StdExpansion3D.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: StdExpansion3D.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Daughter of StdExpansion. This class contains routine
// which are common to 3D expansion. Typically this inolves physiocal
// space operations.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/Foundations/Interp.h>
#include <StdRegions/StdExpansion3D.h>
 
#ifdef max
#undef max
#endif
 
namespace Nektar::StdRegions
{
 
StdExpansion3D::StdExpansion3D(
    [[maybe_unused]] int numcoeffs,
    [[maybe_unused]] const LibUtilities::BasisKey &Ba,
    [[maybe_unused]] const LibUtilities::BasisKey &Bb,
    [[maybe_unused]] const LibUtilities::BasisKey &Bc)
{
}
 
void StdExpansion3D::PhysTensorDeriv(
    const Array<OneD, const NekDouble> &inarray, Array<OneD, NekDouble> &out_dx,
    Array<OneD, NekDouble> &out_dy, Array<OneD, NekDouble> &out_dz)
{
    const int nquad0 = m_base[0]->GetNumPoints();
    const int nquad1 = m_base[1]->GetNumPoints();
    const int nquad2 = m_base[2]->GetNumPoints();
 
    Array<OneD, NekDouble> wsp(nquad0 * nquad1 * nquad2);
 
    // copy inarray to wsp in case inarray is used as outarray
    Vmath::Vcopy(nquad0 * nquad1 * nquad2, &inarray[0], 1, &wsp[0], 1);
 
    if (out_dx.size() > 0)
    {
        NekDouble *D0 = &((m_base[0]->GetD())->GetPtr())[0];
 
        Blas::Dgemm('N', 'N', nquad0, nquad1 * nquad2, nquad0, 1.0, D0, nquad0,
                    &wsp[0], nquad0, 0.0, &out_dx[0], nquad0);
    }
 
    if (out_dy.size() > 0)
    {
        NekDouble *D1 = &((m_base[1]->GetD())->GetPtr())[0];
        for (int j = 0; j < nquad2; ++j)
        {
            Blas::Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0,
                        &wsp[j * nquad0 * nquad1], nquad0, D1, nquad1, 0.0,
                        &out_dy[j * nquad0 * nquad1], nquad0);
        }
    }
 
    if (out_dz.size() > 0)
    {
        NekDouble *D2 = &((m_base[2]->GetD())->GetPtr())[0];
 
        Blas::Dgemm('N', 'T', nquad0 * nquad1, nquad2, nquad2, 1.0, &wsp[0],
                    nquad0 * nquad1, D2, nquad2, 0.0, &out_dz[0],
                    nquad0 * nquad1);
    }
}
 
void StdExpansion3D::BwdTrans_SumFacKernel(
    const Array<OneD, const NekDouble> &base0,
    const Array<OneD, const NekDouble> &base1,
    const Array<OneD, const NekDouble> &base2,
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
    bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
{
    v_BwdTrans_SumFacKernel(base0, base1, base2, inarray, outarray, wsp,
                            doCheckCollDir0, doCheckCollDir1, doCheckCollDir2);
}
 
void StdExpansion3D::IProductWRTBase_SumFacKernel(
    const Array<OneD, const NekDouble> &base0,
    const Array<OneD, const NekDouble> &base1,
    const Array<OneD, const NekDouble> &base2,
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
    bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
{
    v_IProductWRTBase_SumFacKernel(base0, base1, base2, inarray, outarray, wsp,
                                   doCheckCollDir0, doCheckCollDir1,
                                   doCheckCollDir2);
}
 
void StdExpansion3D::v_GenStdMatBwdDeriv(const int dir, DNekMatSharedPtr &mat)
{
    ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
 
    const int nq0 = m_base[0]->GetNumPoints();
    const int nq1 = m_base[1]->GetNumPoints();
    const int nq2 = m_base[2]->GetNumPoints();
    const int nq  = nq0 * nq1 * nq2;
    const int nm0 = m_base[0]->GetNumModes();
    const int nm1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> alloc(4 * nq + m_ncoeffs + nm0 * nq2 * (nq1 + nm1),
                                 0.0);
    Array<OneD, NekDouble> tmp1(alloc);           // Quad metric
    Array<OneD, NekDouble> tmp2(alloc + nq);      // Dir1 metric
    Array<OneD, NekDouble> tmp3(alloc + 2 * nq);  // Dir2 metric
    Array<OneD, NekDouble> tmp4(alloc + 3 * nq);  // Dir3 metric
    Array<OneD, NekDouble> tmp5(alloc + 4 * nq);  // iprod tmp
    Array<OneD, NekDouble> wsp(tmp5 + m_ncoeffs); // Wsp
    switch (dir)
    {
        case 0:
            for (int i = 0; i < nq; i++)
            {
                tmp2[i] = 1.0;
                IProductWRTBase_SumFacKernel(
                    m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                    m_base[2]->GetBdata(), tmp2, tmp5, wsp, false, true, true);
 
                tmp2[i] = 0.0;
 
                for (int j = 0; j < m_ncoeffs; j++)
                {
                    (*mat)(j, i) = tmp5[j];
                }
            }
            break;
        case 1:
            for (int i = 0; i < nq; i++)
            {
                tmp2[i] = 1.0;
                IProductWRTBase_SumFacKernel(
                    m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                    m_base[2]->GetBdata(), tmp2, tmp5, wsp, true, false, true);
 
                tmp2[i] = 0.0;
 
                for (int j = 0; j < m_ncoeffs; j++)
                {
                    (*mat)(j, i) = tmp5[j];
                }
            }
            break;
        case 2:
            for (int i = 0; i < nq; i++)
            {
                tmp2[i] = 1.0;
                IProductWRTBase_SumFacKernel(
                    m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                    m_base[2]->GetDbdata(), tmp2, tmp5, wsp, true, true, false);
                tmp2[i] = 0.0;
 
                for (int j = 0; j < m_ncoeffs; j++)
                {
                    (*mat)(j, i) = tmp5[j];
                }
            }
            break;
        default:
            NEKERROR(ErrorUtil::efatal, "Not a 2D expansion.");
            break;
    }
}
 
NekDouble StdExpansion3D::v_PhysEvaluate(
    const Array<OneD, const NekDouble> &coords,
    const Array<OneD, const NekDouble> &physvals)
{
    Array<OneD, NekDouble> eta(3);
 
    WARNINGL2(coords[0] >= -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
    WARNINGL2(coords[0] <= 1 + NekConstants::kNekZeroTol, "coord[0] >  1");
    WARNINGL2(coords[1] >= -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
    WARNINGL2(coords[1] <= 1 + NekConstants::kNekZeroTol, "coord[1] >  1");
    WARNINGL2(coords[2] >= -1 - NekConstants::kNekZeroTol, "coord[2] < -1");
    WARNINGL2(coords[2] <= 1 + NekConstants::kNekZeroTol, "coord[2] >  1");
 
    // Obtain local collapsed coordinate from Cartesian coordinate.
    LocCoordToLocCollapsed(coords, eta);
 
    const int nq0 = m_base[0]->GetNumPoints();
    const int nq1 = m_base[1]->GetNumPoints();
    const int nq2 = m_base[2]->GetNumPoints();
 
    Array<OneD, NekDouble> wsp1(nq1 * nq2), wsp2(nq2);
 
    // Construct the 2D square...
    const NekDouble *ptr = &physvals[0];
    for (int i = 0; i < nq1 * nq2; ++i, ptr += nq0)
    {
        wsp1[i] = StdExpansion::BaryEvaluate<0>(eta[0], ptr);
    }
 
    for (int i = 0; i < nq2; ++i)
    {
        wsp2[i] = StdExpansion::BaryEvaluate<1>(eta[1], &wsp1[i * nq1]);
    }
 
    return StdExpansion::BaryEvaluate<2>(eta[2], &wsp2[0]);
}
 
NekDouble StdExpansion3D::v_PhysEvaluateInterp(
    const Array<OneD, DNekMatSharedPtr> &I,
    const Array<OneD, const NekDouble> &physvals)
{
    NekDouble value;
 
    int Qx = m_base[0]->GetNumPoints();
    int Qy = m_base[1]->GetNumPoints();
    int Qz = m_base[2]->GetNumPoints();
 
    Array<OneD, NekDouble> sumFactorization_qr =
        Array<OneD, NekDouble>(Qy * Qz);
    Array<OneD, NekDouble> sumFactorization_r = Array<OneD, NekDouble>(Qz);
 
    // Lagrangian interpolation matrix
    NekDouble *interpolatingNodes = nullptr;
 
    // Interpolate first coordinate direction
    interpolatingNodes = &I[0]->GetPtr()[0];
 
    Blas::Dgemv('T', Qx, Qy * Qz, 1.0, &physvals[0], Qx, &interpolatingNodes[0],
                1, 0.0, &sumFactorization_qr[0], 1);
 
    // Interpolate in second coordinate direction
    interpolatingNodes = &I[1]->GetPtr()[0];
 
    Blas::Dgemv('T', Qy, Qz, 1.0, &sumFactorization_qr[0], Qy,
                &interpolatingNodes[0], 1, 0.0, &sumFactorization_r[0], 1);
 
    // Interpolate in third coordinate direction
    interpolatingNodes = &I[2]->GetPtr()[0];
    value = Blas::Ddot(Qz, interpolatingNodes, 1, &sumFactorization_r[0], 1);
 
    return value;
}
 
/**
 * @param   inarray     Input coefficients.
 * @param   output      Output coefficients.
 * @param   mkey        Matrix key
 */
void StdExpansion3D::v_LaplacianMatrixOp_MatFree(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdRegions::StdMatrixKey &mkey)
{
    if (mkey.GetNVarCoeff() == 0 &&
        !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
        !mkey.ConstFactorExists(eFactorSVVCutoffRatio))
    {
        // This implementation is only valid when there are no
        // coefficients associated to the Laplacian operator
        int nqtot = GetTotPoints();
 
        const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
        const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
        const Array<OneD, const NekDouble> &base2 = m_base[2]->GetBdata();
 
        // Allocate temporary storage
        Array<OneD, NekDouble> wsp0(7 * nqtot);
        Array<OneD, NekDouble> wsp1(wsp0 + nqtot);
 
        if (!(m_base[0]->Collocation() && m_base[1]->Collocation() &&
              m_base[2]->Collocation()))
        {
            // LAPLACIAN MATRIX OPERATION
            // wsp0 = u       = B   * u_hat
            // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
            // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
            BwdTrans_SumFacKernel(base0, base1, base2, inarray, wsp0, wsp1,
                                  true, true, true);
            LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
        }
        else
        {
            LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
        }
    }
    else
    {
        StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                            mkey);
    }
}
 
void StdExpansion3D::v_HelmholtzMatrixOp_MatFree(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdRegions::StdMatrixKey &mkey)
{
    if (mkey.GetNVarCoeff() == 0 &&
        !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00))
    {
        using std::max;
 
        int nquad0  = m_base[0]->GetNumPoints();
        int nquad1  = m_base[1]->GetNumPoints();
        int nquad2  = m_base[2]->GetNumPoints();
        int nmodes0 = m_base[0]->GetNumModes();
        int nmodes1 = m_base[1]->GetNumModes();
        int nmodes2 = m_base[2]->GetNumModes();
        int wspsize = max(nquad0 * nmodes2 * (nmodes1 + nquad1),
                          nquad0 * nquad1 * (nquad2 + nmodes0) +
                              nmodes0 * nmodes1 * nquad2);
 
        NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
 
        const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
        const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
        const Array<OneD, const NekDouble> &base2 = m_base[2]->GetBdata();
        Array<OneD, NekDouble> wsp0(8 * wspsize);
        Array<OneD, NekDouble> wsp1(wsp0 + 1 * wspsize);
        Array<OneD, NekDouble> wsp2(wsp0 + 2 * wspsize);
 
        if (!(m_base[0]->Collocation() && m_base[1]->Collocation() &&
              m_base[2]->Collocation()))
        {
            // MASS MATRIX OPERATION
            // The following is being calculated:
            // wsp0     = B   * u_hat = u
            // wsp1     = W   * wsp0
            // outarray = B^T * wsp1  = B^T * W * B * u_hat = M * u_hat
            BwdTrans_SumFacKernel(base0, base1, base2, inarray, wsp0, wsp2,
                                  true, true, true);
            MultiplyByQuadratureMetric(wsp0, wsp1);
            IProductWRTBase_SumFacKernel(base0, base1, base2, wsp1, outarray,
                                         wsp2, true, true, true);
            LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
        }
        else
        {
            // specialised implementation for the classical spectral
            // element method
            MultiplyByQuadratureMetric(inarray, outarray);
            LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
        }
 
        // outarray = lambda * outarray + wsp1
        //          = (lambda * M + L ) * u_hat
        Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1, &wsp1[0], 1,
                     &outarray[0], 1);
    }
    else
    {
        StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
                                                            mkey);
    }
}
 
NekDouble StdExpansion3D::v_Integral(
    const Array<OneD, const NekDouble> &inarray)
{
    const int nqtot = GetTotPoints();
    Array<OneD, NekDouble> tmp(GetTotPoints());
    v_MultiplyByStdQuadratureMetric(inarray, tmp);
    return Vmath::Vsum(nqtot, tmp, 1);
}
 
int StdExpansion3D::v_GetNedges(void) const
{
    NEKERROR(ErrorUtil::efatal, "This function is not valid or not defined");
    return 0;
}
 
int StdExpansion3D::v_GetEdgeNcoeffs([[maybe_unused]] const int i) const
{
    NEKERROR(ErrorUtil::efatal, "This function is not valid or not defined");
    return 0;
}
 
void StdExpansion3D::v_GetEdgeInteriorToElementMap(
    [[maybe_unused]] const int tid,
    [[maybe_unused]] Array<OneD, unsigned int> &maparray,
    [[maybe_unused]] Array<OneD, int> &signarray,
    [[maybe_unused]] Orientation traceOrient)
{
    NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
}
 
void StdExpansion3D::v_GetTraceToElementMap(const int tid,
                                            Array<OneD, unsigned int> &maparray,
                                            Array<OneD, int> &signarray,
                                            Orientation traceOrient, int P,
                                            int Q)
{
    Array<OneD, unsigned int> map1, map2;
    GetTraceCoeffMap(tid, map1);
    GetElmtTraceToTraceMap(tid, map2, signarray, traceOrient, P, Q);
 
    if (maparray.size() != map2.size())
    {
        maparray = Array<OneD, unsigned int>(map2.size());
    }
 
    for (int i = 0; i < map2.size(); ++i)
    {
        maparray[i] = map1[map2[i]];
    }
}
 
LibUtilities::BasisKey EvaluateQuadFaceBasisKey(
    [[maybe_unused]] const int facedir,
    const LibUtilities::BasisType faceDirBasisType, const int numpoints,
    const int nummodes)
{
 
    switch (faceDirBasisType)
    {
        case LibUtilities::eModified_A:
        {
            const LibUtilities::PointsKey pkey(
                numpoints, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eModified_A, nummodes,
                                          pkey);
        }
        case LibUtilities::eModified_B:
        case LibUtilities::eModified_C:
        {
            const LibUtilities::PointsKey pkey(
                numpoints + 1, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eModified_A, nummodes,
                                          pkey);
        }
        case LibUtilities::eGLL_Lagrange:
        {
            const LibUtilities::PointsKey pkey(
                numpoints, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eGLL_Lagrange, nummodes,
                                          pkey);
        }
        case LibUtilities::eOrtho_A:
        {
            const LibUtilities::PointsKey pkey(
                numpoints, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eOrtho_A, nummodes,
                                          pkey);
        }
        case LibUtilities::eOrtho_B:
        case LibUtilities::eOrtho_C:
        {
            const LibUtilities::PointsKey pkey(
                numpoints + 1, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eOrtho_A, nummodes,
                                          pkey);
        }
        default:
        {
            NEKERROR(ErrorUtil::efatal, "expansion type unknown");
            break;
        }
    }
 
    // Keep things happy by returning a value.
    return LibUtilities::NullBasisKey;
}
 
LibUtilities::BasisKey EvaluateTriFaceBasisKey(
    const int facedir, const LibUtilities::BasisType faceDirBasisType,
    const int numpoints, const int nummodes, bool UseGLL)
{
    switch (faceDirBasisType)
    {
        case LibUtilities::eModified_A:
        {
            const LibUtilities::PointsKey pkey(
                numpoints, LibUtilities::eGaussLobattoLegendre);
            return LibUtilities::BasisKey(LibUtilities::eModified_A, nummodes,
                                          pkey);
        }
        case LibUtilities::eModified_B:
        case LibUtilities::eModified_C:
        case LibUtilities::eModifiedPyr_C:
        {
            switch (facedir)
            {
                case 0:
                {
                    const LibUtilities::PointsKey pkey(
                        numpoints + 1, LibUtilities::eGaussLobattoLegendre);
                    return LibUtilities::BasisKey(LibUtilities::eModified_A,
                                                  nummodes, pkey);
                }
                case 1:
                {
                    LibUtilities::PointsKey pkey;
 
                    if (UseGLL)
                    {
                        pkey = LibUtilities::PointsKey(
                            numpoints + 1, LibUtilities::eGaussLobattoLegendre);
                    }
                    else
                    {
                        pkey = LibUtilities::PointsKey(
                            numpoints, LibUtilities::eGaussRadauMAlpha1Beta0);
                    }
                    return LibUtilities::BasisKey(LibUtilities::eModified_B,
                                                  nummodes, pkey);
                }
                default:
                {
 
                    NEKERROR(ErrorUtil::efatal, "invalid value to flag");
                    break;
                }
            }
            break;
        }
 
        case LibUtilities::eGLL_Lagrange:
        {
            switch (facedir)
            {
                case 0:
                {
                    const LibUtilities::PointsKey pkey(
                        numpoints, LibUtilities::eGaussLobattoLegendre);
                    return LibUtilities::BasisKey(LibUtilities::eOrtho_A,
                                                  nummodes, pkey);
                }
                case 1:
                {
                    const LibUtilities::PointsKey pkey(
                        numpoints, LibUtilities::eGaussRadauMAlpha1Beta0);
                    return LibUtilities::BasisKey(LibUtilities::eOrtho_B,
                                                  nummodes, pkey);
                }
                default:
                {
                    NEKERROR(ErrorUtil::efatal, "invalid value to flag");
                    break;
                }
            }
            break;
        }
 
        case LibUtilities::eOrtho_A:
        case LibUtilities::eOrtho_B:
        case LibUtilities::eOrtho_C:
        case LibUtilities::eOrthoPyr_C:
        {
            switch (facedir)
            {
                case 0:
                {
                    const LibUtilities::PointsKey pkey(
                        numpoints, LibUtilities::eGaussLobattoLegendre);
                    return LibUtilities::BasisKey(LibUtilities::eOrtho_A,
                                                  nummodes, pkey);
                }
                case 1:
                {
                    const LibUtilities::PointsKey pkey(
                        numpoints, LibUtilities::eGaussRadauMAlpha1Beta0);
                    return LibUtilities::BasisKey(LibUtilities::eOrtho_B,
                                                  nummodes, pkey);
                }
                default:
                {
                    NEKERROR(ErrorUtil::efatal, "invalid value to flag");
                    break;
                }
            }
            break;
        }
        default:
        {
            NEKERROR(ErrorUtil::efatal, "expansion type unknown");
            break;
        }
    }
 
    // Keep things happy by returning a value.
    return LibUtilities::NullBasisKey;
}
 
void StdExpansion3D::v_PhysInterp(std::shared_ptr<StdExpansion> fromExp,
                                  const Array<OneD, const NekDouble> &fromData,
                                  Array<OneD, NekDouble> &toData)
{
 
    LibUtilities::Interp3D(fromExp->GetBasis(0)->GetPointsKey(),
                           fromExp->GetBasis(1)->GetPointsKey(),
                           fromExp->GetBasis(2)->GetPointsKey(), fromData,
                           m_base[0]->GetPointsKey(), m_base[1]->GetPointsKey(),
                           m_base[2]->GetPointsKey(), toData);
}
 
} // namespace Nektar::StdRegions