PrismExp.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File PrismExp.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:  PrismExp routines
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <LibUtilities/Foundations/Interp.h>
#include <LibUtilities/Foundations/InterpCoeff.h>
#include <LocalRegions/PrismExp.h>
#include <SpatialDomains/SegGeom.h>
 
using namespace std;
 
namespace Nektar
{
namespace LocalRegions
{
 
PrismExp::PrismExp(const LibUtilities::BasisKey &Ba,
                   const LibUtilities::BasisKey &Bb,
                   const LibUtilities::BasisKey &Bc,
                   const SpatialDomains::PrismGeomSharedPtr &geom)
    : StdExpansion(LibUtilities::StdPrismData::getNumberOfCoefficients(
                       Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
                   3, Ba, Bb, Bc),
      StdExpansion3D(LibUtilities::StdPrismData::getNumberOfCoefficients(
                         Ba.GetNumModes(), Bb.GetNumModes(), Bc.GetNumModes()),
                     Ba, Bb, Bc),
      StdPrismExp(Ba, Bb, Bc), Expansion(geom), Expansion3D(geom),
      m_matrixManager(
          std::bind(&Expansion3D::CreateMatrix, this, std::placeholders::_1),
          std::string("PrismExpMatrix")),
      m_staticCondMatrixManager(std::bind(&Expansion::CreateStaticCondMatrix,
                                          this, std::placeholders::_1),
                                std::string("PrismExpStaticCondMatrix"))
{
}
 
PrismExp::PrismExp(const PrismExp &T)
    : StdExpansion(T), StdExpansion3D(T), StdPrismExp(T), Expansion(T),
      Expansion3D(T), m_matrixManager(T.m_matrixManager),
      m_staticCondMatrixManager(T.m_staticCondMatrixManager)
{
}
 
PrismExp::~PrismExp()
{
}
 
//-------------------------------
// Integration Methods
//-------------------------------
 
/**
 * \brief Integrate the physical point list \a inarray over prismatic
 * region and return the value.
 *
 * Inputs:\n
 *
 * - \a inarray: definition of function to be returned at quadrature
 * point of expansion.
 *
 * Outputs:\n
 *
 * - returns \f$\int^1_{-1}\int^1_{-1}\int^1_{-1} u(\bar \eta_1,
 *  \xi_2, \xi_3) J[i,j,k] d \bar \eta_1 d \xi_2 d \xi_3 \f$ \n \f$ =
 *  \sum_{i=0}^{Q_1 - 1} \sum_{j=0}^{Q_2 - 1} \sum_{k=0}^{Q_3 - 1}
 *  u(\bar \eta_{1i}^{0,0}, \xi_{2j}^{0,0},\xi_{3k}^{1,0})w_{i}^{0,0}
 *  w_{j}^{0,0} \hat w_{k}^{1,0} \f$ \n where \f$ inarray[i,j, k] =
 *  u(\bar \eta_{1i}^{0,0}, \xi_{2j}^{0,0},\xi_{3k}^{1,0}) \f$, \n
 *  \f$\hat w_{i}^{1,0} = \frac {w_{j}^{1,0}} {2} \f$ \n and \f$
 *  J[i,j,k] \f$ is the Jacobian evaluated at the quadrature point.
 */
NekDouble PrismExp::v_Integral(const Array<OneD, const NekDouble> &inarray)
{
    int nquad0                       = m_base[0]->GetNumPoints();
    int nquad1                       = m_base[1]->GetNumPoints();
    int nquad2                       = m_base[2]->GetNumPoints();
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    Array<OneD, NekDouble> tmp(nquad0 * nquad1 * nquad2);
 
    // Multiply inarray with Jacobian
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nquad0 * nquad1 * nquad2, &jac[0], 1,
                    (NekDouble *)&inarray[0], 1, &tmp[0], 1);
    }
    else
    {
        Vmath::Smul(nquad0 * nquad1 * nquad2, (NekDouble)jac[0],
                    (NekDouble *)&inarray[0], 1, &tmp[0], 1);
    }
 
    // Call StdPrismExp version.
    return StdPrismExp::v_Integral(tmp);
}
 
//----------------------------
// Differentiation Methods
//----------------------------
void PrismExp::v_PhysDeriv(const Array<OneD, const NekDouble> &inarray,
                           Array<OneD, NekDouble> &out_d0,
                           Array<OneD, NekDouble> &out_d1,
                           Array<OneD, NekDouble> &out_d2)
{
    int nqtot = GetTotPoints();
 
    Array<TwoD, const NekDouble> df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    Array<OneD, NekDouble> diff0(nqtot);
    Array<OneD, NekDouble> diff1(nqtot);
    Array<OneD, NekDouble> diff2(nqtot);
 
    StdPrismExp::v_PhysDeriv(inarray, diff0, diff1, diff2);
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        if (out_d0.size())
        {
            Vmath::Vmul(nqtot, &df[0][0], 1, &diff0[0], 1, &out_d0[0], 1);
            Vmath::Vvtvp(nqtot, &df[1][0], 1, &diff1[0], 1, &out_d0[0], 1,
                         &out_d0[0], 1);
            Vmath::Vvtvp(nqtot, &df[2][0], 1, &diff2[0], 1, &out_d0[0], 1,
                         &out_d0[0], 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Vmul(nqtot, &df[3][0], 1, &diff0[0], 1, &out_d1[0], 1);
            Vmath::Vvtvp(nqtot, &df[4][0], 1, &diff1[0], 1, &out_d1[0], 1,
                         &out_d1[0], 1);
            Vmath::Vvtvp(nqtot, &df[5][0], 1, &diff2[0], 1, &out_d1[0], 1,
                         &out_d1[0], 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Vmul(nqtot, &df[6][0], 1, &diff0[0], 1, &out_d2[0], 1);
            Vmath::Vvtvp(nqtot, &df[7][0], 1, &diff1[0], 1, &out_d2[0], 1,
                         &out_d2[0], 1);
            Vmath::Vvtvp(nqtot, &df[8][0], 1, &diff2[0], 1, &out_d2[0], 1,
                         &out_d2[0], 1);
        }
    }
    else // regular geometry
    {
        if (out_d0.size())
        {
            Vmath::Smul(nqtot, df[0][0], &diff0[0], 1, &out_d0[0], 1);
            Blas::Daxpy(nqtot, df[1][0], &diff1[0], 1, &out_d0[0], 1);
            Blas::Daxpy(nqtot, df[2][0], &diff2[0], 1, &out_d0[0], 1);
        }
 
        if (out_d1.size())
        {
            Vmath::Smul(nqtot, df[3][0], &diff0[0], 1, &out_d1[0], 1);
            Blas::Daxpy(nqtot, df[4][0], &diff1[0], 1, &out_d1[0], 1);
            Blas::Daxpy(nqtot, df[5][0], &diff2[0], 1, &out_d1[0], 1);
        }
 
        if (out_d2.size())
        {
            Vmath::Smul(nqtot, df[6][0], &diff0[0], 1, &out_d2[0], 1);
            Blas::Daxpy(nqtot, df[7][0], &diff1[0], 1, &out_d2[0], 1);
            Blas::Daxpy(nqtot, df[8][0], &diff2[0], 1, &out_d2[0], 1);
        }
    }
}
 
//---------------------------------------
// Transforms
//---------------------------------------
 
/**
 * \brief Forward transform from physical quadrature space stored in
 * \a inarray and evaluate the expansion coefficients and store in \a
 * (this)->m_coeffs
 *
 * Inputs:\n
 *
 * - \a inarray: array of physical quadrature points to be transformed
 *
 * Outputs:\n
 *
 * - (this)->_coeffs: updated array of expansion coefficients.
 */
void PrismExp::v_FwdTrans(const Array<OneD, const NekDouble> &inarray,
                          Array<OneD, NekDouble> &outarray)
{
    if (m_base[0]->Collocation() && m_base[1]->Collocation() &&
        m_base[2]->Collocation())
    {
        Vmath::Vcopy(GetNcoeffs(), &inarray[0], 1, &outarray[0], 1);
    }
    else
    {
        v_IProductWRTBase(inarray, outarray);
 
        // get Mass matrix inverse
        MatrixKey masskey(StdRegions::eInvMass, DetShapeType(), *this);
        DNekScalMatSharedPtr matsys = m_matrixManager[masskey];
 
        // copy inarray in case inarray == outarray
        DNekVec in(m_ncoeffs, outarray);
        DNekVec out(m_ncoeffs, outarray, eWrapper);
 
        out = (*matsys) * in;
    }
}
 
//---------------------------------------
// Inner product functions
//---------------------------------------
 
/**
 * \brief Calculate the inner product of inarray with respect to the
 * basis B=base0*base1*base2 and put into outarray:
 *
 * \f$ \begin{array}{rcl} I_{pqr} = (\phi_{pqr}, u)_{\delta} & = &
 * \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \sum_{k=0}^{nq_2} \psi_{p}^{a}
 * (\bar \eta_{1i}) \psi_{q}^{a} (\xi_{2j}) \psi_{pr}^{b} (\xi_{3k})
 * w_i w_j w_k u(\bar \eta_{1,i} \xi_{2,j} \xi_{3,k}) J_{i,j,k}\\ & =
 * & \sum_{i=0}^{nq_0} \psi_p^a(\bar \eta_{1,i}) \sum_{j=0}^{nq_1}
 * \psi_{q}^a(\xi_{2,j}) \sum_{k=0}^{nq_2} \psi_{pr}^b u(\bar
 * \eta_{1i},\xi_{2j},\xi_{3k}) J_{i,j,k} \end{array} \f$ \n
 *
 * where
 *
 * \f$ \phi_{pqr} (\xi_1 , \xi_2 , \xi_3) = \psi_p^a (\bar \eta_1)
 * \psi_{q}^a (\xi_2) \psi_{pr}^b (\xi_3) \f$ \n
 *
 * which can be implemented as \n \f$f_{pr} (\xi_{3k}) =
 * \sum_{k=0}^{nq_3} \psi_{pr}^b u(\bar \eta_{1i},\xi_{2j},\xi_{3k})
 * J_{i,j,k} = {\bf B_3 U} \f$ \n \f$ g_{q} (\xi_{3k}) =
 * \sum_{j=0}^{nq_1} \psi_{q}^a (\xi_{2j}) f_{pr} (\xi_{3k}) = {\bf
 * B_2 F} \f$ \n \f$ (\phi_{pqr}, u)_{\delta} = \sum_{k=0}^{nq_0}
 * \psi_{p}^a (\xi_{3k}) g_{q} (\xi_{3k}) = {\bf B_1 G} \f$
 */
void PrismExp::v_IProductWRTBase(const Array<OneD, const NekDouble> &inarray,
                                 Array<OneD, NekDouble> &outarray)
{
    v_IProductWRTBase_SumFac(inarray, outarray);
}
 
void PrismExp::v_IProductWRTBase_SumFac(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, bool multiplybyweights)
{
    const int nquad0 = m_base[0]->GetNumPoints();
    const int nquad1 = m_base[1]->GetNumPoints();
    const int nquad2 = m_base[2]->GetNumPoints();
    const int order0 = m_base[0]->GetNumModes();
    const int order1 = m_base[1]->GetNumModes();
 
    Array<OneD, NekDouble> wsp(order0 * nquad2 * (nquad1 + order1));
 
    if (multiplybyweights)
    {
        Array<OneD, NekDouble> tmp(nquad0 * nquad1 * nquad2);
 
        MultiplyByQuadratureMetric(inarray, tmp);
 
        IProductWRTBase_SumFacKernel(
            m_base[0]->GetBdata(), m_base[1]->GetBdata(), m_base[2]->GetBdata(),
            tmp, outarray, wsp, true, true, true);
    }
    else
    {
        IProductWRTBase_SumFacKernel(
            m_base[0]->GetBdata(), m_base[1]->GetBdata(), m_base[2]->GetBdata(),
            inarray, outarray, wsp, true, true, true);
    }
}
 
/**
 * @brief Calculates the inner product \f$ I_{pqr} = (u,
 * \partial_{x_i} \phi_{pqr}) \f$.
 *
 * The derivative of the basis functions is performed using the chain
 * rule in order to incorporate the geometric factors. Assuming that
 * the basis functions are a tensor product
 * \f$\phi_{pqr}(\eta_1,\eta_2,\eta_3) =
 * \phi_1(\eta_1)\phi_2(\eta_2)\phi_3(\eta_3)\f$, this yields the
 * result
 *
 * \f[
 * I_{pqr} = \sum_{j=1}^3 \left(u, \frac{\partial u}{\partial \eta_j}
 * \frac{\partial \eta_j}{\partial x_i}\right)
 * \f]
 *
 * In the tetrahedral element, we must also incorporate a second set
 * of geometric factors which incorporate the collapsed co-ordinate
 * system, so that
 *
 * \f[ \frac{\partial\eta_j}{\partial x_i} = \sum_{k=1}^3
 * \frac{\partial\eta_j}{\partial\xi_k}\frac{\partial\xi_k}{\partial
 * x_i} \f]
 *
 * These derivatives can be found on p152 of Sherwin & Karniadakis.
 *
 * @param dir       Direction in which to take the derivative.
 * @param inarray   The function \f$ u \f$.
 * @param outarray  Value of the inner product.
 */
void PrismExp::v_IProductWRTDerivBase(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    v_IProductWRTDerivBase_SumFac(dir, inarray, outarray);
}
 
void PrismExp::v_IProductWRTDerivBase_SumFac(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray)
{
    const int nquad0 = m_base[0]->GetNumPoints();
    const int nquad1 = m_base[1]->GetNumPoints();
    const int nquad2 = m_base[2]->GetNumPoints();
    const int order0 = m_base[0]->GetNumModes();
    const int order1 = m_base[1]->GetNumModes();
    const int nqtot  = nquad0 * nquad1 * nquad2;
 
    Array<OneD, NekDouble> tmp1(nqtot);
    Array<OneD, NekDouble> tmp2(nqtot);
    Array<OneD, NekDouble> tmp3(nqtot);
    Array<OneD, NekDouble> tmp4(nqtot);
    Array<OneD, NekDouble> tmp6(m_ncoeffs);
    Array<OneD, NekDouble> wsp(order0 * nquad2 * (nquad1 + order1));
 
    MultiplyByQuadratureMetric(inarray, tmp1);
 
    Array<OneD, Array<OneD, NekDouble>> tmp2D{3};
    tmp2D[0] = tmp2;
    tmp2D[1] = tmp3;
    tmp2D[2] = tmp4;
 
    PrismExp::v_AlignVectorToCollapsedDir(dir, tmp1, tmp2D);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetBdata(), tmp2, outarray, wsp,
                                 true, true, true);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
                                 m_base[2]->GetBdata(), tmp3, tmp6, wsp, true,
                                 true, true);
 
    Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);
 
    IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
                                 m_base[2]->GetDbdata(), tmp4, tmp6, wsp, true,
                                 true, true);
 
    Vmath::Vadd(m_ncoeffs, tmp6, 1, outarray, 1, outarray, 1);
}
 
void PrismExp::v_AlignVectorToCollapsedDir(
    const int dir, const Array<OneD, const NekDouble> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    const int nquad0 = m_base[0]->GetNumPoints();
    const int nquad1 = m_base[1]->GetNumPoints();
    const int nquad2 = m_base[2]->GetNumPoints();
    const int order0 = m_base[0]->GetNumModes();
    const int order1 = m_base[1]->GetNumModes();
    const int nqtot  = nquad0 * nquad1 * nquad2;
 
    const Array<OneD, const NekDouble> &z0 = m_base[0]->GetZ();
    const Array<OneD, const NekDouble> &z2 = m_base[2]->GetZ();
 
    Array<OneD, NekDouble> gfac0(nquad0);
    Array<OneD, NekDouble> gfac2(nquad2);
    Array<OneD, NekDouble> tmp1(nqtot);
    Array<OneD, NekDouble> tmp5(nqtot);
    Array<OneD, NekDouble> tmp6(m_ncoeffs);
    Array<OneD, NekDouble> wsp(order0 * nquad2 * (nquad1 + order1));
 
    Array<OneD, NekDouble> tmp2 = outarray[0];
    Array<OneD, NekDouble> tmp3 = outarray[1];
    Array<OneD, NekDouble> tmp4 = outarray[2];
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    Vmath::Vcopy(nqtot, inarray, 1, tmp1, 1); // Dir3 metric
 
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vmul(nqtot, &df[3 * dir][0], 1, tmp1.get(), 1, tmp2.get(), 1);
        Vmath::Vmul(nqtot, &df[3 * dir + 1][0], 1, tmp1.get(), 1, tmp3.get(),
                    1);
        Vmath::Vmul(nqtot, &df[3 * dir + 2][0], 1, tmp1.get(), 1, tmp4.get(),
                    1);
    }
    else
    {
        Vmath::Smul(nqtot, df[3 * dir][0], tmp1.get(), 1, tmp2.get(), 1);
        Vmath::Smul(nqtot, df[3 * dir + 1][0], tmp1.get(), 1, tmp3.get(), 1);
        Vmath::Smul(nqtot, df[3 * dir + 2][0], tmp1.get(), 1, tmp4.get(), 1);
    }
 
    // set up geometric factor: (1+z0)/2
    for (int i = 0; i < nquad0; ++i)
    {
        gfac0[i] = 0.5 * (1 + z0[i]);
    }
 
    // Set up geometric factor: 2/(1-z2)
    for (int i = 0; i < nquad2; ++i)
    {
        gfac2[i] = 2.0 / (1 - z2[i]);
    }
 
    const int nq01 = nquad0 * nquad1;
 
    for (int i = 0; i < nquad2; ++i)
    {
        Vmath::Smul(nq01, gfac2[i], &tmp2[0] + i * nq01, 1, &tmp2[0] + i * nq01,
                    1);
        Vmath::Smul(nq01, gfac2[i], &tmp4[0] + i * nq01, 1, &tmp5[0] + i * nq01,
                    1);
    }
 
    for (int i = 0; i < nquad1 * nquad2; ++i)
    {
        Vmath::Vmul(nquad0, &gfac0[0], 1, &tmp5[0] + i * nquad0, 1,
                    &tmp5[0] + i * nquad0, 1);
    }
 
    Vmath::Vadd(nqtot, &tmp2[0], 1, &tmp5[0], 1, &tmp2[0], 1);
}
 
//---------------------------------------
// Evaluation functions
//---------------------------------------
 
StdRegions::StdExpansionSharedPtr PrismExp::v_GetStdExp(void) const
{
    return MemoryManager<StdRegions::StdPrismExp>::AllocateSharedPtr(
        m_base[0]->GetBasisKey(), m_base[1]->GetBasisKey(),
        m_base[2]->GetBasisKey());
}
 
StdRegions::StdExpansionSharedPtr PrismExp::v_GetLinStdExp(void) const
{
    LibUtilities::BasisKey bkey0(m_base[0]->GetBasisType(), 2,
                                 m_base[0]->GetPointsKey());
    LibUtilities::BasisKey bkey1(m_base[1]->GetBasisType(), 2,
                                 m_base[1]->GetPointsKey());
    LibUtilities::BasisKey bkey2(m_base[2]->GetBasisType(), 2,
                                 m_base[2]->GetPointsKey());
 
    return MemoryManager<StdRegions::StdPrismExp>::AllocateSharedPtr(
        bkey0, bkey1, bkey2);
}
 
/**
 * @brief Get the coordinates #coords at the local coordinates
 * #Lcoords.
 */
void PrismExp::v_GetCoord(const Array<OneD, const NekDouble> &Lcoords,
                          Array<OneD, NekDouble> &coords)
{
    int i;
 
    ASSERTL1(Lcoords[0] <= -1.0 && Lcoords[0] >= 1.0 && Lcoords[1] <= -1.0 &&
                 Lcoords[1] >= 1.0 && Lcoords[2] <= -1.0 && Lcoords[2] >= 1.0,
             "Local coordinates are not in region [-1,1]");
 
    m_geom->FillGeom();
 
    for (i = 0; i < m_geom->GetCoordim(); ++i)
    {
        coords[i] = m_geom->GetCoord(i, Lcoords);
    }
}
 
void PrismExp::v_GetCoords(Array<OneD, NekDouble> &coords_0,
                           Array<OneD, NekDouble> &coords_1,
                           Array<OneD, NekDouble> &coords_2)
{
    Expansion::v_GetCoords(coords_0, coords_1, coords_2);
}
 
/**
 * Given the local cartesian coordinate \a Lcoord evaluate the
 * value of physvals at this point by calling through to the
 * StdExpansion method
 */
NekDouble PrismExp::v_StdPhysEvaluate(
    const Array<OneD, const NekDouble> &Lcoord,
    const Array<OneD, const NekDouble> &physvals)
{
    // Evaluate point in local (eta) coordinates.
    return StdPrismExp::v_PhysEvaluate(Lcoord, physvals);
}
 
NekDouble PrismExp::v_PhysEvaluate(const Array<OneD, const NekDouble> &coord,
                                   const Array<OneD, const NekDouble> &physvals)
{
    Array<OneD, NekDouble> Lcoord(3);
 
    ASSERTL0(m_geom, "m_geom not defined");
 
    m_geom->GetLocCoords(coord, Lcoord);
 
    return StdPrismExp::v_PhysEvaluate(Lcoord, physvals);
}
 
//---------------------------------------
// Helper functions
//---------------------------------------
 
int PrismExp::v_GetCoordim()
{
    return m_geom->GetCoordim();
}
 
void PrismExp::v_ExtractDataToCoeffs(
    const NekDouble *data, const std::vector<unsigned int> &nummodes,
    const int mode_offset, NekDouble *coeffs,
    std::vector<LibUtilities::BasisType> &fromType)
{
    boost::ignore_unused(fromType);
 
    int data_order0 = nummodes[mode_offset];
    int fillorder0  = min(m_base[0]->GetNumModes(), data_order0);
    int data_order1 = nummodes[mode_offset + 1];
    int order1      = m_base[1]->GetNumModes();
    int fillorder1  = min(order1, data_order1);
    int data_order2 = nummodes[mode_offset + 2];
    int order2      = m_base[2]->GetNumModes();
    int fillorder2  = min(order2, data_order2);
 
    switch (m_base[0]->GetBasisType())
    {
        case LibUtilities::eModified_A:
        {
            int i, j;
            int cnt  = 0;
            int cnt1 = 0;
 
            ASSERTL1(m_base[1]->GetBasisType() == LibUtilities::eModified_A,
                     "Extraction routine not set up for this basis");
            ASSERTL1(m_base[2]->GetBasisType() == LibUtilities::eModified_B,
                     "Extraction routine not set up for this basis");
 
            Vmath::Zero(m_ncoeffs, coeffs, 1);
            for (j = 0; j < fillorder0; ++j)
            {
                for (i = 0; i < fillorder1; ++i)
                {
                    Vmath::Vcopy(fillorder2 - j, &data[cnt], 1, &coeffs[cnt1],
                                 1);
                    cnt += data_order2 - j;
                    cnt1 += order2 - j;
                }
 
                // count out data for j iteration
                for (i = fillorder1; i < data_order1; ++i)
                {
                    cnt += data_order2 - j;
                }
 
                for (i = fillorder1; i < order1; ++i)
                {
                    cnt1 += order2 - j;
                }
            }
        }
        break;
        default:
            ASSERTL0(false, "basis is either not set up or not "
                            "hierarchicial");
    }
}
 
void PrismExp::v_GetTracePhysMap(const int face, Array<OneD, int> &outarray)
{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int nq0    = 0;
    int nq1    = 0;
 
    switch (face)
    {
        case 0:
            nq0 = nquad0;
            nq1 = nquad1;
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Directions A and B positive
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                outarray[i] = i;
            }
            break;
        case 1:
 
            nq0 = nquad0;
            nq1 = nquad2;
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Direction A and B positive
            for (int k = 0; k < nquad2; k++)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    outarray[k * nquad0 + i] = (nquad0 * nquad1 * k) + i;
                }
            }
 
            break;
        case 2:
 
            nq0 = nquad1;
            nq1 = nquad2;
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Directions A and B positive
            for (int j = 0; j < nquad1 * nquad2; ++j)
            {
                outarray[j] = nquad0 - 1 + j * nquad0;
            }
            break;
        case 3:
            nq0 = nquad0;
            nq1 = nquad2;
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Direction A and B positive
            for (int k = 0; k < nquad2; k++)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    outarray[k * nquad0 + i] =
                        nquad0 * (nquad1 - 1) + (nquad0 * nquad1 * k) + i;
                }
            }
            break;
        case 4:
 
            nq0 = nquad1;
            nq1 = nquad2;
            if (outarray.size() != nq0 * nq1)
            {
                outarray = Array<OneD, int>(nq0 * nq1);
            }
 
            // Directions A and B positive
            for (int j = 0; j < nquad1 * nquad2; ++j)
            {
                outarray[j] = j * nquad0;
            }
            break;
        default:
            ASSERTL0(false, "face value (> 4) is out of range");
            break;
    }
}
 
/** \brief  Get the normals along specficied face
 * Get the face normals interplated to a points0 x points 0
 * type distribution
 **/
void PrismExp::v_ComputeTraceNormal(const int face)
{
    const SpatialDomains::GeomFactorsSharedPtr &geomFactors =
        GetGeom()->GetMetricInfo();
 
    LibUtilities::PointsKeyVector ptsKeys = GetPointsKeys();
    for (int i = 0; i < ptsKeys.size(); ++i)
    {
        // Need at least 2 points for computing normals
        if (ptsKeys[i].GetNumPoints() == 1)
        {
            LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
            ptsKeys[i] = pKey;
        }
    }
 
    SpatialDomains::GeomType type = geomFactors->GetGtype();
    const Array<TwoD, const NekDouble> &df =
        geomFactors->GetDerivFactors(ptsKeys);
    const Array<OneD, const NekDouble> &jac = geomFactors->GetJac(ptsKeys);
 
    int nq0  = ptsKeys[0].GetNumPoints();
    int nq1  = ptsKeys[1].GetNumPoints();
    int nq2  = ptsKeys[2].GetNumPoints();
    int nq01 = nq0 * nq1;
    int nqtot;
 
    LibUtilities::BasisKey tobasis0 = GetTraceBasisKey(face, 0);
    LibUtilities::BasisKey tobasis1 = GetTraceBasisKey(face, 1);
 
    // Number of quadrature points in face expansion.
    int nq_face = tobasis0.GetNumPoints() * tobasis1.GetNumPoints();
 
    int vCoordDim = GetCoordim();
    int i;
 
    m_traceNormals[face] = Array<OneD, Array<OneD, NekDouble>>(vCoordDim);
    Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[face];
    for (i = 0; i < vCoordDim; ++i)
    {
        normal[i] = Array<OneD, NekDouble>(nq_face);
    }
 
    size_t nqb                     = nq_face;
    size_t nbnd                    = face;
    m_elmtBndNormDirElmtLen[nbnd]  = Array<OneD, NekDouble>{nqb, 0.0};
    Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
 
    // Regular geometry case
    if (type == SpatialDomains::eRegular ||
        type == SpatialDomains::eMovingRegular)
    {
        NekDouble fac;
        // Set up normals
        switch (face)
        {
            case 0:
            {
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i + 2][0];
                    ;
                }
                break;
            }
            case 1:
            {
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i + 1][0];
                }
                break;
            }
            case 2:
            {
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = df[3 * i][0] + df[3 * i + 2][0];
                }
                break;
            }
            case 3:
            {
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = df[3 * i + 1][0];
                }
                break;
            }
            case 4:
            {
                for (i = 0; i < vCoordDim; ++i)
                {
                    normal[i][0] = -df[3 * i][0];
                }
                break;
            }
            default:
                ASSERTL0(false, "face is out of range (face < 4)");
        }
 
        // Normalise resulting vector.
        fac = 0.0;
        for (i = 0; i < vCoordDim; ++i)
        {
            fac += normal[i][0] * normal[i][0];
        }
        fac = 1.0 / sqrt(fac);
 
        Vmath::Fill(nqb, fac, length, 1);
 
        for (i = 0; i < vCoordDim; ++i)
        {
            Vmath::Fill(nq_face, fac * normal[i][0], normal[i], 1);
        }
    }
    else
    {
        // Set up deformed normals.
        int j, k;
 
        // Determine number of quadrature points on the face of 3D elmt
        if (face == 0)
        {
            nqtot = nq0 * nq1;
        }
        else if (face == 1 || face == 3)
        {
            nqtot = nq0 * nq2;
        }
        else
        {
            nqtot = nq1 * nq2;
        }
 
        LibUtilities::PointsKey points0;
        LibUtilities::PointsKey points1;
 
        Array<OneD, NekDouble> faceJac(nqtot);
        Array<OneD, NekDouble> normals(vCoordDim * nqtot, 0.0);
 
        // Extract Jacobian along face and recover local derivatives
        // (dx/dr) for polynomial interpolation by multiplying m_gmat by
        // jacobian
        switch (face)
        {
            case 0:
            {
                for (j = 0; j < nq01; ++j)
                {
                    normals[j]             = -df[2][j] * jac[j];
                    normals[nqtot + j]     = -df[5][j] * jac[j];
                    normals[2 * nqtot + j] = -df[8][j] * jac[j];
                    faceJac[j]             = jac[j];
                }
 
                points0 = ptsKeys[0];
                points1 = ptsKeys[1];
                break;
            }
 
            case 1:
            {
                for (j = 0; j < nq0; ++j)
                {
                    for (k = 0; k < nq2; ++k)
                    {
                        int tmp                      = j + nq01 * k;
                        normals[j + k * nq0]         = -df[1][tmp] * jac[tmp];
                        normals[nqtot + j + k * nq0] = -df[4][tmp] * jac[tmp];
                        normals[2 * nqtot + j + k * nq0] =
                            -df[7][tmp] * jac[tmp];
                        faceJac[j + k * nq0] = jac[tmp];
                    }
                }
 
                points0 = ptsKeys[0];
                points1 = ptsKeys[2];
                break;
            }
 
            case 2:
            {
                for (j = 0; j < nq1; ++j)
                {
                    for (k = 0; k < nq2; ++k)
                    {
                        int tmp = nq0 - 1 + nq0 * j + nq01 * k;
                        normals[j + k * nq1] =
                            (df[0][tmp] + df[2][tmp]) * jac[tmp];
                        normals[nqtot + j + k * nq1] =
                            (df[3][tmp] + df[5][tmp]) * jac[tmp];
                        normals[2 * nqtot + j + k * nq1] =
                            (df[6][tmp] + df[8][tmp]) * jac[tmp];
                        faceJac[j + k * nq1] = jac[tmp];
                    }
                }
 
                points0 = ptsKeys[1];
                points1 = ptsKeys[2];
                break;
            }
 
            case 3:
            {
                for (j = 0; j < nq0; ++j)
                {
                    for (k = 0; k < nq2; ++k)
                    {
                        int tmp              = nq0 * (nq1 - 1) + j + nq01 * k;
                        normals[j + k * nq0] = df[1][tmp] * jac[tmp];
                        normals[nqtot + j + k * nq0] = df[4][tmp] * jac[tmp];
                        normals[2 * nqtot + j + k * nq0] =
                            df[7][tmp] * jac[tmp];
                        faceJac[j + k * nq0] = jac[tmp];
                    }
                }
 
                points0 = ptsKeys[0];
                points1 = ptsKeys[2];
                break;
            }
 
            case 4:
            {
                for (j = 0; j < nq1; ++j)
                {
                    for (k = 0; k < nq2; ++k)
                    {
                        int tmp                      = j * nq0 + nq01 * k;
                        normals[j + k * nq1]         = -df[0][tmp] * jac[tmp];
                        normals[nqtot + j + k * nq1] = -df[3][tmp] * jac[tmp];
                        normals[2 * nqtot + j + k * nq1] =
                            -df[6][tmp] * jac[tmp];
                        faceJac[j + k * nq1] = jac[tmp];
                    }
                }
 
                points0 = ptsKeys[1];
                points1 = ptsKeys[2];
                break;
            }
 
            default:
                ASSERTL0(false, "face is out of range (face < 4)");
        }
 
        Array<OneD, NekDouble> work(nq_face, 0.0);
        // Interpolate Jacobian and invert
        LibUtilities::Interp2D(points0, points1, faceJac,
                               tobasis0.GetPointsKey(), tobasis1.GetPointsKey(),
                               work);
        Vmath::Sdiv(nq_face, 1.0, &work[0], 1, &work[0], 1);
 
        // Interpolate normal and multiply by inverse Jacobian.
        for (i = 0; i < vCoordDim; ++i)
        {
            LibUtilities::Interp2D(points0, points1, &normals[i * nqtot],
                                   tobasis0.GetPointsKey(),
                                   tobasis1.GetPointsKey(), &normal[i][0]);
            Vmath::Vmul(nq_face, work, 1, normal[i], 1, normal[i], 1);
        }
 
        // Normalise to obtain unit normals.
        Vmath::Zero(nq_face, work, 1);
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vvtvp(nq_face, normal[i], 1, normal[i], 1, work, 1, work, 1);
        }
 
        Vmath::Vsqrt(nq_face, work, 1, work, 1);
        Vmath::Sdiv(nq_face, 1.0, work, 1, work, 1);
 
        Vmath::Vcopy(nqb, work, 1, length, 1);
 
        for (i = 0; i < GetCoordim(); ++i)
        {
            Vmath::Vmul(nq_face, normal[i], 1, work, 1, normal[i], 1);
        }
    }
}
 
void PrismExp::v_MassMatrixOp(const Array<OneD, const NekDouble> &inarray,
                              Array<OneD, NekDouble> &outarray,
                              const StdRegions::StdMatrixKey &mkey)
{
    StdExpansion::MassMatrixOp_MatFree(inarray, outarray, mkey);
}
 
void PrismExp::v_LaplacianMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD, NekDouble> &outarray,
                                   const StdRegions::StdMatrixKey &mkey)
{
    PrismExp::LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
}
 
void PrismExp::v_LaplacianMatrixOp(const int k1, const int k2,
                                   const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD, NekDouble> &outarray,
                                   const StdRegions::StdMatrixKey &mkey)
{
    StdExpansion::LaplacianMatrixOp_MatFree(k1, k2, inarray, outarray, mkey);
}
 
void PrismExp::v_HelmholtzMatrixOp(const Array<OneD, const NekDouble> &inarray,
                                   Array<OneD, NekDouble> &outarray,
                                   const StdRegions::StdMatrixKey &mkey)
{
    PrismExp::v_HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
}
 
void PrismExp::v_GeneralMatrixOp_MatOp(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, const StdRegions::StdMatrixKey &mkey)
{
    DNekScalMatSharedPtr mat = GetLocMatrix(mkey);
 
    if (inarray.get() == outarray.get())
    {
        Array<OneD, NekDouble> tmp(m_ncoeffs);
        Vmath::Vcopy(m_ncoeffs, inarray.get(), 1, tmp.get(), 1);
 
        Blas::Dgemv('N', m_ncoeffs, m_ncoeffs, mat->Scale(),
                    (mat->GetOwnedMatrix())->GetPtr().get(), m_ncoeffs,
                    tmp.get(), 1, 0.0, outarray.get(), 1);
    }
    else
    {
        Blas::Dgemv('N', m_ncoeffs, m_ncoeffs, mat->Scale(),
                    (mat->GetOwnedMatrix())->GetPtr().get(), m_ncoeffs,
                    inarray.get(), 1, 0.0, outarray.get(), 1);
    }
}
 
void PrismExp::v_SVVLaplacianFilter(Array<OneD, NekDouble> &array,
                                    const StdRegions::StdMatrixKey &mkey)
{
    int nq = GetTotPoints();
 
    // Calculate sqrt of the Jacobian
    Array<OneD, const NekDouble> jac = m_metricinfo->GetJac(GetPointsKeys());
    Array<OneD, NekDouble> sqrt_jac(nq);
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        Vmath::Vsqrt(nq, jac, 1, sqrt_jac, 1);
    }
    else
    {
        Vmath::Fill(nq, sqrt(jac[0]), sqrt_jac, 1);
    }
 
    // Multiply array by sqrt(Jac)
    Vmath::Vmul(nq, sqrt_jac, 1, array, 1, array, 1);
 
    // Apply std region filter
    StdPrismExp::v_SVVLaplacianFilter(array, mkey);
 
    // Divide by sqrt(Jac)
    Vmath::Vdiv(nq, array, 1, sqrt_jac, 1, array, 1);
}
 
//---------------------------------------
// Matrix creation functions
//---------------------------------------
 
DNekMatSharedPtr PrismExp::v_GenMatrix(const StdRegions::StdMatrixKey &mkey)
{
    DNekMatSharedPtr returnval;
 
    switch (mkey.GetMatrixType())
    {
        case StdRegions::eHybridDGHelmholtz:
        case StdRegions::eHybridDGLamToU:
        case StdRegions::eHybridDGLamToQ0:
        case StdRegions::eHybridDGLamToQ1:
        case StdRegions::eHybridDGLamToQ2:
        case StdRegions::eHybridDGHelmBndLam:
        case StdRegions::eInvLaplacianWithUnityMean:
            returnval = Expansion3D::v_GenMatrix(mkey);
            break;
        default:
            returnval = StdPrismExp::v_GenMatrix(mkey);
            break;
    }
 
    return returnval;
}
 
DNekMatSharedPtr PrismExp::v_CreateStdMatrix(
    const StdRegions::StdMatrixKey &mkey)
{
    LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
    LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
    LibUtilities::BasisKey bkey2 = m_base[2]->GetBasisKey();
    StdRegions::StdPrismExpSharedPtr tmp =
        MemoryManager<StdPrismExp>::AllocateSharedPtr(bkey0, bkey1, bkey2);
 
    return tmp->GetStdMatrix(mkey);
}
 
DNekScalMatSharedPtr PrismExp::v_GetLocMatrix(const MatrixKey &mkey)
{
    return m_matrixManager[mkey];
}
 
DNekScalBlkMatSharedPtr PrismExp::v_GetLocStaticCondMatrix(
    const MatrixKey &mkey)
{
    return m_staticCondMatrixManager[mkey];
}
 
void PrismExp::v_DropLocStaticCondMatrix(const MatrixKey &mkey)
{
    m_staticCondMatrixManager.DeleteObject(mkey);
}
 
/**
 * @brief Calculate the Laplacian multiplication in a matrix-free
 * manner.
 *
 * This function is the kernel of the Laplacian matrix-free operator,
 * and is used in #v_HelmholtzMatrixOp_MatFree to determine the effect
 * of the Helmholtz operator in a similar fashion.
 *
 * The majority of the calculation is precisely the same as in the
 * hexahedral expansion; however the collapsed co-ordinate system must
 * be taken into account when constructing the geometric factors. How
 * this is done is detailed more exactly in the tetrahedral expansion.
 * On entry to this function, the input #inarray must be in its
 * backwards-transformed state (i.e. \f$\mathbf{u} =
 * \mathbf{B}\hat{\mathbf{u}}\f$). The output is in coefficient space.
 *
 * @see %TetExp::v_HelmholtzMatrixOp_MatFree
 */
void PrismExp::v_LaplacianMatrixOp_MatFree_Kernel(
    const Array<OneD, const NekDouble> &inarray,
    Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp)
{
    int nquad0 = m_base[0]->GetNumPoints();
    int nquad1 = m_base[1]->GetNumPoints();
    int nquad2 = m_base[2]->GetNumPoints();
    int nqtot  = nquad0 * nquad1 * nquad2;
    int i;
 
    // Set up temporary storage.
    Array<OneD, NekDouble> alloc(11 * nqtot, 0.0);
    Array<OneD, NekDouble> wsp1(alloc);              // TensorDeriv 1
    Array<OneD, NekDouble> wsp2(alloc + 1 * nqtot);  // TensorDeriv 2
    Array<OneD, NekDouble> wsp3(alloc + 2 * nqtot);  // TensorDeriv 3
    Array<OneD, NekDouble> g0(alloc + 3 * nqtot);    // g0
    Array<OneD, NekDouble> g1(alloc + 4 * nqtot);    // g1
    Array<OneD, NekDouble> g2(alloc + 5 * nqtot);    // g2
    Array<OneD, NekDouble> g3(alloc + 6 * nqtot);    // g3
    Array<OneD, NekDouble> g4(alloc + 7 * nqtot);    // g4
    Array<OneD, NekDouble> g5(alloc + 8 * nqtot);    // g5
    Array<OneD, NekDouble> h0(alloc + 3 * nqtot);    // h0   == g0
    Array<OneD, NekDouble> h1(alloc + 6 * nqtot);    // h1   == g3
    Array<OneD, NekDouble> wsp4(alloc + 4 * nqtot);  // wsp4 == g1
    Array<OneD, NekDouble> wsp5(alloc + 5 * nqtot);  // wsp5 == g2
    Array<OneD, NekDouble> wsp6(alloc + 8 * nqtot);  // wsp6 == g5
    Array<OneD, NekDouble> wsp7(alloc + 3 * nqtot);  // wsp7 == g0
    Array<OneD, NekDouble> wsp8(alloc + 9 * nqtot);  // wsp8
    Array<OneD, NekDouble> wsp9(alloc + 10 * nqtot); // wsp9
 
    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();
    const Array<OneD, const NekDouble> &dbase0 = m_base[0]->GetDbdata();
    const Array<OneD, const NekDouble> &dbase1 = m_base[1]->GetDbdata();
    const Array<OneD, const NekDouble> &dbase2 = m_base[2]->GetDbdata();
 
    // Step 1. LAPLACIAN MATRIX OPERATION
    // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
    // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
    // wsp3 = du_dxi3 = D_xi3 * wsp0 = D_xi3 * u
    StdExpansion3D::PhysTensorDeriv(inarray, wsp1, wsp2, wsp3);
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
    const Array<OneD, const NekDouble> &z0 = m_base[0]->GetZ();
    const Array<OneD, const NekDouble> &z2 = m_base[2]->GetZ();
 
    // Step 2. Calculate the metric terms of the collapsed
    // coordinate transformation (Spencer's book P152)
    for (i = 0; i < nquad2; ++i)
    {
        Vmath::Fill(nquad0 * nquad1, 2.0 / (1.0 - z2[i]),
                    &h0[0] + i * nquad0 * nquad1, 1);
        Vmath::Fill(nquad0 * nquad1, 2.0 / (1.0 - z2[i]),
                    &h1[0] + i * nquad0 * nquad1, 1);
    }
    for (i = 0; i < nquad0; i++)
    {
        Blas::Dscal(nquad1 * nquad2, 0.5 * (1 + z0[i]), &h1[0] + i, nquad0);
    }
 
    // Step 3. Construct combined metric terms for physical space to
    // collapsed coordinate system.  Order of construction optimised
    // to minimise temporary storage
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        // wsp4 = d eta_1/d x_1
        Vmath::Vvtvvtp(nqtot, &df[0][0], 1, &h0[0], 1, &df[2][0], 1, &h1[0], 1,
                       &wsp4[0], 1);
        // wsp5 = d eta_2/d x_1
        Vmath::Vvtvvtp(nqtot, &df[3][0], 1, &h0[0], 1, &df[5][0], 1, &h1[0], 1,
                       &wsp5[0], 1);
        // wsp6 = d eta_3/d x_1d
        Vmath::Vvtvvtp(nqtot, &df[6][0], 1, &h0[0], 1, &df[8][0], 1, &h1[0], 1,
                       &wsp6[0], 1);
 
        // g0 (overwrites h0)
        Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0],
                       1, &g0[0], 1);
        Vmath::Vvtvp(nqtot, &wsp6[0], 1, &wsp6[0], 1, &g0[0], 1, &g0[0], 1);
 
        // g3 (overwrites h1)
        Vmath::Vvtvvtp(nqtot, &df[1][0], 1, &wsp4[0], 1, &df[4][0], 1, &wsp5[0],
                       1, &g3[0], 1);
        Vmath::Vvtvp(nqtot, &df[7][0], 1, &wsp6[0], 1, &g3[0], 1, &g3[0], 1);
 
        // g4
        Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &wsp4[0], 1, &df[5][0], 1, &wsp5[0],
                       1, &g4[0], 1);
        Vmath::Vvtvp(nqtot, &df[8][0], 1, &wsp6[0], 1, &g4[0], 1, &g4[0], 1);
 
        // Overwrite wsp4/5/6 with g1/2/5
        // g1
        Vmath::Vvtvvtp(nqtot, &df[1][0], 1, &df[1][0], 1, &df[4][0], 1,
                       &df[4][0], 1, &g1[0], 1);
        Vmath::Vvtvp(nqtot, &df[7][0], 1, &df[7][0], 1, &g1[0], 1, &g1[0], 1);
 
        // g2
        Vmath::Vvtvvtp(nqtot, &df[2][0], 1, &df[2][0], 1, &df[5][0], 1,
                       &df[5][0], 1, &g2[0], 1);
        Vmath::Vvtvp(nqtot, &df[8][0], 1, &df[8][0], 1, &g2[0], 1, &g2[0], 1);
 
        // g5
        Vmath::Vvtvvtp(nqtot, &df[1][0], 1, &df[2][0], 1, &df[4][0], 1,
                       &df[5][0], 1, &g5[0], 1);
        Vmath::Vvtvp(nqtot, &df[7][0], 1, &df[8][0], 1, &g5[0], 1, &g5[0], 1);
    }
    else
    {
        // wsp4 = d eta_1/d x_1
        Vmath::Svtsvtp(nqtot, df[0][0], &h0[0], 1, df[2][0], &h1[0], 1,
                       &wsp4[0], 1);
        // wsp5 = d eta_2/d x_1
        Vmath::Svtsvtp(nqtot, df[3][0], &h0[0], 1, df[5][0], &h1[0], 1,
                       &wsp5[0], 1);
        // wsp6 = d eta_3/d x_1
        Vmath::Svtsvtp(nqtot, df[6][0], &h0[0], 1, df[8][0], &h1[0], 1,
                       &wsp6[0], 1);
 
        // g0 (overwrites h0)
        Vmath::Vvtvvtp(nqtot, &wsp4[0], 1, &wsp4[0], 1, &wsp5[0], 1, &wsp5[0],
                       1, &g0[0], 1);
        Vmath::Vvtvp(nqtot, &wsp6[0], 1, &wsp6[0], 1, &g0[0], 1, &g0[0], 1);
 
        // g3 (overwrites h1)
        Vmath::Svtsvtp(nqtot, df[1][0], &wsp4[0], 1, df[4][0], &wsp5[0], 1,
                       &g3[0], 1);
        Vmath::Svtvp(nqtot, df[7][0], &wsp6[0], 1, &g3[0], 1, &g3[0], 1);
 
        // g4
        Vmath::Svtsvtp(nqtot, df[2][0], &wsp4[0], 1, df[5][0], &wsp5[0], 1,
                       &g4[0], 1);
        Vmath::Svtvp(nqtot, df[8][0], &wsp6[0], 1, &g4[0], 1, &g4[0], 1);
 
        // Overwrite wsp4/5/6 with g1/2/5
        // g1
        Vmath::Fill(nqtot,
                    df[1][0] * df[1][0] + df[4][0] * df[4][0] +
                        df[7][0] * df[7][0],
                    &g1[0], 1);
 
        // g2
        Vmath::Fill(nqtot,
                    df[2][0] * df[2][0] + df[5][0] * df[5][0] +
                        df[8][0] * df[8][0],
                    &g2[0], 1);
 
        // g5
        Vmath::Fill(nqtot,
                    df[1][0] * df[2][0] + df[4][0] * df[5][0] +
                        df[7][0] * df[8][0],
                    &g5[0], 1);
    }
    // Compute component derivatives into wsp7, 8, 9 (wsp7 overwrites
    // g0).
    Vmath::Vvtvvtp(nqtot, &g0[0], 1, &wsp1[0], 1, &g3[0], 1, &wsp2[0], 1,
                   &wsp7[0], 1);
    Vmath::Vvtvp(nqtot, &g4[0], 1, &wsp3[0], 1, &wsp7[0], 1, &wsp7[0], 1);
    Vmath::Vvtvvtp(nqtot, &g1[0], 1, &wsp2[0], 1, &g3[0], 1, &wsp1[0], 1,
                   &wsp8[0], 1);
    Vmath::Vvtvp(nqtot, &g5[0], 1, &wsp3[0], 1, &wsp8[0], 1, &wsp8[0], 1);
    Vmath::Vvtvvtp(nqtot, &g2[0], 1, &wsp3[0], 1, &g4[0], 1, &wsp1[0], 1,
                   &wsp9[0], 1);
    Vmath::Vvtvp(nqtot, &g5[0], 1, &wsp2[0], 1, &wsp9[0], 1, &wsp9[0], 1);
 
    // Step 4.
    // Multiply by quadrature metric
    MultiplyByQuadratureMetric(wsp7, wsp7);
    MultiplyByQuadratureMetric(wsp8, wsp8);
    MultiplyByQuadratureMetric(wsp9, wsp9);
 
    // Perform inner product w.r.t derivative bases.
    IProductWRTBase_SumFacKernel(dbase0, base1, base2, wsp7, wsp1, wsp, false,
                                 true, true);
    IProductWRTBase_SumFacKernel(base0, dbase1, base2, wsp8, wsp2, wsp, true,
                                 false, true);
    IProductWRTBase_SumFacKernel(base0, base1, dbase2, wsp9, outarray, wsp,
                                 true, true, false);
 
    // Step 5.
    // Sum contributions from wsp1, wsp2 and outarray.
    Vmath::Vadd(m_ncoeffs, wsp1.get(), 1, outarray.get(), 1, outarray.get(), 1);
    Vmath::Vadd(m_ncoeffs, wsp2.get(), 1, outarray.get(), 1, outarray.get(), 1);
}
 
void PrismExp::v_GetSimplexEquiSpacedConnectivity(Array<OneD, int> &conn,
                                                  bool oldstandard)
{
    boost::ignore_unused(oldstandard);
 
    int np0 = m_base[0]->GetNumPoints();
    int np1 = m_base[1]->GetNumPoints();
    int np2 = m_base[2]->GetNumPoints();
    int np  = max(np0, max(np1, np2));
    Array<OneD, int> prismpt(6);
    bool standard = true;
 
    int vid0   = m_geom->GetVid(0);
    int vid1   = m_geom->GetVid(1);
    int vid2   = m_geom->GetVid(4);
    int rotate = 0;
 
    // sort out prism rotation according to
    if ((vid2 < vid1) && (vid2 < vid0)) // top triangle vertex is lowest id
    {
        rotate = 0;
        if (vid0 > vid1)
        {
            standard = false; // reverse base direction
        }
    }
    else if ((vid1 < vid2) && (vid1 < vid0))
    {
        rotate = 1;
        if (vid2 > vid0)
        {
            standard = false; // reverse base direction
        }
    }
    else if ((vid0 < vid2) && (vid0 < vid1))
    {
        rotate = 2;
        if (vid1 > vid2)
        {
            standard = false; // reverse base direction
        }
    }
 
    conn = Array<OneD, int>(12 * (np - 1) * (np - 1) * (np - 1));
 
    int row     = 0;
    int rowp1   = 0;
    int plane   = 0;
    int row1    = 0;
    int row1p1  = 0;
    int planep1 = 0;
    int cnt     = 0;
 
    Array<OneD, int> rot(3);
 
    rot[0] = (0 + rotate) % 3;
    rot[1] = (1 + rotate) % 3;
    rot[2] = (2 + rotate) % 3;
 
    // lower diagonal along 1-3 on base
    for (int i = 0; i < np - 1; ++i)
    {
        planep1 += (np - i) * np;
        row    = 0; // current plane row offset
        rowp1  = 0; // current plane row plus one offset
        row1   = 0; // next plane row offset
        row1p1 = 0; // nex plane row plus one offset
        if (standard == false)
        {
            for (int j = 0; j < np - 1; ++j)
            {
                rowp1 += np - i;
                row1p1 += np - i - 1;
                for (int k = 0; k < np - i - 2; ++k)
                {
                    // bottom prism block
                    prismpt[rot[0]] = plane + row + k;
                    prismpt[rot[1]] = plane + row + k + 1;
                    prismpt[rot[2]] = planep1 + row1 + k;
 
                    prismpt[3 + rot[0]] = plane + rowp1 + k;
                    prismpt[3 + rot[1]] = plane + rowp1 + k + 1;
                    prismpt[3 + rot[2]] = planep1 + row1p1 + k;
 
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[1];
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[2];
 
                    conn[cnt++] = prismpt[5];
                    conn[cnt++] = prismpt[2];
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[4];
 
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[1];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[2];
 
                    // upper prism block.
                    prismpt[rot[0]] = planep1 + row1 + k + 1;
                    prismpt[rot[1]] = planep1 + row1 + k;
                    prismpt[rot[2]] = plane + row + k + 1;
 
                    prismpt[3 + rot[0]] = planep1 + row1p1 + k + 1;
                    prismpt[3 + rot[1]] = planep1 + row1p1 + k;
                    prismpt[3 + rot[2]] = plane + rowp1 + k + 1;
 
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[1];
                    conn[cnt++] = prismpt[2];
                    conn[cnt++] = prismpt[5];
 
                    conn[cnt++] = prismpt[5];
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[1];
 
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[5];
                }
 
                // bottom prism block
                prismpt[rot[0]] = plane + row + np - i - 2;
                prismpt[rot[1]] = plane + row + np - i - 1;
                prismpt[rot[2]] = planep1 + row1 + np - i - 2;
 
                prismpt[3 + rot[0]] = plane + rowp1 + np - i - 2;
                prismpt[3 + rot[1]] = plane + rowp1 + np - i - 1;
                prismpt[3 + rot[2]] = planep1 + row1p1 + np - i - 2;
 
                conn[cnt++] = prismpt[0];
                conn[cnt++] = prismpt[1];
                conn[cnt++] = prismpt[3];
                conn[cnt++] = prismpt[2];
 
                conn[cnt++] = prismpt[5];
                conn[cnt++] = prismpt[2];
                conn[cnt++] = prismpt[3];
                conn[cnt++] = prismpt[4];
 
                conn[cnt++] = prismpt[3];
                conn[cnt++] = prismpt[1];
                conn[cnt++] = prismpt[4];
                conn[cnt++] = prismpt[2];
 
                row += np - i;
                row1 += np - i - 1;
            }
        }
        else
        { // lower diagonal along 0-4 on base
            for (int j = 0; j < np - 1; ++j)
            {
                rowp1 += np - i;
                row1p1 += np - i - 1;
                for (int k = 0; k < np - i - 2; ++k)
                {
                    // bottom prism block
                    prismpt[rot[0]] = plane + row + k;
                    prismpt[rot[1]] = plane + row + k + 1;
                    prismpt[rot[2]] = planep1 + row1 + k;
 
                    prismpt[3 + rot[0]] = plane + rowp1 + k;
                    prismpt[3 + rot[1]] = plane + rowp1 + k + 1;
                    prismpt[3 + rot[2]] = planep1 + row1p1 + k;
 
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[1];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[2];
 
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[2];
 
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[5];
                    conn[cnt++] = prismpt[2];
 
                    // upper prism block.
                    prismpt[rot[0]] = planep1 + row1 + k + 1;
                    prismpt[rot[1]] = planep1 + row1 + k;
                    prismpt[rot[2]] = plane + row + k + 1;
 
                    prismpt[3 + rot[0]] = planep1 + row1p1 + k + 1;
                    prismpt[3 + rot[1]] = planep1 + row1p1 + k;
                    prismpt[3 + rot[2]] = plane + rowp1 + k + 1;
 
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[2];
                    conn[cnt++] = prismpt[1];
                    conn[cnt++] = prismpt[5];
 
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[5];
                    conn[cnt++] = prismpt[0];
                    conn[cnt++] = prismpt[1];
 
                    conn[cnt++] = prismpt[5];
                    conn[cnt++] = prismpt[3];
                    conn[cnt++] = prismpt[4];
                    conn[cnt++] = prismpt[1];
                }
 
                // bottom prism block
                prismpt[rot[0]] = plane + row + np - i - 2;
                prismpt[rot[1]] = plane + row + np - i - 1;
                prismpt[rot[2]] = planep1 + row1 + np - i - 2;
 
                prismpt[3 + rot[0]] = plane + rowp1 + np - i - 2;
                prismpt[3 + rot[1]] = plane + rowp1 + np - i - 1;
                prismpt[3 + rot[2]] = planep1 + row1p1 + np - i - 2;
 
                conn[cnt++] = prismpt[0];
                conn[cnt++] = prismpt[1];
                conn[cnt++] = prismpt[4];
                conn[cnt++] = prismpt[2];
 
                conn[cnt++] = prismpt[4];
                conn[cnt++] = prismpt[3];
                conn[cnt++] = prismpt[0];
                conn[cnt++] = prismpt[2];
 
                conn[cnt++] = prismpt[3];
                conn[cnt++] = prismpt[4];
                conn[cnt++] = prismpt[5];
                conn[cnt++] = prismpt[2];
 
                row += np - i;
                row1 += np - i - 1;
            }
        }
        plane += (np - i) * np;
    }
}
 
/** @brief: This method gets all of the factors which are
    required as part of the Gradient Jump Penalty
    stabilisation and involves the product of the normal and
    geometric factors along the element trace.
*/
void PrismExp::v_NormalTraceDerivFactors(
    Array<OneD, Array<OneD, NekDouble>> &d0factors,
    Array<OneD, Array<OneD, NekDouble>> &d1factors,
    Array<OneD, Array<OneD, NekDouble>> &d2factors)
{
    int nquad0 = GetNumPoints(0);
    int nquad1 = GetNumPoints(1);
    int nquad2 = GetNumPoints(2);
 
    const Array<TwoD, const NekDouble> &df =
        m_metricinfo->GetDerivFactors(GetPointsKeys());
 
    if (d0factors.size() != 5)
    {
        d0factors = Array<OneD, Array<OneD, NekDouble>>(5);
        d1factors = Array<OneD, Array<OneD, NekDouble>>(5);
        d2factors = Array<OneD, Array<OneD, NekDouble>>(5);
    }
 
    if (d0factors[0].size() != nquad0 * nquad1)
    {
        d0factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d1factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
        d2factors[0] = Array<OneD, NekDouble>(nquad0 * nquad1);
    }
 
    if (d0factors[1].size() != nquad0 * nquad2)
    {
        d0factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d0factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d1factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[1] = Array<OneD, NekDouble>(nquad0 * nquad2);
        d2factors[3] = Array<OneD, NekDouble>(nquad0 * nquad2);
    }
 
    if (d0factors[2].size() != nquad1 * nquad2)
    {
        d0factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d0factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d1factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[2] = Array<OneD, NekDouble>(nquad1 * nquad2);
        d2factors[4] = Array<OneD, NekDouble>(nquad1 * nquad2);
    }
 
    // Outwards normals
    const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
        GetTraceNormal(0);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
        GetTraceNormal(1);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_2 =
        GetTraceNormal(2);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_3 =
        GetTraceNormal(3);
    const Array<OneD, const Array<OneD, NekDouble>> &normal_4 =
        GetTraceNormal(4);
 
    int ncoords = normal_0.size();
 
    // first gather together standard cartesian inner products
    if (m_metricinfo->GetGtype() == SpatialDomains::eDeformed)
    {
        // face 0
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][i] * normal_0[0][i];
            d1factors[0][i] = df[1][i] * normal_0[0][i];
            d2factors[0][i] = df[2][i] * normal_0[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][i] * normal_0[n][i];
                d1factors[0][i] += df[3 * n + 1][i] * normal_0[n][i];
                d2factors[0][i] += df[3 * n + 2][i] * normal_0[n][i];
            }
        }
 
        // faces 1 and 3
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad0; ++i)
            {
                d0factors[1][i] = df[0][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d0factors[3][i] =
                    df[0][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d1factors[1][i] = df[1][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d1factors[3][i] =
                    df[1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
                d2factors[1][i] = df[2][j * nquad0 * nquad1 + i] *
                                  normal_1[0][j * nquad0 + i];
                d2factors[3][i] =
                    df[2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                    normal_3[0][j * nquad0 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad0; ++i)
                {
                    d0factors[1][i] = df[3 * n][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d0factors[3][i] =
                        df[3 * n][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d1factors[1][i] = df[3 * n + 1][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d1factors[3][i] =
                        df[3 * n + 1][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                    d2factors[1][i] = df[3 * n + 2][j * nquad0 * nquad1 + i] *
                                      normal_1[0][j * nquad0 + i];
                    d2factors[3][i] =
                        df[3 * n + 2][(j + 1) * nquad0 * nquad1 - nquad0 + i] *
                        normal_3[0][j * nquad0 + i];
                }
            }
        }
 
        // faces 2 and 4
        for (int j = 0; j < nquad2; ++j)
        {
            for (int i = 0; i < nquad1; ++i)
            {
                d0factors[2][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d0factors[4][j * nquad1 + i] =
                    df[0][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d1factors[2][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d1factors[4][j * nquad1 + i] =
                    df[1][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
                d2factors[2][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                    normal_2[0][j * nquad1 + i];
                d2factors[4][j * nquad1 + i] =
                    df[2][j * nquad0 * nquad1 + i * nquad0] *
                    normal_4[0][j * nquad1 + i];
            }
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int j = 0; j < nquad2; ++j)
            {
                for (int i = 0; i < nquad1; ++i)
                {
                    d0factors[2][j * nquad1 + i] +=
                        df[3 * n][j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d0factors[4][j * nquad0 + i] +=
                        df[3 * n][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                    d1factors[2][j * nquad1 + i] +=
                        df[3 * n + 1]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d1factors[4][j * nquad0 + i] +=
                        df[3 * n + 1][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                    d2factors[2][j * nquad1 + i] +=
                        df[3 * n + 2]
                          [j * nquad0 * nquad1 + (i + 1) * nquad0 - 1] *
                        normal_2[n][j * nquad0 + i];
                    d2factors[4][j * nquad0 + i] +=
                        df[3 * n + 2][i * nquad0 + j * nquad0 * nquad1] *
                        normal_4[n][j * nquad0 + i];
                }
            }
        }
    }
    else
    {
        // Face 0
        for (int i = 0; i < nquad0 * nquad1; ++i)
        {
            d0factors[0][i] = df[0][0] * normal_0[0][i];
            d1factors[0][i] = df[1][0] * normal_0[0][i];
            d2factors[0][i] = df[2][0] * normal_0[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad1; ++i)
            {
                d0factors[0][i] += df[3 * n][0] * normal_0[n][i];
                d1factors[0][i] += df[3 * n + 1][0] * normal_0[n][i];
                d2factors[0][i] += df[3 * n + 2][0] * normal_0[n][i];
            }
        }
 
        // faces 1 and 3
        for (int i = 0; i < nquad0 * nquad2; ++i)
        {
            d0factors[1][i] = df[0][0] * normal_1[0][i];
            d0factors[3][i] = df[0][0] * normal_3[0][i];
 
            d1factors[1][i] = df[1][0] * normal_1[0][i];
            d1factors[3][i] = df[1][0] * normal_3[0][i];
 
            d2factors[1][i] = df[2][0] * normal_1[0][i];
            d2factors[3][i] = df[2][0] * normal_3[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad0 * nquad2; ++i)
            {
                d0factors[1][i] += df[3 * n][0] * normal_1[n][i];
                d0factors[3][i] += df[3 * n][0] * normal_3[n][i];
 
                d1factors[1][i] += df[3 * n + 1][0] * normal_1[n][i];
                d1factors[3][i] += df[3 * n + 1][0] * normal_3[n][i];
 
                d2factors[1][i] += df[3 * n + 2][0] * normal_1[n][i];
                d2factors[3][i] += df[3 * n + 2][0] * normal_3[n][i];
            }
        }
 
        // faces 2 and 4
        for (int i = 0; i < nquad1 * nquad2; ++i)
        {
            d0factors[2][i] = df[0][0] * normal_2[0][i];
            d0factors[4][i] = df[0][0] * normal_4[0][i];
 
            d1factors[2][i] = df[1][0] * normal_2[0][i];
            d1factors[4][i] = df[1][0] * normal_4[0][i];
 
            d2factors[2][i] = df[2][0] * normal_2[0][i];
            d2factors[4][i] = df[2][0] * normal_4[0][i];
        }
 
        for (int n = 1; n < ncoords; ++n)
        {
            for (int i = 0; i < nquad1 * nquad2; ++i)
            {
                d0factors[2][i] += df[3 * n][0] * normal_2[n][i];
                d0factors[4][i] += df[3 * n][0] * normal_4[n][i];
 
                d1factors[2][i] += df[3 * n + 1][0] * normal_2[n][i];
                d1factors[4][i] += df[3 * n + 1][0] * normal_4[n][i];
 
                d2factors[2][i] += df[3 * n + 2][0] * normal_2[n][i];
                d2factors[4][i] += df[3 * n + 2][0] * normal_4[n][i];
            }
        }
    }
}
} // namespace LocalRegions
} // namespace Nektar