1070 lines
36 KiB
C++
1070 lines
36 KiB
C++
// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
|
|
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
|
|
// LICENSE and NOTICE for details. LLNL-CODE-806117.
|
|
//
|
|
// This file is part of the MFEM library. For more information and source code
|
|
// availability visit https://mfem.org.
|
|
//
|
|
// MFEM is free software; you can redistribute it and/or modify it under the
|
|
// terms of the BSD-3 license. We welcome feedback and contributions, see file
|
|
// CONTRIBUTING.md for details.
|
|
|
|
#include "../general/forall.hpp"
|
|
#include "bilininteg.hpp"
|
|
#include "gridfunc.hpp"
|
|
|
|
using namespace std;
|
|
|
|
namespace mfem
|
|
{
|
|
|
|
// PA Divergence Integrator
|
|
|
|
// PA Divergence Assemble 2D kernel
|
|
static void PADivergenceSetup2D(const int Q1D,
|
|
const int NE,
|
|
const Array<double> &w,
|
|
const Vector &j,
|
|
const double COEFF,
|
|
Vector &op)
|
|
{
|
|
const int NQ = Q1D*Q1D;
|
|
auto W = w.Read();
|
|
auto J = Reshape(j.Read(), NQ, 2, 2, NE);
|
|
auto y = Reshape(op.Write(), NQ, 2, 2, NE);
|
|
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
for (int q = 0; q < NQ; ++q)
|
|
{
|
|
const double J11 = J(q,0,0,e);
|
|
const double J12 = J(q,0,1,e);
|
|
const double J21 = J(q,1,0,e);
|
|
const double J22 = J(q,1,1,e);
|
|
// Store wq * Q * adj(J)
|
|
y(q,0,0,e) = W[q] * COEFF * J22; // 1,1
|
|
y(q,0,1,e) = W[q] * COEFF * -J12; // 1,2
|
|
y(q,1,0,e) = W[q] * COEFF * -J21; // 2,1
|
|
y(q,1,1,e) = W[q] * COEFF * J11; // 2,2
|
|
}
|
|
});
|
|
}
|
|
|
|
// PA Divergence Assemble 3D kernel
|
|
static void PADivergenceSetup3D(const int Q1D,
|
|
const int NE,
|
|
const Array<double> &w,
|
|
const Vector &j,
|
|
const double COEFF,
|
|
Vector &op)
|
|
{
|
|
const int NQ = Q1D*Q1D*Q1D;
|
|
auto W = w.Read();
|
|
auto J = Reshape(j.Read(), NQ, 3, 3, NE);
|
|
auto y = Reshape(op.Write(), NQ, 3, 3, NE);
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
for (int q = 0; q < NQ; ++q)
|
|
{
|
|
const double J11 = J(q,0,0,e);
|
|
const double J21 = J(q,1,0,e);
|
|
const double J31 = J(q,2,0,e);
|
|
const double J12 = J(q,0,1,e);
|
|
const double J22 = J(q,1,1,e);
|
|
const double J32 = J(q,2,1,e);
|
|
const double J13 = J(q,0,2,e);
|
|
const double J23 = J(q,1,2,e);
|
|
const double J33 = J(q,2,2,e);
|
|
const double cw = W[q] * COEFF;
|
|
// adj(J)
|
|
const double A11 = (J22 * J33) - (J23 * J32);
|
|
const double A12 = (J32 * J13) - (J12 * J33);
|
|
const double A13 = (J12 * J23) - (J22 * J13);
|
|
const double A21 = (J31 * J23) - (J21 * J33);
|
|
const double A22 = (J11 * J33) - (J13 * J31);
|
|
const double A23 = (J21 * J13) - (J11 * J23);
|
|
const double A31 = (J21 * J32) - (J31 * J22);
|
|
const double A32 = (J31 * J12) - (J11 * J32);
|
|
const double A33 = (J11 * J22) - (J12 * J21);
|
|
// Store wq * Q * adj(J)
|
|
y(q,0,0,e) = cw * A11; // 1,1
|
|
y(q,0,1,e) = cw * A12; // 1,2
|
|
y(q,0,2,e) = cw * A13; // 1,3
|
|
y(q,1,0,e) = cw * A21; // 2,1
|
|
y(q,1,1,e) = cw * A22; // 2,2
|
|
y(q,1,2,e) = cw * A23; // 2,3
|
|
y(q,2,0,e) = cw * A31; // 3,1
|
|
y(q,2,1,e) = cw * A32; // 3,2
|
|
y(q,2,2,e) = cw * A33; // 3,3
|
|
}
|
|
});
|
|
}
|
|
|
|
static void PADivergenceSetup(const int dim,
|
|
const int TR_D1D,
|
|
const int TE_D1D,
|
|
const int Q1D,
|
|
const int NE,
|
|
const Array<double> &W,
|
|
const Vector &J,
|
|
const double COEFF,
|
|
Vector &op)
|
|
{
|
|
if (dim == 1) { MFEM_ABORT("dim==1 not supported in PADivergenceSetup"); }
|
|
if (dim == 2)
|
|
{
|
|
PADivergenceSetup2D(Q1D, NE, W, J, COEFF, op);
|
|
}
|
|
if (dim == 3)
|
|
{
|
|
PADivergenceSetup3D(Q1D, NE, W, J, COEFF, op);
|
|
}
|
|
}
|
|
|
|
void VectorDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
|
|
const FiniteElementSpace &test_fes)
|
|
{
|
|
// Assumes tensor-product elements ordered by nodes
|
|
MFEM_ASSERT(trial_fes.GetOrdering() == Ordering::byNODES,
|
|
"PA Only supports Ordering::byNODES!");
|
|
Mesh *mesh = trial_fes.GetMesh();
|
|
const FiniteElement &trial_fe = *trial_fes.GetFE(0);
|
|
const FiniteElement &test_fe = *test_fes.GetFE(0);
|
|
ElementTransformation *trans = mesh->GetElementTransformation(0);
|
|
const IntegrationRule *ir = IntRule ? IntRule : &GetRule(trial_fe, test_fe,
|
|
*trans);
|
|
const int dims = trial_fe.GetDim();
|
|
const int dimsToStore = dims * dims;
|
|
const int nq = ir->GetNPoints();
|
|
dim = mesh->Dimension();
|
|
ne = trial_fes.GetNE();
|
|
geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
|
|
trial_maps = &trial_fe.GetDofToQuad(*ir, DofToQuad::TENSOR);
|
|
trial_dofs1D = trial_maps->ndof;
|
|
quad1D = trial_maps->nqpt;
|
|
test_maps = &test_fe.GetDofToQuad(*ir, DofToQuad::TENSOR);
|
|
test_dofs1D = test_maps->ndof;
|
|
MFEM_ASSERT(quad1D == test_maps->nqpt,
|
|
"PA requires test and trial space to have same number of quadrature points!");
|
|
pa_data.SetSize(nq * dimsToStore * ne, Device::GetMemoryType());
|
|
double coeff = 1.0;
|
|
if (Q)
|
|
{
|
|
ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient*>(Q);
|
|
MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
|
|
coeff = cQ->constant;
|
|
}
|
|
PADivergenceSetup(dim, trial_dofs1D, test_dofs1D, quad1D,
|
|
ne, ir->GetWeights(), geom->J, coeff, pa_data);
|
|
}
|
|
|
|
// PA Divergence Apply 2D kernel
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
|
|
static void PADivergenceApply2D(const int NE,
|
|
const Array<double> &b,
|
|
const Array<double> &g,
|
|
const Array<double> &bt,
|
|
const Vector &_op,
|
|
const Vector &_x,
|
|
Vector &_y,
|
|
const int tr_d1d = 0,
|
|
const int te_d1d = 0,
|
|
const int q1d = 0)
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
MFEM_VERIFY(TR_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(TE_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
|
|
auto B = Reshape(b.Read(), Q1D, TR_D1D);
|
|
auto G = Reshape(g.Read(), Q1D, TR_D1D);
|
|
auto Bt = Reshape(bt.Read(), TE_D1D, Q1D);
|
|
auto op = Reshape(_op.Read(), Q1D*Q1D, 2,2, NE);
|
|
auto x = Reshape(_x.Read(), TR_D1D, TR_D1D, 2, NE);
|
|
auto y = Reshape(_y.ReadWrite(), TE_D1D, TE_D1D, NE);
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
const int VDIM = 2;
|
|
// the following variables are evaluated at compile time
|
|
constexpr int max_TE_D1D = T_TE_D1D ? T_TE_D1D : MAX_D1D;
|
|
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
|
|
|
|
double grad[max_Q1D][max_Q1D][VDIM];
|
|
double div[max_Q1D][max_Q1D];
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
div[qy][qx] = 0.0;
|
|
}
|
|
}
|
|
|
|
for (int c = 0; c < VDIM; ++c)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
grad[qy][qx][0] = 0.0;
|
|
grad[qy][qx][1] = 0.0;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
double gradX[max_Q1D][VDIM];
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradX[qx][0] = 0.0;
|
|
gradX[qx][1] = 0.0;
|
|
}
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
const double s = x(dx,dy,c,e);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradX[qx][0] += s * G(qx,dx);
|
|
gradX[qx][1] += s * B(qx,dx);
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
const double wy = B(qy,dy);
|
|
const double wDy = G(qy,dy);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
grad[qy][qx][0] += gradX[qx][0] * wy;
|
|
grad[qy][qx][1] += gradX[qx][1] * wDy;
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated grad(u_c) = [Dxy_1, xDy_2] in plane
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const int q = qx + qy * Q1D;
|
|
const double gradX = grad[qy][qx][0];
|
|
const double gradY = grad[qy][qx][1];
|
|
|
|
div[qy][qx] += gradX*op(q,0,c,e) + gradY*op(q,1,c,e);
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated div = reshape(div phi * op) * u
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
double opX[max_TE_D1D];
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
opX[dx] = 0.0;
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
opX[dx] += Bt(dx,qx)*div[qy][qx];
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
y(dx,dy,e) += Bt(dy,qy)*opX[dx];
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated y = p * div
|
|
});
|
|
}
|
|
|
|
// Shared memory PA Divergence Apply 2D kernel
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0,
|
|
const int T_NBZ = 0>
|
|
static void SmemPADivergenceApply2D(const int NE,
|
|
const Array<double> &_b,
|
|
const Array<double> &_g,
|
|
const Array<double> &_bt,
|
|
const Vector &_op,
|
|
const Vector &_x,
|
|
Vector &_y,
|
|
const int tr_d1d = 0,
|
|
const int te_d1d = 0,
|
|
const int q1d = 0)
|
|
{
|
|
// TODO
|
|
MFEM_ASSERT(false, "SHARED MEM NOT PROGRAMMED YET");
|
|
}
|
|
|
|
// PA Divergence Apply 2D kernel transpose
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
|
|
static void PADivergenceApplyTranspose2D(const int NE,
|
|
const Array<double> &bt,
|
|
const Array<double> >,
|
|
const Array<double> &b,
|
|
const Vector &_op,
|
|
const Vector &_x,
|
|
Vector &_y,
|
|
const int tr_d1d = 0,
|
|
const int te_d1d = 0,
|
|
const int q1d = 0)
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
MFEM_VERIFY(TR_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(TE_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
|
|
auto Bt = Reshape(bt.Read(), TR_D1D, Q1D);
|
|
auto Gt = Reshape(gt.Read(), TR_D1D, Q1D);
|
|
auto B = Reshape(b.Read(), Q1D, TE_D1D);
|
|
auto op = Reshape(_op.Read(), Q1D*Q1D, 2,2, NE);
|
|
auto x = Reshape(_x.Read(), TE_D1D, TE_D1D, NE);
|
|
auto y = Reshape(_y.ReadWrite(), TR_D1D, TR_D1D, 2, NE);
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
const int VDIM = 2;
|
|
// the following variables are evaluated at compile time
|
|
constexpr int max_TR_D1D = T_TR_D1D ? T_TR_D1D : MAX_D1D;
|
|
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
|
|
|
|
double quadTest[max_Q1D][max_Q1D];
|
|
double grad[max_Q1D][max_Q1D][VDIM];
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTest[qy][qx] = 0.0;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
double quadTestX[max_Q1D];
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestX[qx] = 0.0;
|
|
}
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
const double s = x(dx,dy,e);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestX[qx] += s * B(qx,dx);
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
const double wy = B(qy,dy);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTest[qy][qx] += quadTestX[qx] * wy;
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated x on the quads
|
|
for (int c = 0; c < VDIM; ++c)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const int q = qx + qy * Q1D;
|
|
grad[qy][qx][0] = quadTest[qy][qx]*op(q,0,c,e);
|
|
grad[qy][qx][1] = quadTest[qy][qx]*op(q,1,c,e);
|
|
}
|
|
}
|
|
// We've now calculated op_c^T * x
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
double gradX[max_TR_D1D][VDIM];
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
gradX[dx][0] = 0.0;
|
|
gradX[dx][1] = 0.0;
|
|
}
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const double gX = grad[qy][qx][0];
|
|
const double gY = grad[qy][qx][1];
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
const double wx = Bt(dx,qx);
|
|
const double wDx = Gt(dx,qx);
|
|
gradX[dx][0] += gX * wDx;
|
|
gradX[dx][1] += gY * wx;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
const double wy = Bt(dy,qy);
|
|
const double wDy = Gt(dy,qy);
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
y(dx,dy,c,e) += ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated y = reshape(div u * op^T) * x
|
|
});
|
|
}
|
|
|
|
// PA Vector Divergence Apply 3D kernel
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
|
|
static void PADivergenceApply3D(const int NE,
|
|
const Array<double> &b,
|
|
const Array<double> &g,
|
|
const Array<double> &bt,
|
|
const Vector &_op,
|
|
const Vector &_x,
|
|
Vector &_y,
|
|
int tr_d1d = 0,
|
|
int te_d1d = 0,
|
|
int q1d = 0)
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
MFEM_VERIFY(TR_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(TE_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
|
|
auto B = Reshape(b.Read(), Q1D, TR_D1D);
|
|
auto G = Reshape(g.Read(), Q1D, TR_D1D);
|
|
auto Bt = Reshape(bt.Read(), TE_D1D, Q1D);
|
|
auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 3,3, NE);
|
|
auto x = Reshape(_x.Read(), TR_D1D, TR_D1D, TR_D1D, 3, NE);
|
|
auto y = Reshape(_y.ReadWrite(), TE_D1D, TE_D1D, TE_D1D, NE);
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
const int VDIM = 3;
|
|
// the following variables are evaluated at compile time
|
|
constexpr int max_TE_D1D = T_TE_D1D ? T_TE_D1D : MAX_D1D;
|
|
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
|
|
|
|
double grad[max_Q1D][max_Q1D][max_Q1D][VDIM];
|
|
double div[max_Q1D][max_Q1D][max_Q1D];
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
div[qz][qy][qx] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int c = 0; c < VDIM; ++c)
|
|
{
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
grad[qz][qy][qx][0] = 0.0;
|
|
grad[qz][qy][qx][1] = 0.0;
|
|
grad[qz][qy][qx][2] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
for (int dz = 0; dz < TR_D1D; ++dz)
|
|
{
|
|
double gradXY[max_Q1D][max_Q1D][VDIM];
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradXY[qy][qx][0] = 0.0;
|
|
gradXY[qy][qx][1] = 0.0;
|
|
gradXY[qy][qx][2] = 0.0;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
double gradX[max_Q1D][VDIM];
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradX[qx][0] = 0.0;
|
|
gradX[qx][1] = 0.0;
|
|
gradX[qx][2] = 0.0;
|
|
}
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
const double s = x(dx,dy,dz,c,e);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradX[qx][0] += s * G(qx,dx);
|
|
gradX[qx][1] += s * B(qx,dx);
|
|
gradX[qx][2] += s * B(qx,dx);
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
const double wy = B(qy,dy);
|
|
const double wDy = G(qy,dy);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
gradXY[qy][qx][0] += gradX[qx][0] * wy;
|
|
gradXY[qy][qx][1] += gradX[qx][1] * wDy;
|
|
gradXY[qy][qx][2] += gradX[qx][2] * wy;
|
|
}
|
|
}
|
|
}
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
const double wz = B(qz,dz);
|
|
const double wDz = G(qz,dz);
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
grad[qz][qy][qx][0] += gradXY[qy][qx][0] * wz;
|
|
grad[qz][qy][qx][1] += gradXY[qy][qx][1] * wz;
|
|
grad[qz][qy][qx][2] += gradXY[qy][qx][2] * wDz;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated grad(u_c) = [Dxyz_1, xDyz_2, xyDz_3] in plane
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const int q = qx + (qy + qz * Q1D) * Q1D;
|
|
const double gradX = grad[qz][qy][qx][0];
|
|
const double gradY = grad[qz][qy][qx][1];
|
|
const double gradZ = grad[qz][qy][qx][2];
|
|
|
|
div[qz][qy][qx] += gradX*op(q,0,c,e) + gradY*op(q,1,c,e) + gradZ*op(q,2,c,e);
|
|
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated div = reshape(div phi * op) * u
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
double opXY[max_TE_D1D][max_TE_D1D];
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
opXY[dy][dx] = 0.0;
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
double opX[max_TE_D1D];
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
opX[dx] = 0.0;
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
opX[dx] += Bt(dx,qx)*div[qz][qy][qx];
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
opXY[dy][dx] += Bt(dy,qy)*opX[dx];
|
|
}
|
|
}
|
|
}
|
|
for (int dz = 0; dz < TE_D1D; ++dz)
|
|
{
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
y(dx,dy,dz,e) += Bt(dz,qz)*opXY[dy][dx];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated y = p * div
|
|
});
|
|
}
|
|
|
|
// PA Vector Divergence Apply 3D kernel
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
|
|
static void PADivergenceApplyTranspose3D(const int NE,
|
|
const Array<double> &bt,
|
|
const Array<double> >,
|
|
const Array<double> &b,
|
|
const Vector &_op,
|
|
const Vector &_x,
|
|
Vector &_y,
|
|
int tr_d1d = 0,
|
|
int te_d1d = 0,
|
|
int q1d = 0)
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
MFEM_VERIFY(TR_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(TE_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
|
|
auto Bt = Reshape(bt.Read(), TR_D1D, Q1D);
|
|
auto Gt = Reshape(gt.Read(), TR_D1D, Q1D);
|
|
auto B = Reshape(b.Read(), Q1D, TE_D1D);
|
|
auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 3,3, NE);
|
|
auto x = Reshape(_x.Read(), TE_D1D, TE_D1D, TE_D1D, NE);
|
|
auto y = Reshape(_y.ReadWrite(), TR_D1D, TR_D1D, TR_D1D, 3, NE);
|
|
MFEM_FORALL(e, NE,
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
const int VDIM = 3;
|
|
// the following variables are evaluated at compile time
|
|
constexpr int max_TR_D1D = T_TR_D1D ? T_TR_D1D : MAX_D1D;
|
|
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
|
|
|
|
double quadTest[max_Q1D][max_Q1D][max_Q1D];
|
|
double grad[max_Q1D][max_Q1D][max_Q1D][VDIM];
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTest[qz][qy][qx] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
for (int dz = 0; dz < TE_D1D; ++dz)
|
|
{
|
|
double quadTestXY[max_Q1D][max_Q1D];
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestXY[qy][qx] = 0.0;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TE_D1D; ++dy)
|
|
{
|
|
double quadTestX[max_Q1D];
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestX[qx] = 0.0;
|
|
}
|
|
for (int dx = 0; dx < TE_D1D; ++dx)
|
|
{
|
|
const double s = x(dx,dy,dz,e);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestX[qx] += s * B(qx,dx);
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
const double wy = B(qy,dy);
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTestXY[qy][qx] += quadTestX[qx] * wy;
|
|
}
|
|
}
|
|
}
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
const double wz = B(qz,dz);
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
quadTest[qz][qy][qx] += quadTestXY[qy][qx] * wz;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated x on the quads
|
|
for (int c = 0; c < VDIM; ++c)
|
|
{
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const int q = qx + (qy + qz * Q1D) * Q1D;
|
|
grad[qz][qy][qx][0] = quadTest[qz][qy][qx]*op(q,0,c,e);
|
|
grad[qz][qy][qx][1] = quadTest[qz][qy][qx]*op(q,1,c,e);
|
|
grad[qz][qy][qx][2] = quadTest[qz][qy][qx]*op(q,2,c,e);
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated op_c^T * x
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
double gradXY[max_TR_D1D][max_TR_D1D][VDIM];
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
gradXY[dy][dx][0] = 0.0;
|
|
gradXY[dy][dx][1] = 0.0;
|
|
gradXY[dy][dx][2] = 0.0;
|
|
}
|
|
}
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
double gradX[max_TR_D1D][VDIM];
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
gradX[dx][0] = 0.0;
|
|
gradX[dx][1] = 0.0;
|
|
gradX[dx][2] = 0.0;
|
|
}
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
const double gX = grad[qz][qy][qx][0];
|
|
const double gY = grad[qz][qy][qx][1];
|
|
const double gZ = grad[qz][qy][qx][2];
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
const double wx = Bt(dx,qx);
|
|
const double wDx = Gt(dx,qx);
|
|
gradX[dx][0] += gX * wDx;
|
|
gradX[dx][1] += gY * wx;
|
|
gradX[dx][2] += gZ * wx;
|
|
}
|
|
}
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
const double wy = Bt(dy,qy);
|
|
const double wDy = Gt(dy,qy);
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
gradXY[dy][dx][0] += gradX[dx][0] * wy;
|
|
gradXY[dy][dx][1] += gradX[dx][1] * wDy;
|
|
gradXY[dy][dx][2] += gradX[dx][2] * wy;
|
|
}
|
|
}
|
|
}
|
|
for (int dz = 0; dz < TR_D1D; ++dz)
|
|
{
|
|
const double wz = Bt(dz,qz);
|
|
const double wDz = Gt(dz,qz);
|
|
for (int dy = 0; dy < TR_D1D; ++dy)
|
|
{
|
|
for (int dx = 0; dx < TR_D1D; ++dx)
|
|
{
|
|
y(dx,dy,dz,c,e) +=
|
|
((gradXY[dy][dx][0] * wz) +
|
|
(gradXY[dy][dx][1] * wz) +
|
|
(gradXY[dy][dx][2] * wDz));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// We've now calculated y = reshape(div u * op^T) * x
|
|
});
|
|
}
|
|
|
|
// Shared memory PA Vector Divergence Apply 3D kernel
|
|
template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
|
|
static void SmemPADivergenceApply3D(const int NE,
|
|
const Array<double> &b_,
|
|
const Array<double> &g_,
|
|
const Array<double> &bt_,
|
|
const Vector &q_,
|
|
const Vector &x_,
|
|
Vector &y_,
|
|
const int tr_d1d = 0,
|
|
const int te_d1d = 0,
|
|
const int q1d = 0)
|
|
{
|
|
const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
|
|
MFEM_VERIFY(TR_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(TE_D1D <= MAX_D1D, "");
|
|
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
|
|
|
|
auto b = Reshape(b_.Read(), Q1D, TR_D1D);
|
|
auto g = Reshape(g_.Read(), Q1D, TR_D1D);
|
|
auto bt = Reshape(bt_.Read(), TE_D1D, Q1D);
|
|
auto Q = Reshape(q_.Read(), Q1D*Q1D*Q1D, 3,3, NE);
|
|
auto x = Reshape(x_.Read(), TR_D1D, TR_D1D, TR_D1D, 3, NE);
|
|
auto y = Reshape(y_.ReadWrite(), TE_D1D, TE_D1D, TE_D1D, NE);
|
|
|
|
MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
|
|
{
|
|
constexpr int VDIM = 3;
|
|
const int tidz = MFEM_THREAD_ID(z);
|
|
const int D1DR = T_TR_D1D ? T_TR_D1D : tr_d1d;
|
|
const int D1DE = T_TE_D1D ? T_TE_D1D : te_d1d;
|
|
const int Q1D = T_Q1D ? T_Q1D : q1d;
|
|
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
|
|
constexpr int MD1R = T_TR_D1D ? T_TR_D1D : MAX_D1D;
|
|
constexpr int MD1E = T_TE_D1D ? T_TE_D1D : MAX_D1D;
|
|
constexpr int MD1 = MD1E > MD1R ? MD1E : MD1R;
|
|
constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
|
|
MFEM_SHARED double sBG[2][MQ1*MD1];
|
|
double (*B)[MD1] = (double (*)[MD1]) (sBG+0);
|
|
double (*G)[MD1] = (double (*)[MD1]) (sBG+1);
|
|
double (*Bt)[MQ1] = (double (*)[MQ1]) (sBG+0);
|
|
MFEM_SHARED double sm0[3][MDQ*MDQ*MDQ];
|
|
MFEM_SHARED double sm1[3][MDQ*MDQ*MDQ];
|
|
double (*X)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+2);
|
|
double (*DDQ0)[MD1][MQ1] = (double (*)[MD1][MQ1]) (sm0+0);
|
|
double (*DDQ1)[MD1][MQ1] = (double (*)[MD1][MQ1]) (sm0+1);
|
|
double (*DQQ0)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+0);
|
|
double (*DQQ1)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+1);
|
|
double (*DQQ2)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+2);
|
|
double (*QQQ0)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+0);
|
|
double (*QQQ1)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+1);
|
|
double (*QQQ2)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+2);
|
|
double (*QQD0)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+0);
|
|
double (*QDD0)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+0);
|
|
MFEM_SHARED double div[MQ1][MQ1][MQ1];
|
|
|
|
if (tidz == 0)
|
|
{
|
|
MFEM_FOREACH_THREAD(d,y,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(q,x,Q1D)
|
|
{
|
|
B[q][d] = b(q,d);
|
|
G[q][d] = g(q,d);
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
div[qz][qy][qx] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
|
|
for (int c = 0; c < VDIM; ++c)
|
|
{
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
QQQ0[qz][qy][qx] = 0.0;
|
|
QQQ1[qz][qy][qx] = 0.0;
|
|
QQQ2[qz][qy][qx] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(dz,z,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(dy,y,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(dx,x,D1DR)
|
|
{
|
|
X[dz][dy][dx] = x(dx,dy,dz,c,e);
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(dz,z,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(dy,y,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
double u = 0.0;
|
|
double v = 0.0;
|
|
for (int dx = 0; dx < D1DR; ++dx)
|
|
{
|
|
const double coord = X[dz][dy][dx];
|
|
u += coord * B[qx][dx];
|
|
v += coord * G[qx][dx];
|
|
}
|
|
DDQ0[dz][dy][qx] = u;
|
|
DDQ1[dz][dy][qx] = v;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(dz,z,D1DR)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
double u = 0.0;
|
|
double v = 0.0;
|
|
double w = 0.0;
|
|
for (int dy = 0; dy < D1DR; ++dy)
|
|
{
|
|
u += DDQ1[dz][dy][qx] * B[qy][dy];
|
|
v += DDQ0[dz][dy][qx] * G[qy][dy];
|
|
w += DDQ0[dz][dy][qx] * B[qy][dy];
|
|
}
|
|
DQQ0[dz][qy][qx] = u;
|
|
DQQ1[dz][qy][qx] = v;
|
|
DQQ2[dz][qy][qx] = w;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
double u = 0.0;
|
|
double v = 0.0;
|
|
double w = 0.0;
|
|
for (int dz = 0; dz < D1DR; ++dz)
|
|
{
|
|
u += DQQ0[dz][qy][qx] * B[qz][dz];
|
|
v += DQQ1[dz][qy][qx] * B[qz][dz];
|
|
w += DQQ2[dz][qy][qx] * G[qz][dz];
|
|
}
|
|
QQQ0[qz][qy][qx] = u;
|
|
QQQ1[qz][qy][qx] = v;
|
|
QQQ2[qz][qy][qx] = w;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qx,x,Q1D)
|
|
{
|
|
const int q = qx + (qy + qz * Q1D) * Q1D;
|
|
const double gX = QQQ0[qz][qy][qx];
|
|
const double gY = QQQ1[qz][qy][qx];
|
|
const double gZ = QQQ2[qz][qy][qx];
|
|
div[qz][qy][qx] += gX*Q(q,0,c,e) + gY*Q(q,1,c,e) + gZ*Q(q,2,c,e);
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
}
|
|
|
|
if (tidz == 0)
|
|
{
|
|
MFEM_FOREACH_THREAD(d,y,D1DE)
|
|
{
|
|
MFEM_FOREACH_THREAD(q,x,Q1D)
|
|
{
|
|
Bt[d][q] = bt(d,q);
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(qy,y,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(dx,x,D1DE)
|
|
{
|
|
double u = 0.0;
|
|
for (int qx = 0; qx < Q1D; ++qx)
|
|
{
|
|
u += div[qz][qy][qx] * Bt[dx][qx];
|
|
}
|
|
QQD0[qz][qy][dx] = u;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(qz,z,Q1D)
|
|
{
|
|
MFEM_FOREACH_THREAD(dy,y,D1DE)
|
|
{
|
|
MFEM_FOREACH_THREAD(dx,x,D1DE)
|
|
{
|
|
double u = 0.0;
|
|
for (int qy = 0; qy < Q1D; ++qy)
|
|
{
|
|
u += QQD0[qz][qy][dx] * Bt[dy][qy];
|
|
}
|
|
QDD0[qz][dy][dx] = u;
|
|
}
|
|
}
|
|
}
|
|
MFEM_SYNC_THREAD;
|
|
MFEM_FOREACH_THREAD(dz,z,D1DE)
|
|
{
|
|
MFEM_FOREACH_THREAD(dy,y,D1DE)
|
|
{
|
|
MFEM_FOREACH_THREAD(dx,x,D1DE)
|
|
{
|
|
double u = 0.0;
|
|
for (int qz = 0; qz < Q1D; ++qz)
|
|
{
|
|
u += QDD0[qz][dy][dx] * Bt[dz][qz];
|
|
}
|
|
y(dx,dy,dz,e) += u;
|
|
}
|
|
}
|
|
}
|
|
});
|
|
}
|
|
|
|
static void PADivergenceApply(const int dim,
|
|
const int TR_D1D,
|
|
const int TE_D1D,
|
|
const int Q1D,
|
|
const int NE,
|
|
const Array<double> &B,
|
|
const Array<double> &G,
|
|
const Array<double> &Bt,
|
|
const Vector &op,
|
|
const Vector &x,
|
|
Vector &y,
|
|
bool transpose=false)
|
|
{
|
|
if (dim == 2)
|
|
{
|
|
return PADivergenceApply2D(NE,B,G,Bt,op,x,y,TR_D1D,TE_D1D,Q1D);
|
|
}
|
|
if (dim == 3)
|
|
{
|
|
return PADivergenceApply3D(NE,B,G,Bt,op,x,y,TR_D1D,TE_D1D,Q1D);
|
|
}
|
|
MFEM_ABORT("Unknown kernel.");
|
|
}
|
|
|
|
// PA Divergence Apply kernel
|
|
void VectorDivergenceIntegrator::AddMultPA(const Vector &x, Vector &y) const
|
|
{
|
|
PADivergenceApply(dim, trial_dofs1D, test_dofs1D, quad1D, ne,
|
|
trial_maps->B, trial_maps->G, test_maps->Bt, pa_data, x, y,
|
|
false);
|
|
}
|
|
|
|
// PA Divergence Apply kernel
|
|
void VectorDivergenceIntegrator::AddMultTransposePA(const Vector &x,
|
|
Vector &y) const
|
|
{
|
|
PADivergenceApply(dim, trial_dofs1D, test_dofs1D, quad1D, ne,
|
|
trial_maps->Bt, trial_maps->Gt, test_maps->B, pa_data, x, y,
|
|
true);
|
|
}
|
|
|
|
} // namespace mfem
|