m_sameBlock[i].first;
        int nbndcoeffs = m_sameBlock[i].second;
        Blas::Dgemm('T', 'N', nbndcoeffs, nexp, nbndcoeffs, 1.0,
                    &(R.GetBlock(cnt1, cnt1)->GetPtr()[0]), nbndcoeffs,
                    pLocalIn.get() + cnt, nbndcoeffs, 0.0, pInOut.get() + cnt,
                    nbndcoeffs);
        cnt += nbndcoeffs * nexp;
        cnt1 += nexp;
    }
 
    Vmath::Vmul(nLocBndDofs, pInOut, 1, m_variablePmask, 1, pInOut, 1);
}
 
/**
 * \brief Multiply by the block inverse transformation matrix
 * This transforms the bassi from Low Energy to original basis
 *
 * Note; not typically required
 */
 
void PreconditionerLowEnergy::v_DoTransformBasisFromLowEnergy(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput)
{
    int nLocBndDofs = m_locToGloMap.lock()->GetNumLocalBndCoeffs();
 
    ASSERTL1(pInput.size() >= nLocBndDofs,
             "Input array is smaller than nLocBndDofs");
    ASSERTL1(pOutput.size() >= nLocBndDofs,
             "Output array is smaller than nLocBndDofs");
 
    // Block inverse transformation matrix
    DNekBlkMat &invR = *m_InvRBlk;
 
    Array<OneD, NekDouble> pLocalIn(nLocBndDofs, pInput.get());
 
    // Multiply by the inverse transformation matrix
    int cnt  = 0;
    int cnt1 = 0;
    for (int i = 0; i < m_sameBlock.size(); ++i)
    {
        int nexp       = m_sameBlock[i].first;
        int nbndcoeffs = m_sameBlock[i].second;
        Blas::Dgemm('N', 'N', nbndcoeffs, nexp, nbndcoeffs, 1.0,
                    &(invR.GetBlock(cnt1, cnt1)->GetPtr()[0]), nbndcoeffs,
                    pLocalIn.get() + cnt, nbndcoeffs, 0.0, pOutput.get() + cnt,
                    nbndcoeffs);
        cnt += nbndcoeffs * nexp;
        cnt1 += nexp;
    }
}
 
/**
 * \brief Multiply by the block tranposed inverse
 * transformation matrix (R^T)^{-1} which is equivlaent to
 * transforming coefficients to LowEnergy space
 *
 * In JCP 2001 paper on low energy this is seen as (C^T)^{-1}
 */
void PreconditionerLowEnergy::v_DoTransformCoeffsToLowEnergy(
    const Array<OneD, NekDouble> &pInput, Array<OneD, NekDouble> &pOutput)
{
    int nLocBndDofs = m_locToGloMap.lock()->GetNumLocalBndCoeffs();
 
    ASSERTL1(pInput.size() >= nLocBndDofs,
             "Input array is less than nLocBndDofs");
    ASSERTL1(pOutput.size() >= nLocBndDofs,
             "Output array is less than nLocBndDofs");
 
    // Block inverse transformation matrix
    DNekBlkMat &invR = *m_InvRBlk;
 
    Array<OneD, NekDouble> pLocalIn(nLocBndDofs, pInput.get());
 
    // Multiply by the transpose of block transformation matrix
    int cnt  = 0;
    int cnt1 = 0;
    for (int i = 0; i < m_sameBlock.size(); ++i)
    {
        int nexp       = m_sameBlock[i].first;
        int nbndcoeffs = m_sameBlock[i].second;
        Blas::Dgemm('T', 'N', nbndcoeffs, nexp, nbndcoeffs, 1.0,
                    &(invR.GetBlock(cnt1, cnt1)->GetPtr()[0]), nbndcoeffs,
                    pLocalIn.get() + cnt, nbndcoeffs, 0.0, pOutput.get() + cnt,
                    nbndcoeffs);
        cnt += nbndcoeffs * nexp;
        cnt1 += nexp;
    }
}
 
/**
 * \brief Set up the transformed block  matrix system
 *
 * Sets up a block elemental matrix in which each of the block matrix is
 * the low energy equivalent
 * i.e. \f$\mathbf{S}_{2}=\mathbf{R}\mathbf{S}_{1}\mathbf{R}^{T}\f$
 */
DNekScalMatSharedPtr PreconditionerLowEnergy::v_TransformedSchurCompl(
    int n, int bndoffset, const std::shared_ptr<DNekScalMat> &loc_mat)
{
    std::shared_ptr<MultiRegions::ExpList> expList =
        ((m_linsys.lock())->GetLocMat()).lock();
 
    LocalRegions::ExpansionSharedPtr locExpansion;
    locExpansion      = expList->GetExp(n);
    unsigned int nbnd = locExpansion->NumBndryCoeffs();
 
    MatrixStorage storage = eFULL;
    DNekMatSharedPtr pS2 =
        MemoryManager<DNekMat>::AllocateSharedPtr(nbnd, nbnd, 0.0, storage);
 
    // transformation matrices
    DNekMat &R = (*m_RBlk->GetBlock(n, n));
 
    // Original Schur Complement
    DNekScalMat &S1 = (*loc_mat);
 
    DNekMat Sloc(nbnd, nbnd);
 
    // For variable p we need to just use the active modes
    NekDouble val;
 
    for (int i = 0; i < nbnd; ++i)
    {
        for (int j = 0; j < nbnd; ++j)
        {
            val = S1(i, j) * m_variablePmask[bndoffset + i] *
                  m_variablePmask[bndoffset + j];
            Sloc.SetValue(i, j, val);
        }
    }
 
    // create low energy matrix
    DNekMat &S2 = (*pS2);
 
    S2 = R * Sloc * Transpose(R);
 
    DNekScalMatSharedPtr return_val;
    return_val = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, pS2);
 
    return return_val;
}
 
/**
 * Create the mask array
 */
void PreconditionerLowEnergy::CreateVariablePMask(void)
{
    auto asmMap          = m_locToGloMap.lock();
    unsigned int nLocBnd = asmMap->GetNumLocalBndCoeffs();
 
    m_signChange = asmMap->GetSignChange();
 
    // Construct a mask array
    m_variablePmask = Array<OneD, NekDouble>(nLocBnd, 1.0);
 
    if (m_signChange)
    {
        unsigned int i;
        const Array<OneD, const NekDouble> &sign =
            asmMap->GetLocalToGlobalBndSign();
 
        for (i = 0; i < nLocBnd; ++i)
        {
            m_variablePmask[i] = fabs(sign[i]);
        }
    }
}
 
/**
 *\brief Sets up the reference prismatic element needed to construct
 *a low energy basis
 */
SpatialDomains::PrismGeomSharedPtr PreconditionerLowEnergy::CreateRefPrismGeom()
{
    //////////////////////////
    // Set up Prism element //
    //////////////////////////
 
    const int three         = 3;
    const int nVerts        = 6;
    const double point[][3] = {
        {-1, -1, 0},
        {1, -1, 0},
        {1, 1, 0},
        {-1, 1, 0},
        {0, -1, sqrt(double(3))},
        {0, 1, sqrt(double(3))},
    };
 
    // std::shared_ptr<SpatialDomains::PointGeom> verts[6];
    SpatialDomains::PointGeomSharedPtr verts[6];
    for (int i = 0; i < nVerts; ++i)
    {
        verts[i] = MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr(
            three, i, point[i][0], point[i][1], point[i][2]);
    }
    const int nEdges                  = 9;
    const int vertexConnectivity[][2] = {{0, 1}, {1, 2}, {3, 2}, {0, 3}, {0, 4},
                                         {1, 4}, {2, 5}, {3, 5}, {4, 5}};
 
    // Populate the list of edges
    SpatialDomains::SegGeomSharedPtr edges[nEdges];
    for (int i = 0; i < nEdges; ++i)
    {
        SpatialDomains::PointGeomSharedPtr vertsArray[2];
        for (int j = 0; j < 2; ++j)
        {
            vertsArray[j] = verts[vertexConnectivity[i][j]];
        }
        edges[i] = MemoryManager<SpatialDomains::SegGeom>::AllocateSharedPtr(
            i, three, vertsArray);
    }
 
    ////////////////////////
    // Set up Prism faces //
    ////////////////////////
 
    const int nFaces = 5;
    // quad-edge connectivity base-face0, vertical-quadface2, vertical-quadface4
    const int quadEdgeConnectivity[][4] = {
        {0, 1, 2, 3}, {1, 6, 8, 5}, {3, 7, 8, 4}};
    // QuadId ordered as 0, 1, 2, otherwise return false
    const int quadId[] = {0, -1, 1, -1, 2};
 
    // triangle-edge connectivity side-triface-1, side triface-3
    const int triEdgeConnectivity[][3] = {{0, 5, 4}, {2, 6, 7}};
    // TriId ordered as 0, 1, otherwise return false
    const int triId[] = {-1, 0, -1, 1, -1};
 
    // Populate the list of faces
    SpatialDomains::Geometry2DSharedPtr faces[nFaces];
    for (int f = 0; f < nFaces; ++f)
    {
        if (f == 1 || f == 3)
        {
            int i = triId[f];
            SpatialDomains::SegGeomSharedPtr edgeArray[3];
            for (int j = 0; j < 3; ++j)
            {
                edgeArray[j] = edges[triEdgeConnectivity[i][j]];
            }
            faces[f] =
                MemoryManager<SpatialDomains::TriGeom>::AllocateSharedPtr(
                    f, edgeArray);
        }
        else
        {
            int i = quadId[f];
            SpatialDomains::SegGeomSharedPtr edgeArray[4];
            for (int j = 0; j < 4; ++j)
            {
                edgeArray[j] = edges[quadEdgeConnectivity[i][j]];
            }
            faces[f] =
                MemoryManager<SpatialDomains::QuadGeom>::AllocateSharedPtr(
                    f, edgeArray);
        }
    }
 
    SpatialDomains::PrismGeomSharedPtr geom =
        MemoryManager<SpatialDomains::PrismGeom>::AllocateSharedPtr(0, faces);
 
    return geom;
}
 
/**
 *\brief Sets up the reference prismatic element needed to construct
 *a low energy basis mapping arrays
 */
SpatialDomains::PyrGeomSharedPtr PreconditionerLowEnergy::CreateRefPyrGeom()
{
    //////////////////////////
    // Set up Pyramid element //
    //////////////////////////
 
    const int nVerts        = 5;
    const double point[][3] = {{-1, -1, 0},
                               {1, -1, 0},
                               {1, 1, 0},
                               {-1, 1, 0},
                               {0, 0, sqrt(double(2))}};
 
    // boost::shared_ptr<SpatialDomains::PointGeom> verts[6];
    const int three = 3;
    SpatialDomains::PointGeomSharedPtr verts[5];
    for (int i = 0; i < nVerts; ++i)
    {
        verts[i] = MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr(
            three, i, point[i][0], point[i][1], point[i][2]);
    }
    const int nEdges                  = 8;
    const int vertexConnectivity[][2] = {{0, 1}, {1, 2}, {2, 3}, {3, 0},
                                         {0, 4}, {1, 4}, {2, 4}, {3, 4}};
 
    // Populate the list of edges
    SpatialDomains::SegGeomSharedPtr edges[nEdges];
    for (int i = 0; i < nEdges; ++i)
    {
        SpatialDomains::PointGeomSharedPtr vertsArray[2];
        for (int j = 0; j < 2; ++j)
        {
            vertsArray[j] = verts[vertexConnectivity[i][j]];
        }
        edges[i] = MemoryManager<SpatialDomains::SegGeom>::AllocateSharedPtr(
            i, three, vertsArray);
    }
 
    ////////////////////////
    // Set up Pyramid faces //
    ////////////////////////
 
    const int nFaces = 5;
    // quad-edge connectivity base-face0,
    const int quadEdgeConnectivity[][4] = {{0, 1, 2, 3}};
 
    // triangle-edge connectivity side-triface-1, side triface-2
    const int triEdgeConnectivity[][3] = {
        {0, 5, 4}, {1, 6, 5}, {2, 7, 6}, {3, 4, 7}};
 
    // Populate the list of faces
    SpatialDomains::Geometry2DSharedPtr faces[nFaces];
    for (int f = 0; f < nFaces; ++f)
    {
        if (f == 0)
        {
            SpatialDomains::SegGeomSharedPtr edgeArray[4];
            for (int j = 0; j < 4; ++j)
            {
                edgeArray[j] = edges[quadEdgeConnectivity[f][j]];
            }
 
            faces[f] =
                MemoryManager<SpatialDomains::QuadGeom>::AllocateSharedPtr(
                    f, edgeArray);
        }
        else
        {
            int i = f - 1;
            SpatialDomains::SegGeomSharedPtr edgeArray[3];
            for (int j = 0; j < 3; ++j)
            {
                edgeArray[j] = edges[triEdgeConnectivity[i][j]];
            }
            faces[f] =
                MemoryManager<SpatialDomains::TriGeom>::AllocateSharedPtr(
                    f, edgeArray);
        }
    }
 
    SpatialDomains::PyrGeomSharedPtr geom =
        MemoryManager<SpatialDomains::PyrGeom>::AllocateSharedPtr(0, faces);
 
    return geom;
}
 
/**
 *\brief Sets up the reference tretrahedral element needed to construct
 *a low energy basis
 */
SpatialDomains::TetGeomSharedPtr PreconditionerLowEnergy::CreateRefTetGeom()
{
    /////////////////////////////////
    // Set up Tetrahedron vertices //
    /////////////////////////////////
 
    int i, j;
    const int three         = 3;
    const int nVerts        = 4;
    const double point[][3] = {{-1, -1 / sqrt(double(3)), -1 / sqrt(double(6))},
                               {1, -1 / sqrt(double(3)), -1 / sqrt(double(6))},
                               {0, 2 / sqrt(double(3)), -1 / sqrt(double(6))},
                               {0, 0, 3 / sqrt(double(6))}};
 
    std::shared_ptr<SpatialDomains::PointGeom> verts[4];
    for (i = 0; i < nVerts; ++i)
    {
        verts[i] = MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr(
            three, i, point[i][0], point[i][1], point[i][2]);
    }
 
    //////////////////////////////
    // Set up Tetrahedron Edges //
    //////////////////////////////
 
    // SegGeom (int id, const int coordim), EdgeComponent(id, coordim)
    const int nEdges                  = 6;
    const int vertexConnectivity[][2] = {{0, 1}, {1, 2}, {0, 2},
                                         {0, 3}, {1, 3}, {2, 3}};
 
    // Populate the list of edges
    SpatialDomains::SegGeomSharedPtr edges[nEdges];
    for (i = 0; i < nEdges; ++i)
    {
        std::shared_ptr<SpatialDomains::PointGeom> vertsArray[2];
        for (j = 0; j < 2; ++j)
        {
            vertsArray[j] = verts[vertexConnectivity[i][j]];
        }
 
        edges[i] = MemoryManager<SpatialDomains::SegGeom>::AllocateSharedPtr(
            i, three, vertsArray);
    }
 
    //////////////////////////////
    // Set up Tetrahedron faces //
    //////////////////////////////
 
    const int nFaces                = 4;
    const int edgeConnectivity[][3] = {
        {0, 1, 2}, {0, 4, 3}, {1, 5, 4}, {2, 5, 3}};
 
    // Populate the list of faces
    SpatialDomains::TriGeomSharedPtr faces[nFaces];
    for (i = 0; i < nFaces; ++i)
    {
        SpatialDomains::SegGeomSharedPtr edgeArray[3];
        for (j = 0; j < 3; ++j)
        {
            edgeArray[j] = edges[edgeConnectivity[i][j]];
        }
 
        faces[i] = MemoryManager<SpatialDomains::TriGeom>::AllocateSharedPtr(
            i, edgeArray);
    }
 
    SpatialDomains::TetGeomSharedPtr geom =
        MemoryManager<SpatialDomains::TetGeom>::AllocateSharedPtr(0, faces);
 
    return geom;
}
 
/**
 *\brief Sets up the reference hexahedral element needed to construct
 *a low energy basis
 */
SpatialDomains::HexGeomSharedPtr PreconditionerLowEnergy::CreateRefHexGeom()
{
    ////////////////////////////////
    // Set up Hexahedron vertices //
    ////////////////////////////////
 
    const int three = 3;
 
    const int nVerts        = 8;
    const double point[][3] = {{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0},
                               {0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1}};
 
    // Populate the list of verts
    SpatialDomains::PointGeomSharedPtr verts[8];
    for (int i = 0; i < nVerts; ++i)
    {
        verts[i] = MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr(
            three, i, point[i][0], point[i][1], point[i][2]);
    }
 
    /////////////////////////////
    // Set up Hexahedron Edges //
    /////////////////////////////
 
    // SegGeom (int id, const int coordim), EdgeComponent(id, coordim)
    const int nEdges                  = 12;
    const int vertexConnectivity[][2] = {{0, 1}, {1, 2}, {2, 3}, {0, 3},
                                         {0, 4}, {1, 5}, {2, 6}, {3, 7},
                                         {4, 5}, {5, 6}, {6, 7}, {4, 7}};
 
    // Populate the list of edges
    SpatialDomains::SegGeomSharedPtr edges[nEdges];
    for (int i = 0; i < nEdges; ++i)
    {
        SpatialDomains::PointGeomSharedPtr vertsArray[2];
        for (int j = 0; j < 2; ++j)
        {
            vertsArray[j] = verts[vertexConnectivity[i][j]];
        }
        edges[i] = MemoryManager<SpatialDomains::SegGeom>::AllocateSharedPtr(
            i, three, vertsArray);
    }
 
    /////////////////////////////
    // Set up Hexahedron faces //
    /////////////////////////////
 
    const int nFaces                = 6;
    const int edgeConnectivity[][4] = {{0, 1, 2, 3},  {0, 5, 8, 4},
                                       {1, 6, 9, 5},  {2, 7, 10, 6},
                                       {3, 7, 11, 4}, {8, 9, 10, 11}};
 
    // Populate the list of faces
    SpatialDomains::QuadGeomSharedPtr faces[nFaces];
    for (int i = 0; i < nFaces; ++i)
    {
        SpatialDomains::SegGeomSharedPtr edgeArray[4];
        for (int j = 0; j < 4; ++j)
        {
            edgeArray[j] = edges[edgeConnectivity[i][j]];
        }
        faces[i] = MemoryManager<SpatialDomains::QuadGeom>::AllocateSharedPtr(
            i, edgeArray);
    }
 
    SpatialDomains::HexGeomSharedPtr geom =
        MemoryManager<SpatialDomains::HexGeom>::AllocateSharedPtr(0, faces);
 
    return geom;
}
 
/**
 * \brief Loop expansion and determine different variants of the
 * transformation matrix
 *
 * Sets up multiple reference elements based on the element expansion.
 */
void PreconditionerLowEnergy::SetUpReferenceElements(
    std::map<ShapeType, DNekScalMatSharedPtr> &maxRmat,
    map<ShapeType, LocalRegions::Expansion3DSharedPtr> &maxElmt,
    map<ShapeType, Array<OneD, unsigned int>> &vertMapMaxR,
    map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &edgeMapMaxR)
{
    std::shared_ptr<MultiRegions::ExpList> expList =
        ((m_linsys.lock())->GetLocMat()).lock();
    GlobalLinSysKey linSysKey = (m_linsys.lock())->GetKey();
 
    LibUtilities::CommSharedPtr vComm = expList->GetComm()->GetSpaceComm();
 
    LocalRegions::ExpansionSharedPtr locExp;
 
    // face maps for pyramid and hybrid meshes - not need to return.
    map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> faceMapMaxR;
 
    /* Determine the maximum expansion order for all elements */
    int nummodesmax = 0;
    Array<OneD, int> Shapes(LibUtilities::SIZE_ShapeType, 0);
 
    for (int n = 0; n < expList->GetNumElmts(); ++n)
    {
        locExp = expList->GetExp(n);
 
        nummodesmax = max(nummodesmax, locExp->GetBasisNumModes(0));
        nummodesmax = max(nummodesmax, locExp->GetBasisNumModes(1));
        nummodesmax = max(nummodesmax, locExp->GetBasisNumModes(2));
 
        Shapes[locExp->DetShapeType()] = 1;
    }
 
    vComm->AllReduce(nummodesmax, ReduceMax);
    vComm->AllReduce(Shapes, ReduceMax);
 
    if (Shapes[ePyramid] || Shapes[ePrism]) // if Pyramids or Prisms used then
                                            // need Tet and Hex expansion
    {
        Shapes[eTetrahedron] = 1;
        Shapes[eHexahedron]  = 1;
    }
 
    StdRegions::MatrixType PreconR;
    if (linSysKey.GetMatrixType() == StdRegions::eMass)
    {
        PreconR = StdRegions::ePreconRMass;
    }
    else
    {
        PreconR = StdRegions::ePreconR;
    }
 
    Array<OneD, unsigned int> vmap;
    Array<OneD, Array<OneD, unsigned int>> emap;
    Array<OneD, Array<OneD, unsigned int>> fmap;
 
    /*
     * Set up a transformation matrices for equal max order
     * polynomial meshes
     */
 
    if (Shapes[eHexahedron])
    {
        SpatialDomains::HexGeomSharedPtr hexgeom = CreateRefHexGeom();
        // Bases for Hex element
        const BasisKey HexBa(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey HexBb(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey HexBc(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
 
        // Create reference Hexahdedral expansion
        LocalRegions::HexExpSharedPtr HexExp;
 
        HexExp = MemoryManager<LocalRegions::HexExp>::AllocateSharedPtr(
            HexBa, HexBb, HexBc, hexgeom);
 
        maxElmt[eHexahedron] = HexExp;
 
        // Hex:
        HexExp->GetInverseBoundaryMaps(vmap, emap, fmap);
        vertMapMaxR[eHexahedron] = vmap;
        edgeMapMaxR[eHexahedron] = emap;
        faceMapMaxR[eHexahedron] = fmap;
 
        // Get hexahedral transformation matrix
        LocalRegions::MatrixKey HexR(PreconR, eHexahedron, *HexExp,
                                     linSysKey.GetConstFactors());
        maxRmat[eHexahedron] = HexExp->GetLocMatrix(HexR);
        HexExp->DropLocMatrix(HexR); // Need to delete reference from manager
    }
 
    if (Shapes[eTetrahedron])
    {
        SpatialDomains::TetGeomSharedPtr tetgeom = CreateRefTetGeom();
        // Bases for Tetrahedral element
        const BasisKey TetBa(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey TetBb(eModified_B, nummodesmax,
                             PointsKey(nummodesmax, eGaussRadauMAlpha1Beta0));
        const BasisKey TetBc(eModified_C, nummodesmax,
                             PointsKey(nummodesmax, eGaussRadauMAlpha2Beta0));
 
        // Create reference tetrahedral expansion
        LocalRegions::TetExpSharedPtr TetExp;
 
        TetExp = MemoryManager<LocalRegions::TetExp>::AllocateSharedPtr(
            TetBa, TetBb, TetBc, tetgeom);
 
        maxElmt[eTetrahedron] = TetExp;
 
        TetExp->GetInverseBoundaryMaps(vmap, emap, fmap);
        vertMapMaxR[eTetrahedron] = vmap;
        edgeMapMaxR[eTetrahedron] = emap;
        faceMapMaxR[eTetrahedron] = fmap;
 
        // Get tetrahedral transformation matrix
        LocalRegions::MatrixKey TetR(PreconR, eTetrahedron, *TetExp,
                                     linSysKey.GetConstFactors());
        maxRmat[eTetrahedron] = TetExp->GetLocMatrix(TetR);
        TetExp->DropLocMatrix(TetR); // Need to delete reference from manager
 
        if ((Shapes[ePyramid]) || (Shapes[eHexahedron]))
        {
            ReSetTetMaxRMat(nummodesmax, TetExp, maxRmat, vertMapMaxR,
                            edgeMapMaxR, faceMapMaxR);
        }
    }
 
    if (Shapes[ePyramid])
    {
        SpatialDomains::PyrGeomSharedPtr pyrgeom = CreateRefPyrGeom();
 
        // Bases for Pyramid element
        const BasisKey PyrBa(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey PyrBb(eModified_A, nummodesmax,
                             PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey PyrBc(eModifiedPyr_C, nummodesmax,
                             PointsKey(nummodesmax, eGaussRadauMAlpha2Beta0));
 
        // Create reference pyramid expansion
        LocalRegions::PyrExpSharedPtr PyrExp;
 
        PyrExp = MemoryManager<LocalRegions::PyrExp>::AllocateSharedPtr(
            PyrBa, PyrBb, PyrBc, pyrgeom);
 
        maxElmt[ePyramid] = PyrExp;
 
        // Pyramid:
        PyrExp->GetInverseBoundaryMaps(vmap, emap, fmap);
        vertMapMaxR[ePyramid] = vmap;
        edgeMapMaxR[ePyramid] = emap;
        faceMapMaxR[ePyramid] = fmap;
 
        // Set up Pyramid Transformation Matrix based on Tet
        // and Hex expansion
        SetUpPyrMaxRMat(nummodesmax, PyrExp, maxRmat, vertMapMaxR, edgeMapMaxR,
                        faceMapMaxR);
    }
 
    if (Shapes[ePrism])
    {
        SpatialDomains::PrismGeomSharedPtr prismgeom = CreateRefPrismGeom();
        // Bases for Prism element
        const BasisKey PrismBa(
            eModified_A, nummodesmax,
            PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey PrismBb(
            eModified_A, nummodesmax,
            PointsKey(nummodesmax + 1, eGaussLobattoLegendre));
        const BasisKey PrismBc(eModified_B, nummodesmax,
                               PointsKey(nummodesmax, eGaussRadauMAlpha1Beta0));
 
        // Create reference prismatic expansion
        LocalRegions::PrismExpSharedPtr PrismExp;
 
        PrismExp = MemoryManager<LocalRegions::PrismExp>::AllocateSharedPtr(
            PrismBa, PrismBb, PrismBc, prismgeom);
        maxElmt[ePrism] = PrismExp;
 
        // Prism:
        PrismExp->GetInverseBoundaryMaps(vmap, emap, fmap);
        vertMapMaxR[ePrism] = vmap;
        edgeMapMaxR[ePrism] = emap;
 
        faceMapMaxR[ePrism] = fmap;
 
        if ((Shapes[ePyramid]) || (Shapes[eHexahedron]))
        {
            ReSetPrismMaxRMat(nummodesmax, PrismExp, maxRmat, vertMapMaxR,
                              edgeMapMaxR, faceMapMaxR, false);
        }
        else
        {
            // Get prismatic transformation matrix
            LocalRegions::MatrixKey PrismR(PreconR, ePrism, *PrismExp,
                                           linSysKey.GetConstFactors());
            maxRmat[ePrism] = PrismExp->GetLocMatrix(PrismR);
            PrismExp->DropLocMatrix(
                PrismR); // Need to delete reference from manager
 
            if (Shapes[eTetrahedron]) // reset triangular faces from Tet
            {
                ReSetPrismMaxRMat(nummodesmax, PrismExp, maxRmat, vertMapMaxR,
                                  edgeMapMaxR, faceMapMaxR, true);
            }
        }
    }
}
 
void PreconditionerLowEnergy::SetUpPyrMaxRMat(
    int nummodesmax, LocalRegions::PyrExpSharedPtr &PyrExp,
    std::map<ShapeType, DNekScalMatSharedPtr> &maxRmat,
    std::map<ShapeType, Array<OneD, unsigned int>> &vertMapMaxR,
    std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &edgeMapMaxR,
    std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &faceMapMaxR)
{
    int nRows = PyrExp->NumBndryCoeffs();
    NekDouble val;
    NekDouble zero = 0.0;
    DNekMatSharedPtr newmat =
        MemoryManager<DNekMat>::AllocateSharedPtr(nRows, nRows, zero, eFULL);
 
    // set diagonal to 1
    for (int i = 0; i < nRows; ++i)
    {
        newmat->SetValue(i, i, 1.0);
    }
 
    // The following lists specify the number of adjacent
    // edges to each vertex (nadj) then the Hex vert to
    // use for each pyramid ver in the vert-edge map (VEVert)
    // followed by the hex edge to use for each pyramid edge
    // in the vert-edge map (VEEdge)
    const int nadjedge[]     = {3, 3, 3, 3, 4};
    const int VEHexVert[][4] = {{0, 0, 0, -1},
                                {1, 1, 1, -1},
                                {2, 2, 2, -1},
                                {3, 3, 3, -1},
                                {4, 5, 6, 7}};
    const int VEHexEdge[][4] = {{0, 3, 4, -1},
                                {0, 1, 5, -1},
                                {1, 2, 6, -1},
                                {2, 3, 7, -1},
                                {4, 5, 6, 7}};
    const int VEPyrEdge[][4] = {{0, 3, 4, -1},
                                {0, 1, 5, -1},
                                {1, 2, 6, -1},
                                {2, 3, 7, -1},
                                {4, 5, 6, 7}};
 
    // fill vertex to edge coupling
    for (int v = 0; v < 5; ++v)
    {
        for (int e = 0; e < nadjedge[v]; ++e)
        {
            for (int i = 0; i < nummodesmax - 2; ++i)
            {
                // Note this is using wrong shape but gives
                // answer that seems to have correct error!
                val = (*maxRmat[eHexahedron])(
                    vertMapMaxR[eHexahedron][VEHexVert[v][e]],
                    edgeMapMaxR[eHexahedron][VEHexEdge[v][e]][i]);
                newmat->SetValue(vertMapMaxR[ePyramid][v],
                                 edgeMapMaxR[ePyramid][VEPyrEdge[v][e]][i],
                                 val);
            }
        }
    }
 
    int nfacemodes;
    nfacemodes = (nummodesmax - 2) * (nummodesmax - 2);
    // First four verties are all adjacent to base face
    for (int v = 0; v < 4; ++v)
    {
        for (int i = 0; i < nfacemodes; ++i)
        {
            val = (*maxRmat[eHexahedron])(vertMapMaxR[eHexahedron][v],
                                          faceMapMaxR[eHexahedron][0][i]);
            newmat->SetValue(vertMapMaxR[ePyramid][v],
                             faceMapMaxR[ePyramid][0][i], val);
        }
    }
 
    const int nadjface[]     = {2, 2, 2, 2, 4};
    const int VFTetVert[][4] = {{0, 0, -1, -1},
                                {1, 1, -1, -1},
                                {2, 2, -1, -1},
                                {0, 2, -1, -1},
                                {3, 3, 3, 3}};
    const int VFTetFace[][4] = {{1, 3, -1, -1},
                                {1, 2, -1, -1},
                                {2, 3, -1, -1},
                                {1, 3, -1, -1},
                                {1, 2, 1, 2}};
    const int VFPyrFace[][4] = {{1, 4, -1, -1},
                                {1, 2, -1, -1},
                                {2, 3, -1, -1},
                                {3, 4, -1, -1},
                                {1, 2, 3, 4}};
 
    // next handle all triangular faces from tetrahedron
    nfacemodes = (nummodesmax - 3) * (nummodesmax - 2) / 2;
    for (int v = 0; v < 5; ++v)
    {
        for (int f = 0; f < nadjface[v]; ++f)
        {
            for (int i = 0; i < nfacemodes; ++i)
            {
                val = (*maxRmat[eTetrahedron])(
                    vertMapMaxR[eTetrahedron][VFTetVert[v][f]],
                    faceMapMaxR[eTetrahedron][VFTetFace[v][f]][i]);
                newmat->SetValue(vertMapMaxR[ePyramid][v],
                                 faceMapMaxR[ePyramid][VFPyrFace[v][f]][i],
                                 val);
            }
        }
    }
 
    // Edge to face coupling
    // all base edges are coupled to face 0
    nfacemodes = (nummodesmax - 2) * (nummodesmax - 2);
    for (int e = 0; e < 4; ++e)
    {
        for (int i = 0; i < nummodesmax - 2; ++i)
        {
            for (int j = 0; j < nfacemodes; ++j)
            {
                int edgemapid = edgeMapMaxR[eHexahedron][e][i];
                int facemapid = faceMapMaxR[eHexahedron][0][j];
 
                val = (*maxRmat[eHexahedron])(edgemapid, facemapid);
                newmat->SetValue(edgeMapMaxR[ePyramid][e][i],
                                 faceMapMaxR[ePyramid][0][j], val);
            }
        }
    }
 
    const int nadjface1[]    = {1, 1, 1, 1, 2, 2, 2, 2};
    const int EFTetEdge[][2] = {{0, -1}, {1, -1}, {0, -1}, {2, -1},
                                {3, 3},  {4, 4},  {5, 5},  {3, 5}};
    const int EFTetFace[][2] = {{1, -1}, {2, -1}, {1, -1}, {3, -1},
                                {1, 3},  {1, 2},  {2, 3},  {1, 3}};
    const int EFPyrFace[][2] = {{1, -1}, {2, -1}, {3, -1}, {4, -1},
                                {1, 4},  {1, 2},  {2, 3},  {3, 4}};
 
    // next handle all triangular faces from tetrahedron
    nfacemodes = (nummodesmax - 3) * (nummodesmax - 2) / 2;
    for (int e = 0; e < 8; ++e)
    {
        for (int f = 0; f < nadjface1[e]; ++f)
        {
            for (int i = 0; i < nummodesmax - 2; ++i)
            {
                for (int j = 0; j < nfacemodes; ++j)
                {
                    int edgemapid =
                        edgeMapMaxR[eTetrahedron][EFTetEdge[e][f]][i];
                    int facemapid =
                        faceMapMaxR[eTetrahedron][EFTetFace[e][f]][j];
 
                    val = (*maxRmat[eTetrahedron])(edgemapid, facemapid);
                    newmat->SetValue(edgeMapMaxR[ePyramid][e][i],
                                     faceMapMaxR[ePyramid][EFPyrFace[e][f]][j],
                                     val);
                }
            }
        }
    }
 
    DNekScalMatSharedPtr PyrR;
    PyrR = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, newmat);
    maxRmat[ePyramid] = PyrR;
}
 
void PreconditionerLowEnergy::ReSetTetMaxRMat(
    int nummodesmax, LocalRegions::TetExpSharedPtr &TetExp,
    std::map<ShapeType, DNekScalMatSharedPtr> &maxRmat,
    std::map<ShapeType, Array<OneD, unsigned int>> &vertMapMaxR,
    std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &edgeMapMaxR,
    [[maybe_unused]] std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>>
        &faceMapMaxR)
{
    int nRows = TetExp->NumBndryCoeffs();
    NekDouble val;
    NekDouble zero = 0.0;
    DNekMatSharedPtr newmat =
        MemoryManager<DNekMat>::AllocateSharedPtr(nRows, nRows, zero, eFULL);
 
    // copy existing system
    for (int i = 0; i < nRows; ++i)
    {
        for (int j = 0; j < nRows; ++j)
        {
            val = (*maxRmat[eTetrahedron])(i, j);
            newmat->SetValue(i, j, val);
        }
    }
 
    // The following lists specify the number of adjacent
    // edges to each vertex (nadj) then the Hex vert to
    // use for each pyramid ver in the vert-edge map (VEVert)
    // followed by the hex edge to use for each Tet edge
    // in the vert-edge map (VEEdge)
    const int VEHexVert[][4] = {{0, 0, 0}, {1, 1, 1}, {2, 2, 2}, {4, 5, 6}};
    const int VEHexEdge[][4] = {{0, 3, 4}, {0, 1, 5}, {1, 2, 6}, {4, 5, 6}};
    const int VETetEdge[][4] = {{0, 2, 3}, {0, 1, 4}, {1, 2, 5}, {3, 4, 5}};
 
    // fill vertex to edge coupling
    for (int v = 0; v < 4; ++v)
    {
        for (int e = 0; e < 3; ++e)
        {
            for (int i = 0; i < nummodesmax - 2; ++i)
            {
                // Note this is using wrong shape but gives
                // answer that seems to have correct error!
                val = (*maxRmat[eHexahedron])(
                    vertMapMaxR[eHexahedron][VEHexVert[v][e]],
                    edgeMapMaxR[eHexahedron][VEHexEdge[v][e]][i]);
                newmat->SetValue(vertMapMaxR[eTetrahedron][v],
                                 edgeMapMaxR[eTetrahedron][VETetEdge[v][e]][i],
                                 val);
            }
        }
    }
 
    DNekScalMatSharedPtr TetR =
        MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, newmat);
 
    maxRmat[eTetrahedron] = TetR;
}
 
void PreconditionerLowEnergy::ReSetPrismMaxRMat(
    int nummodesmax, LocalRegions::PrismExpSharedPtr &PrismExp,
    std::map<ShapeType, DNekScalMatSharedPtr> &maxRmat,
    std::map<ShapeType, Array<OneD, unsigned int>> &vertMapMaxR,
    std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &edgeMapMaxR,
    std::map<ShapeType, Array<OneD, Array<OneD, unsigned int>>> &faceMapMaxR,
    bool UseTetOnly)
{
    int nRows = PrismExp->NumBndryCoeffs();
    NekDouble val;
    NekDouble zero = 0.0;
    DNekMatSharedPtr newmat =
        MemoryManager<DNekMat>::AllocateSharedPtr(nRows, nRows, zero, eFULL);
 
    int nfacemodes;
 
    if (UseTetOnly)
    {
        // copy existing system
        for (int i = 0; i < nRows; ++i)
        {
            for (int j = 0; j < nRows; ++j)
            {
                val = (*maxRmat[ePrism])(i, j);
                newmat->SetValue(i, j, val);
            }
        }
 
        // Reset vertex to edge mapping from tet.
        const int VETetVert[][2]   = {{0, 0}, {1, 1}, {1, 1},
                                      {0, 0}, {3, 3}, {3, 3}};
        const int VETetEdge[][2]   = {{0, 3}, {0, 4}, {0, 4},
                                      {0, 3}, {3, 4}, {4, 3}};
        const int VEPrismEdge[][2] = {{0, 4}, {0, 5}, {2, 6},
                                      {2, 7}, {4, 5}, {6, 7}};
 
        // fill vertex to edge coupling
        for (int v = 0; v < 6; ++v)
        {
            for (int e = 0; e < 2; ++e)
            {
                for (int i = 0; i < nummodesmax - 2; ++i)
                {
                    // Note this is using wrong shape but gives
                    // answer that seems to have correct error!
                    val = (*maxRmat[eTetrahedron])(
                        vertMapMaxR[eTetrahedron][VETetVert[v][e]],
                        edgeMapMaxR[eTetrahedron][VETetEdge[v][e]][i]);
                    newmat->SetValue(vertMapMaxR[ePrism][v],
                                     edgeMapMaxR[ePrism][VEPrismEdge[v][e]][i],
                                     val);
                }
            }
        }
    }
    else
    {
        // set diagonal to 1
        for (int i = 0; i < nRows; ++i)
        {
            newmat->SetValue(i, i, 1.0);
        }
 
        // Set vertex to edge mapping from Hex.
 
        // The following lists specify the number of adjacent
        // edges to each vertex (nadj) then the Hex vert to
        // use for each prism ver in the vert-edge map (VEVert)
        // followed by the hex edge to use for each prism edge
        // in the vert-edge map (VEEdge)
        const int VEHexVert[][3]   = {{0, 0, 0}, {1, 1, 1}, {2, 2, 2},
                                      {3, 3, 3}, {4, 5, 5}, {6, 7, 7}};
        const int VEHexEdge[][3]   = {{0, 3, 4}, {0, 1, 5}, {1, 2, 6},
                                      {2, 3, 7}, {4, 5, 9}, {6, 7, 11}};
        const int VEPrismEdge[][3] = {{0, 3, 4}, {0, 1, 5}, {1, 2, 6},
                                      {2, 3, 7}, {4, 5, 8}, {6, 7, 8}};
 
        // fill vertex to edge coupling
        for (int v = 0; v < 6; ++v)
        {
            for (int e = 0; e < 3; ++e)
            {
                for (int i = 0; i < nummodesmax - 2; ++i)
                {
                    // Note this is using wrong shape but gives
                    // answer that seems to have correct error!
                    val = (*maxRmat[eHexahedron])(
                        vertMapMaxR[eHexahedron][VEHexVert[v][e]],
                        edgeMapMaxR[eHexahedron][VEHexEdge[v][e]][i]);
                    newmat->SetValue(vertMapMaxR[ePrism][v],
                                     edgeMapMaxR[ePrism][VEPrismEdge[v][e]][i],
                                     val);
                }
            }
        }
 
        // Setup vertex to face mapping from Hex
        const int VFHexVert[][2] = {{0, 0}, {1, 1}, {4, 5},
                                    {2, 2}, {3, 3}, {6, 7}};
        const int VFHexFace[][2] = {{0, 4}, {0, 2}, {4, 2},
                                    {0, 2}, {0, 4}, {2, 4}};
 
        const int VQFPrismVert[][2] = {{0, 0}, {1, 1}, {4, 4},
                                       {2, 2}, {3, 3}, {5, 5}};
        const int VQFPrismFace[][2] = {{0, 4}, {0, 2}, {4, 2},
                                       {0, 2}, {0, 4}, {2, 4}};
 
        nfacemodes = (nummodesmax - 2) * (nummodesmax - 2);
        // Replace two Quad faces  on every vertex
        for (int v = 0; v < 6; ++v)
        {
            for (int f = 0; f < 2; ++f)
            {
                for (int i = 0; i < nfacemodes; ++i)
                {
                    val = (*maxRmat[eHexahedron])(
                        vertMapMaxR[eHexahedron][VFHexVert[v][f]],
                        faceMapMaxR[eHexahedron][VFHexFace[v][f]][i]);
                    newmat->SetValue(vertMapMaxR[ePrism][VQFPrismVert[v][f]],
                                     faceMapMaxR[ePrism][VQFPrismFace[v][f]][i],
                                     val);
                }
            }
        }
 
        // Mapping of Hex Edge-Face mappings to Prism Edge-Face Mappings
        const int nadjface[]     = {1, 2, 1, 2, 1, 1, 1, 1, 2};
        const int EFHexEdge[][2] = {{0, -1}, {1, 1},  {2, -1}, {3, 3}, {4, -1},
                                    {5, -1}, {6, -1}, {7, -1}, {9, 11}};
        const int EFHexFace[][2] = {{0, -1}, {0, 2},  {0, -1}, {0, 4}, {4, -1},
                                    {2, -1}, {2, -1}, {4, -1}, {2, 4}};
        const int EQFPrismEdge[][2] = {{0, -1}, {1, 1},  {2, -1},
                                       {3, 3},  {4, -1}, {5, -1},
                                       {6, -1}, {7, -1}, {8, 8}};
        const int EQFPrismFace[][2] = {{0, -1}, {0, 2},  {0, -1},
                                       {0, 4},  {4, -1}, {2, -1},
                                       {2, -1}, {4, -1}, {2, 4}};
 
        // all base edges are coupled to face 0
        nfacemodes = (nummodesmax - 2) * (nummodesmax - 2);
        for (int e = 0; e < 9; ++e)
        {
            for (int f = 0; f < nadjface[e]; ++f)
            {
                for (int i = 0; i < nummodesmax - 2; ++i)
                {
                    for (int j = 0; j < nfacemodes; ++j)
                    {
                        int edgemapid =
                            edgeMapMaxR[eHexahedron][EFHexEdge[e][f]][i];
                        int facemapid =
                            faceMapMaxR[eHexahedron][EFHexFace[e][f]][j];
 
                        val = (*maxRmat[eHexahedron])(edgemapid, facemapid);
 
                        int edgemapid1 =
                            edgeMapMaxR[ePrism][EQFPrismEdge[e][f]][i];
                        int facemapid1 =
                            faceMapMaxR[ePrism][EQFPrismFace[e][f]][j];
                        newmat->SetValue(edgemapid1, facemapid1, val);
                    }
                }
            }
        }
    }
 
    const int VFTetVert[]    = {0, 1, 3, 1, 0, 3};
    const int VFTetFace[]    = {1, 1, 1, 1, 1, 1};
    const int VTFPrismVert[] = {0, 1, 4, 2, 3, 5};
    const int VTFPrismFace[] = {1, 1, 1, 3, 3, 3};
 
    //  Handle all triangular faces from tetrahedron
    nfacemodes = (nummodesmax - 3) * (nummodesmax - 2) / 2;
    for (int v = 0; v < 6; ++v)
    {
        for (int i = 0; i < nfacemodes; ++i)
        {
            val = (*maxRmat[eTetrahedron])(
                vertMapMaxR[eTetrahedron][VFTetVert[v]],
                faceMapMaxR[eTetrahedron][VFTetFace[v]][i]);
 
            newmat->SetValue(vertMapMaxR[ePrism][VTFPrismVert[v]],
                             faceMapMaxR[ePrism][VTFPrismFace[v]][i], val);
        }
    }
 
    // Mapping of Tet Edge-Face mappings to Prism Edge-Face Mappings
    const int EFTetEdge[]    = {0, 3, 4, 0, 4, 3};
    const int EFTetFace[]    = {1, 1, 1, 1, 1, 1};
    const int ETFPrismEdge[] = {0, 4, 5, 2, 6, 7};
    const int ETFPrismFace[] = {1, 1, 1, 3, 3, 3};
 
    // handle all edge to triangular faces from tetrahedron
    // (only 6 this time)
    nfacemodes = (nummodesmax - 3) * (nummodesmax - 2) / 2;
    for (int e = 0; e < 6; ++e)
    {
        for (int i = 0; i < nummodesmax - 2; ++i)
        {
            for (int j = 0; j < nfacemodes; ++j)
            {
                int edgemapid = edgeMapMaxR[eTetrahedron][EFTetEdge[e]][i];
                int facemapid = faceMapMaxR[eTetrahedron][EFTetFace[e]][j];
                val           = (*maxRmat[eTetrahedron])(edgemapid, facemapid);
 
                newmat->SetValue(edgeMapMaxR[ePrism][ETFPrismEdge[e]][i],
                                 faceMapMaxR[ePrism][ETFPrismFace[e]][j], val);
            }
        }
    }
 
    DNekScalMatSharedPtr PrismR =
        MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, newmat);
    maxRmat[ePrism] = PrismR;
}
 
DNekMatSharedPtr PreconditionerLowEnergy::ExtractLocMat(
    LocalRegions::Expansion3DSharedPtr &locExp, DNekScalMatSharedPtr &maxRmat,
    LocalRegions::Expansion3DSharedPtr &maxExp, Array<OneD, unsigned int> &vmap,
    Array<OneD, Array<OneD, unsigned int>> &emap)
{
    NekDouble val;
    NekDouble zero = 0.0;
 
    int nRows = locExp->NumBndryCoeffs();
    DNekMatSharedPtr newmat =
        MemoryManager<DNekMat>::AllocateSharedPtr(nRows, nRows, zero, eFULL);
 
    Array<OneD, unsigned int> vlocmap;
    Array<OneD, Array<OneD, unsigned int>> elocmap;
    Array<OneD, Array<OneD, unsigned int>> flocmap;
 
    locExp->GetInverseBoundaryMaps(vlocmap, elocmap, flocmap);
 
    // fill diagonal
    for (int i = 0; i < nRows; ++i)
    {
        val = 1.0;
        newmat->SetValue(i, i, val);
    }
 
    int nverts = locExp->GetNverts();
    int nedges = locExp->GetNedges();
    int nfaces = locExp->GetNtraces();
 
    // fill vertex to edge coupling
    for (int e = 0; e < nedges; ++e)
    {
        int nEdgeInteriorCoeffs = locExp->GetEdgeNcoeffs(e) - 2;
 
        for (int v = 0; v < nverts; ++v)
        {
            for (int i = 0; i < nEdgeInteriorCoeffs; ++i)
            {
                val = (*maxRmat)(vmap[v], emap[e][i]);
                newmat->SetValue(vlocmap[v], elocmap[e][i], val);
            }
        }
    }
 
    for (int f = 0; f < nfaces; ++f)
    {
        // Get details to extrac this face from max reference matrix
        StdRegions::Orientation FwdOrient =
            StdRegions::eDir1FwdDir1_Dir2FwdDir2;
        int m0, m1; // Local face expansion orders.
 
        int nFaceInteriorCoeffs = locExp->GetTraceIntNcoeffs(f);
 
        locExp->GetTraceNumModes(f, m0, m1, FwdOrient);
 
        Array<OneD, unsigned int> fmapRmat =
            maxExp->GetTraceInverseBoundaryMap(f, FwdOrient, m0, m1);
 
        // fill in vertex to face coupling
        for (int v = 0; v < nverts; ++v)
        {
            for (int i = 0; i < nFaceInteriorCoeffs; ++i)
            {
                val = (*maxRmat)(vmap[v], fmapRmat[i]);
                newmat->SetValue(vlocmap[v], flocmap[f][i], val);
            }
        }
 
        // fill in edges to face coupling
        for (int e = 0; e < nedges; ++e)
        {
            int nEdgeInteriorCoeffs = locExp->GetEdgeNcoeffs(e) - 2;
 
            for (int j = 0; j < nEdgeInteriorCoeffs; ++j)
            {
                for (int i = 0; i < nFaceInteriorCoeffs; ++i)
                {
                    val = (*maxRmat)(emap[e][j], fmapRmat[i]);
                    newmat->SetValue(elocmap[e][j], flocmap[f][i], val);
                }
            }
        }
    }
 
    return newmat;
}
} // namespace MultiRegions
} // namespace Nektar