StdNodalTriExp.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: StdNodalTriExp.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
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// DEALINGS IN THE SOFTWARE.
//
// Description: Nodal triangle routines built upon StdExpansion2D
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <LibUtilities/Foundations/ManagerAccess.h> // for PointsManager, etc
#include <StdRegions/StdNodalTriExp.h>
 
using namespace std;
 
namespace Nektar
{
namespace StdRegions
{
StdNodalTriExp::StdNodalTriExp(const LibUtilities::BasisKey &Ba,
                               const LibUtilities::BasisKey &Bb,
                               LibUtilities::PointsType Ntype)
    : StdExpansion(LibUtilities::StdTriData::getNumberOfCoefficients(
                       Ba.GetNumModes(), Bb.GetNumModes()),
                   2, Ba, Bb),
      StdExpansion2D(LibUtilities::StdTriData::getNumberOfCoefficients(
                         Ba.GetNumModes(), Bb.GetNumModes()),
                     Ba, Bb),
      StdTriExp(Ba, Bb), m_nodalPointsKey(Ba.GetNumModes(), Ntype)
{
    ASSERTL0(m_base[0]->GetNumModes() == m_base[1]->GetNumModes(),
             "Nodal basis initiated with different orders in the a "
             "and b directions");
}
 
StdNodalTriExp::StdNodalTriExp(const StdNodalTriExp &T)
    : StdExpansion(T), StdExpansion2D(T), StdTriExp(T),
      m_nodalPointsKey(T.m_nodalPointsKey)
{
}
 
bool StdNodalTriExp::v_IsNodalNonTensorialExp()
{
    return true;
}
 
//-------------------------------
// Nodal basis specific routines
//-------------------------------
 
void StdNodalTriExp::NodalToModal(const Array<OneD, const NekDouble> &inarray,
                                  Array<OneD, NekDouble> &outarray)
{
    StdMatrixKey Nkey(eInvNBasisTrans, DetShapeType(), *this,
                      NullConstFactorMap, NullVarCoeffMap,
                      m_nodalPointsKey.GetPointsType());
    DNekMatSharedPtr inv_vdm = GetStdMatrix(Nkey);
 
    NekVector<NekDouble> nodal(m_ncoeffs, inarray, eWrapper);
    NekVector<NekDouble> modal(m_ncoeffs, outarray, eWrapper);
    modal = (*inv_vdm) * nodal;
}
 
// Operate with transpose of NodalToModal transformation
void StdNodalTriExp::NodalToModalTranspose(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    StdMatrixKey Nkey(eInvNBasisTrans, DetShapeType(), *this,
                      NullConstFactorMap, NullVarCoeffMap,
                      m_nodalPointsKey.GetPointsType());
    DNekMatSharedPtr inv_vdm = GetStdMatrix(Nkey);
 
    NekVector<NekDouble> nodal(m_ncoeffs, inarray, eCopy);
    NekVector<NekDouble> modal(m_ncoeffs, outarray, eWrapper);
    modal = Transpose(*inv_vdm) * nodal;
}
 
void StdNodalTriExp::ModalToNodal(const Array<OneD, const NekDouble> &inarray,
                                  Array<OneD, NekDouble> &outarray)
{
    StdMatrixKey Nkey(eNBasisTrans, DetShapeType(), *this, NullConstFactorMap,
                      NullVarCoeffMap, m_nodalPointsKey.GetPointsType());
    DNekMatSharedPtr vdm = GetStdMatrix(Nkey);
 
    // Multiply out matrix
    NekVector<NekDouble> modal(m_ncoeffs, inarray, eWrapper);
    NekVector<NekDouble> nodal(m_ncoeffs, outarray, eWrapper);
    nodal = (*vdm) * modal;
}
 
void StdNodalTriExp::GetNodalPoints(Array<OneD, const NekDouble> &x,
                                    Array<OneD, const NekDouble> &y)
{
    LibUtilities::PointsManager()[m_nodalPointsKey]->GetPoints(x, y);
}
 
DNekMatSharedPtr StdNodalTriExp::GenNBasisTransMatrix()
{
    int i, j;
    Array<OneD, const NekDouble> r, s;
    Array<OneD, NekDouble> c(2);
    DNekMatSharedPtr Mat;
 
    Mat = MemoryManager<DNekMat>::AllocateSharedPtr(m_ncoeffs, m_ncoeffs);
    GetNodalPoints(r, s);
 
    // Store the values of m_phys in a temporary array
    int nqtot = GetTotPoints();
    Array<OneD, NekDouble> phys(nqtot);
 
    for (i = 0; i < m_ncoeffs; ++i)
    {
        // fill physical space with mode i
        StdTriExp::v_FillMode(i, phys);
 
        // interpolate mode i to the Nodal points 'j' and
        // store in outarray
        for (j = 0; j < m_ncoeffs; ++j)
        {
            c[0]         = r[j];
            c[1]         = s[j];
            (*Mat)(j, i) = StdExpansion2D::v_PhysEvaluate(c, phys);
        }
    }
    return Mat;
}
 
//---------------------------------------
// Transforms
//---------------------------------------
 
void StdNodalTriExp::v_BwdTrans(const Array<OneD, const NekDouble> &inarray,
                                Array<OneD, NekDouble> &outarray)
{
    v_BwdTrans_SumFac(inarray, outarray);
}
 
void StdNodalTriExp::v_BwdTrans_SumFac(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    Array<OneD, NekDouble> tmp(m_ncoeffs);
    NodalToModal(inarray, tmp);
    StdTriExp::v_BwdTrans_SumFac(tmp, outarray);
}
 
void StdNodalTriExp::v_FwdTrans(const Array<OneD, const NekDouble> &inarray,
                                Array<OneD, NekDouble> &outarray)
{
    v_IProductWRTBase(inarray, outarray);
 
    // get Mass matrix inverse
    StdMatrixKey masskey(eInvMass, DetShapeType(), *this, NullConstFactorMap,
                         NullVarCoeffMap, m_nodalPointsKey.GetPointsType());
    DNekMatSharedPtr matsys = GetStdMatrix(masskey);
 
    // copy inarray in case inarray == outarray
    NekVector<NekDouble> in(m_ncoeffs, outarray, eCopy);
    NekVector<NekDouble> out(m_ncoeffs, outarray, eWrapper);
 
    out = (*matsys) * in;
}
 
//---------------------------------------
// Inner product functions
//---------------------------------------
 
void StdNodalTriExp::v_IProductWRTBase(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    v_IProductWRTBase_SumFac(inarray, outarray);
}
 
void StdNodalTriExp::v_IProductWRTBase_SumFac(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, bool multiplybyweights)
{
    StdTriExp::v_IProductWRTBase_SumFac(inarray, outarray, multiplybyweights);
    NodalToModalTranspose(outarray, outarray);
}
 
void StdNodalTriExp::v_IProductWRTDerivBase(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}
 
void StdNodalTriExp::v_IProductWRTDerivBase_SumFac(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    StdTriExp::v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
    NodalToModalTranspose(outarray, outarray);
}
 
//---------------------------------------
// Evaluation functions
//---------------------------------------
 
void StdNodalTriExp::v_FillMode(const int mode,
                                Array<OneD, NekDouble> &outarray)
{
    ASSERTL2(mode >= m_ncoeffs,
             "calling argument mode is larger than total expansion order");
 
    Vmath::Zero(m_ncoeffs, outarray, 1);
    outarray[mode] = 1.0;
    v_BwdTrans(outarray, outarray);
}
 
//---------------------------
// Helper functions
//---------------------------
 
int StdNodalTriExp::v_NumBndryCoeffs() const
{
    return 3 + (GetBasisNumModes(0) - 2) + 2 * (GetBasisNumModes(1) - 2);
}
 
//--------------------------
// Mappings
//--------------------------
 
int StdNodalTriExp::v_GetVertexMap(const int localVertexId,
                                   bool useCoeffPacking)
{
    boost::ignore_unused(useCoeffPacking);
    ASSERTL0(localVertexId >= 0 && localVertexId <= 2,
             "Local Vertex ID must be between 0 and 2");
    return localVertexId;
}
 
void StdNodalTriExp::v_GetTraceToElementMap(const int eid,
                                            Array<OneD, unsigned int> &maparray,
                                            Array<OneD, int> &signarray,
                                            Orientation edgeOrient, int P,
                                            int Q)
{
    boost::ignore_unused(Q);
 
    ASSERTL0(eid >= 0 && eid <= 2, "Local Edge ID must be between 0 and 2");
 
    const int nEdgeCoeffs = GetTraceNcoeffs(eid);
 
    ASSERTL0(P == -1 || P == nEdgeCoeffs,
             "Nodal triangle not set up to deal with variable "
             "polynomial order.");
 
    if (maparray.size() != nEdgeCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nEdgeCoeffs);
    }
 
    if (signarray.size() != nEdgeCoeffs)
    {
        signarray = Array<OneD, int>(nEdgeCoeffs, 1);
    }
    else
    {
        fill(signarray.get(), signarray.get() + nEdgeCoeffs, 1);
    }
 
    Orientation orient = edgeOrient;
    if (eid == 2)
    {
        orient = orient == eForwards ? eBackwards : eForwards;
    }
 
    maparray[0]               = eid;
    maparray[nEdgeCoeffs - 1] = eid == 2 ? 0 : eid + 1;
    for (int i = 2; i < nEdgeCoeffs; i++)
    {
        maparray[i - 1] = eid * (nEdgeCoeffs - 2) + 1 + i;
    }
 
    if (orient == eBackwards)
    {
        reverse(maparray.get(), maparray.get() + nEdgeCoeffs);
    }
}
 
void StdNodalTriExp::v_GetTraceInteriorToElementMap(
    const int eid, Array<OneD, unsigned int> &maparray,
    Array<OneD, int> &signarray, const Orientation edgeOrient)
{
    ASSERTL0(eid >= 0 && eid <= 2, "Local Edge ID must be between 0 and 2");
 
    const int nEdgeIntCoeffs = GetTraceNcoeffs(eid) - 2;
 
    if (maparray.size() != nEdgeIntCoeffs)
    {
        maparray = Array<OneD, unsigned int>(nEdgeIntCoeffs);
    }
 
    if (signarray.size() != nEdgeIntCoeffs)
    {
        signarray = Array<OneD, int>(nEdgeIntCoeffs, 1);
    }
    else
    {
        fill(signarray.get(), signarray.get() + nEdgeIntCoeffs, 1);
    }
 
    Orientation orient = edgeOrient;
    if (eid == 2)
    {
        orient = orient == eForwards ? eBackwards : eForwards;
    }
 
    for (int i = 0; i < nEdgeIntCoeffs; i++)
    {
        maparray[i] = eid * nEdgeIntCoeffs + 3 + i;
    }
 
    if (orient == eBackwards)
    {
        reverse(maparray.get(), maparray.get() + nEdgeIntCoeffs);
    }
}
 
void StdNodalTriExp::v_GetInteriorMap(Array<OneD, unsigned int> &outarray)
{
    unsigned int i;
    if (outarray.size() != GetNcoeffs() - NumBndryCoeffs())
    {
        outarray = Array<OneD, unsigned int>(GetNcoeffs() - NumBndryCoeffs());
    }
 
    for (i = NumBndryCoeffs(); i < GetNcoeffs(); i++)
    {
        outarray[i - NumBndryCoeffs()] = i;
    }
}
 
void StdNodalTriExp::v_GetBoundaryMap(Array<OneD, unsigned int> &outarray)
{
    unsigned int i;
    if (outarray.size() != NumBndryCoeffs())
    {
        outarray = Array<OneD, unsigned int>(NumBndryCoeffs());
    }
 
    for (i = 0; i < NumBndryCoeffs(); i++)
    {
        outarray[i] = i;
    }
}
 
//---------------------------------------
// Wrapper functions
//---------------------------------------
 
DNekMatSharedPtr StdNodalTriExp::v_GenMatrix(const StdMatrixKey &mkey)
{
    DNekMatSharedPtr Mat;
 
    switch (mkey.GetMatrixType())
    {
        case eNBasisTrans:
            Mat = GenNBasisTransMatrix();
            break;
        default:
            Mat = StdExpansion::CreateGeneralMatrix(mkey);
            break;
    }
 
    return Mat;
}
 
DNekMatSharedPtr StdNodalTriExp::v_CreateStdMatrix(const StdMatrixKey &mkey)
{
    return StdNodalTriExp::v_GenMatrix(mkey);
}
 
//---------------------------------------
// Operator evaluation functions
//---------------------------------------
 
void StdNodalTriExp::v_MassMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                    Array<OneD, NekDouble> &outarray,
                                    const StdMatrixKey &mkey)
{
    StdExpansion::MassMatrixOp_MatFree(inarray, outarray, mkey);
}
 
void StdNodalTriExp::v_LaplacianMatrixOp(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdMatrixKey &mkey)
{
    StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                        mkey);
}
 
void StdNodalTriExp::v_LaplacianMatrixOp(
    const int k1, const int k2, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdMatrixKey &mkey)
 
{
    StdExpansion::LaplacianMatrixOp_MatFree(k1, k2, inarray, outarray, mkey);
}
 
void StdNodalTriExp::v_WeakDerivMatrixOp(
    const int i, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdMatrixKey &mkey)
{
    StdExpansion::WeakDerivMatrixOp_MatFree(i, inarray, outarray, mkey);
}
 
void StdNodalTriExp::v_HelmholtzMatrixOp(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdMatrixKey &mkey)
{
    StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                        mkey);
}
 
//---------------------------------------
// Private helper functions
//---------------------------------------
 
} // namespace StdRegions
} // namespace Nektar