Files
mfem/fem/bilininteg_diffusion.cpp
T

1128 lines
39 KiB
C++

// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
// reserved. See file COPYRIGHT for details.
//
// This file is part of the MFEM library. For more information and source code
// availability see http://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License (as published by the Free
// Software Foundation) version 2.1 dated February 1999.
#include "../general/forall.hpp"
#include "bilininteg.hpp"
#include "gridfunc.hpp"
using namespace std;
namespace mfem
{
// PA Diffusion Integrator
// OCCA 2D Assemble kernel
#ifdef MFEM_USE_OCCA
static void OccaPADiffusionSetup2D(const int D1D,
const int Q1D,
const int NE,
const Array<double> &W,
const Vector &J,
const Vector &C,
Vector &op)
{
occa::properties props;
props["defines/D1D"] = D1D;
props["defines/Q1D"] = Q1D;
const occa::memory o_W = OccaMemoryRead(W.GetMemory(), W.Size());
const occa::memory o_J = OccaMemoryRead(J.GetMemory(), J.Size());
const occa::memory o_C = OccaMemoryRead(C.GetMemory(), C.Size());
occa::memory o_op = OccaMemoryWrite(op.GetMemory(), op.Size());
const bool const_c = C.Size() == 1;
const occa_id_t id = std::make_pair(D1D,Q1D);
static occa_kernel_t OccaDiffSetup2D_ker;
if (OccaDiffSetup2D_ker.find(id) == OccaDiffSetup2D_ker.end())
{
const occa::kernel DiffusionSetup2D =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionSetup2D", props);
OccaDiffSetup2D_ker.emplace(id, DiffusionSetup2D);
}
OccaDiffSetup2D_ker.at(id)(NE, o_W, o_J, o_C, o_op, const_c);
}
static void OccaPADiffusionSetup3D(const int D1D,
const int Q1D,
const int NE,
const Array<double> &W,
const Vector &J,
const Vector &C,
Vector &op)
{
occa::properties props;
props["defines/D1D"] = D1D;
props["defines/Q1D"] = Q1D;
const occa::memory o_W = OccaMemoryRead(W.GetMemory(), W.Size());
const occa::memory o_J = OccaMemoryRead(J.GetMemory(), J.Size());
const occa::memory o_C = OccaMemoryRead(C.GetMemory(), C.Size());
occa::memory o_op = OccaMemoryWrite(op.GetMemory(), op.Size());
const bool const_c = C.Size() == 1;
const occa_id_t id = std::make_pair(D1D,Q1D);
static occa_kernel_t OccaDiffSetup3D_ker;
if (OccaDiffSetup3D_ker.find(id) == OccaDiffSetup3D_ker.end())
{
const occa::kernel DiffusionSetup3D =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionSetup3D", props);
OccaDiffSetup3D_ker.emplace(id, DiffusionSetup3D);
}
OccaDiffSetup3D_ker.at(id)(NE, o_W, o_J, o_C, o_op, const_c);
}
#endif // MFEM_USE_OCCA
// PA Diffusion Assemble 2D kernel
static void PADiffusionSetup2D(const int Q1D,
const int NE,
const Array<double> &w,
const Vector &j,
const Vector &c,
Vector &d)
{
const int NQ = Q1D*Q1D;
const bool const_c = c.Size() == 1;
auto W = w.Read();
auto J = Reshape(j.Read(), NQ, 2, 2, NE);
auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
auto D = Reshape(d.Write(), NQ, 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 J12 = J(q,0,1,e);
const double J22 = J(q,1,1,e);
const double coeff = const_c ? C(0,0) : C(q,e);
const double c_detJ = W[q] * coeff / ((J11*J22)-(J21*J12));
D(q,0,e) = c_detJ * (J12*J12 + J22*J22); // 1,1
D(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
D(q,2,e) = c_detJ * (J11*J11 + J21*J21); // 2,2
}
});
}
// PA Diffusion Assemble 3D kernel
static void PADiffusionSetup3D(const int Q1D,
const int NE,
const Array<double> &w,
const Vector &j,
const Vector &c,
Vector &d)
{
const int NQ = Q1D*Q1D*Q1D;
const bool const_c = c.Size() == 1;
auto W = w.Read();
auto J = Reshape(j.Read(), NQ, 3, 3, NE);
auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
auto D = Reshape(d.Write(), NQ, 6, 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 detJ = J11 * (J22 * J33 - J32 * J23) -
/* */ J21 * (J12 * J33 - J32 * J13) +
/* */ J31 * (J12 * J23 - J22 * J13);
const double coeff = const_c ? C(0,0) : C(q,e);
const double c_detJ = W[q] * coeff / detJ;
// 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);
// detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
}
});
}
static void PADiffusionSetup(const int dim,
const int D1D,
const int Q1D,
const int NE,
const Array<double> &W,
const Vector &J,
const Vector &C,
Vector &D)
{
if (dim == 1) { MFEM_ABORT("dim==1 not supported in PADiffusionSetup"); }
if (dim == 2)
{
#ifdef MFEM_USE_OCCA
if (DeviceCanUseOcca())
{
OccaPADiffusionSetup2D(D1D, Q1D, NE, W, J, C, D);
return;
}
#endif // MFEM_USE_OCCA
PADiffusionSetup2D(Q1D, NE, W, J, C, D);
}
if (dim == 3)
{
#ifdef MFEM_USE_OCCA
if (DeviceCanUseOcca())
{
OccaPADiffusionSetup3D(D1D, Q1D, NE, W, J, C, D);
return;
}
#endif // MFEM_USE_OCCA
PADiffusionSetup3D(Q1D, NE, W, J, C, D);
}
}
void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
{
// Assumes tensor-product elements
Mesh *mesh = fes.GetMesh();
const FiniteElement &el = *fes.GetFE(0);
const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
const int dims = el.GetDim();
const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
const int nq = ir->GetNPoints();
dim = mesh->Dimension();
ne = fes.GetNE();
geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
dofs1D = maps->ndof;
quad1D = maps->nqpt;
pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
Vector coeff;
if (Q == nullptr)
{
coeff.SetSize(1);
coeff(0) = 1.0;
}
else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
{
coeff.SetSize(1);
coeff(0) = cQ->constant;
}
else
{
coeff.SetSize(nq * ne);
auto C = Reshape(coeff.HostWrite(), nq, ne);
for (int e = 0; e < ne; ++e)
{
ElementTransformation& T = *fes.GetElementTransformation(e);
for (int q = 0; q < nq; ++q)
{
C(q,e) = Q->Eval(T, ir->IntPoint(q));
}
}
}
PADiffusionSetup(dim, dofs1D, quad1D, ne, ir->GetWeights(), geom->J, coeff,
pa_data);
}
#ifdef MFEM_USE_OCCA
// OCCA PA Diffusion Apply 2D kernel
static void OccaPADiffusionApply2D(const int D1D,
const int Q1D,
const int NE,
const Array<double> &B,
const Array<double> &G,
const Array<double> &Bt,
const Array<double> &Gt,
const Vector &op,
const Vector &x,
Vector &y)
{
occa::properties props;
props["defines/D1D"] = D1D;
props["defines/Q1D"] = Q1D;
const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
const occa::memory o_G = OccaMemoryRead(G.GetMemory(), G.Size());
const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
const occa::memory o_Gt = OccaMemoryRead(Gt.GetMemory(), Gt.Size());
const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
const occa_id_t id = std::make_pair(D1D,Q1D);
if (!Device::Allows(Backend::OCCA_CUDA))
{
static occa_kernel_t OccaDiffApply2D_cpu;
if (OccaDiffApply2D_cpu.find(id) == OccaDiffApply2D_cpu.end())
{
const occa::kernel DiffusionApply2D_CPU =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionApply2D_CPU", props);
OccaDiffApply2D_cpu.emplace(id, DiffusionApply2D_CPU);
}
OccaDiffApply2D_cpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
}
else
{
static occa_kernel_t OccaDiffApply2D_gpu;
if (OccaDiffApply2D_gpu.find(id) == OccaDiffApply2D_gpu.end())
{
const occa::kernel DiffusionApply2D_GPU =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionApply2D_GPU", props);
OccaDiffApply2D_gpu.emplace(id, DiffusionApply2D_GPU);
}
OccaDiffApply2D_gpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
}
}
// OCCA PA Diffusion Apply 3D kernel
static void OccaPADiffusionApply3D(const int D1D,
const int Q1D,
const int NE,
const Array<double> &B,
const Array<double> &G,
const Array<double> &Bt,
const Array<double> &Gt,
const Vector &op,
const Vector &x,
Vector &y)
{
occa::properties props;
props["defines/D1D"] = D1D;
props["defines/Q1D"] = Q1D;
const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
const occa::memory o_G = OccaMemoryRead(G.GetMemory(), G.Size());
const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
const occa::memory o_Gt = OccaMemoryRead(Gt.GetMemory(), Gt.Size());
const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
const occa_id_t id = std::make_pair(D1D,Q1D);
if (!Device::Allows(Backend::OCCA_CUDA))
{
static occa_kernel_t OccaDiffApply3D_cpu;
if (OccaDiffApply3D_cpu.find(id) == OccaDiffApply3D_cpu.end())
{
const occa::kernel DiffusionApply3D_CPU =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionApply3D_CPU", props);
OccaDiffApply3D_cpu.emplace(id, DiffusionApply3D_CPU);
}
OccaDiffApply3D_cpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
}
else
{
static occa_kernel_t OccaDiffApply3D_gpu;
if (OccaDiffApply3D_gpu.find(id) == OccaDiffApply3D_gpu.end())
{
const occa::kernel DiffusionApply3D_GPU =
mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
"DiffusionApply3D_GPU", props);
OccaDiffApply3D_gpu.emplace(id, DiffusionApply3D_GPU);
}
OccaDiffApply3D_gpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
}
}
#endif // MFEM_USE_OCCA
// PA Diffusion Apply 2D kernel
template<int T_D1D = 0, int T_Q1D = 0> static
void PADiffusionApply2D(const int NE,
const Array<double> &b,
const Array<double> &g,
const Array<double> &bt,
const Array<double> &gt,
const Vector &_op,
const Vector &_x,
Vector &_y,
const int d1d = 0,
const int q1d = 0)
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
MFEM_VERIFY(D1D <= MAX_D1D, "");
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
auto B = Reshape(b.Read(), Q1D, D1D);
auto G = Reshape(g.Read(), Q1D, D1D);
auto Bt = Reshape(bt.Read(), D1D, Q1D);
auto Gt = Reshape(gt.Read(), D1D, Q1D);
auto op = Reshape(_op.Read(), Q1D*Q1D, 3, NE);
auto x = Reshape(_x.Read(), D1D, D1D, NE);
auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
MFEM_FORALL(e, NE,
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
// the following variables are evaluated at compile time
constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
double grad[max_Q1D][max_Q1D][2];
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 < D1D; ++dy)
{
double gradX[max_Q1D][2];
for (int qx = 0; qx < Q1D; ++qx)
{
gradX[qx][0] = 0.0;
gradX[qx][1] = 0.0;
}
for (int dx = 0; dx < D1D; ++dx)
{
const double s = x(dx,dy,e);
for (int qx = 0; qx < Q1D; ++qx)
{
gradX[qx][0] += s * B(qx,dx);
gradX[qx][1] += s * G(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][1] * wy;
grad[qy][qx][1] += gradX[qx][0] * wDy;
}
}
}
// Calculate Dxy, xDy in plane
for (int qy = 0; qy < Q1D; ++qy)
{
for (int qx = 0; qx < Q1D; ++qx)
{
const int q = qx + qy * Q1D;
const double O11 = op(q,0,e);
const double O12 = op(q,1,e);
const double O22 = op(q,2,e);
const double gradX = grad[qy][qx][0];
const double gradY = grad[qy][qx][1];
grad[qy][qx][0] = (O11 * gradX) + (O12 * gradY);
grad[qy][qx][1] = (O12 * gradX) + (O22 * gradY);
}
}
for (int qy = 0; qy < Q1D; ++qy)
{
double gradX[max_D1D][2];
for (int dx = 0; dx < D1D; ++dx)
{
gradX[dx][0] = 0;
gradX[dx][1] = 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 < 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 < D1D; ++dy)
{
const double wy = Bt(dy,qy);
const double wDy = Gt(dy,qy);
for (int dx = 0; dx < D1D; ++dx)
{
y(dx,dy,e) += ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
}
}
}
});
}
// Shared memory PA Diffusion Apply 2D kernel
template<const int T_D1D = 0,
const int T_Q1D = 0,
const int T_NBZ = 0>
static void SmemPADiffusionApply2D(const int NE,
const Array<double> &_b,
const Array<double> &_g,
const Array<double> &_bt,
const Array<double> &_gt,
const Vector &_op,
const Vector &_x,
Vector &_y,
const int d1d = 0,
const int q1d = 0)
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int NBZ = T_NBZ ? T_NBZ : 1;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
MFEM_VERIFY(D1D <= MD1, "");
MFEM_VERIFY(Q1D <= MQ1, "");
auto b = Reshape(_b.Read(), Q1D, D1D);
auto g = Reshape(_g.Read(), Q1D, D1D);
auto op = Reshape(_op.Read(), Q1D*Q1D, 3, NE);
auto x = Reshape(_x.Read(), D1D, D1D, NE);
auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
{
const int tidz = MFEM_THREAD_ID(z);
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int NBZ = T_NBZ ? T_NBZ : 1;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
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);
double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
MFEM_SHARED double Xz[NBZ][MD1][MD1];
MFEM_SHARED double GD[2][NBZ][MD1][MQ1];
MFEM_SHARED double GQ[2][NBZ][MD1][MQ1];
double (*X)[MD1] = (double (*)[MD1])(Xz + tidz);
double (*DQ0)[MD1] = (double (*)[MD1])(GD[0] + tidz);
double (*DQ1)[MD1] = (double (*)[MD1])(GD[1] + tidz);
double (*QQ0)[MD1] = (double (*)[MD1])(GQ[0] + tidz);
double (*QQ1)[MD1] = (double (*)[MD1])(GQ[1] + tidz);
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
X[dy][dx] = x(dx,dy,e);
}
}
if (tidz == 0)
{
MFEM_FOREACH_THREAD(d,y,D1D)
{
MFEM_FOREACH_THREAD(q,x,Q1D)
{
B[q][d] = b(q,d);
G[q][d] = g(q,d);
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(qx,x,Q1D)
{
double u = 0.0;
double v = 0.0;
for (int dx = 0; dx < D1D; ++dx)
{
const double coords = X[dy][dx];
u += B[qx][dx] * coords;
v += G[qx][dx] * coords;
}
DQ0[dy][qx] = u;
DQ1[dy][qx] = v;
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(qy,y,Q1D)
{
MFEM_FOREACH_THREAD(qx,x,Q1D)
{
double u = 0.0;
double v = 0.0;
for (int dy = 0; dy < D1D; ++dy)
{
u += DQ1[dy][qx] * B[qy][dy];
v += DQ0[dy][qx] * G[qy][dy];
}
QQ0[qy][qx] = u;
QQ1[qy][qx] = v;
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(qy,y,Q1D)
{
MFEM_FOREACH_THREAD(qx,x,Q1D)
{
const int q = (qx + ((qy) * Q1D));
const double O11 = op(q,0,e);
const double O12 = op(q,1,e);
const double O22 = op(q,2,e);
const double gX = QQ0[qy][qx];
const double gY = QQ1[qy][qx];
QQ0[qy][qx] = (O11 * gX) + (O12 * gY);
QQ1[qy][qx] = (O12 * gX) + (O22 * gY);
}
}
MFEM_SYNC_THREAD;
if (tidz == 0)
{
MFEM_FOREACH_THREAD(d,y,D1D)
{
MFEM_FOREACH_THREAD(q,x,Q1D)
{
Bt[d][q] = b(q,d);
Gt[d][q] = g(q,d);
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(qy,y,Q1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
double u = 0.0;
double v = 0.0;
for (int qx = 0; qx < Q1D; ++qx)
{
u += Gt[dx][qx] * QQ0[qy][qx];
v += Bt[dx][qx] * QQ1[qy][qx];
}
DQ0[qy][dx] = u;
DQ1[qy][dx] = v;
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
double u = 0.0;
double v = 0.0;
for (int qy = 0; qy < Q1D; ++qy)
{
u += DQ0[qy][dx] * Bt[dy][qy];
v += DQ1[qy][dx] * Gt[dy][qy];
}
y(dx,dy,e) += (u + v);
}
}
});
}
// PA Diffusion Apply 3D kernel
template<const int T_D1D = 0,
const int T_Q1D = 0> static
void PADiffusionApply3D(const int NE,
const Array<double> &b,
const Array<double> &g,
const Array<double> &bt,
const Array<double> &gt,
const Vector &_op,
const Vector &_x,
Vector &_y,
int d1d = 0, int q1d = 0)
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
MFEM_VERIFY(D1D <= MAX_D1D, "");
MFEM_VERIFY(Q1D <= MAX_Q1D, "");
auto B = Reshape(b.Read(), Q1D, D1D);
auto G = Reshape(g.Read(), Q1D, D1D);
auto Bt = Reshape(bt.Read(), D1D, Q1D);
auto Gt = Reshape(gt.Read(), D1D, Q1D);
auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 6, NE);
auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
MFEM_FORALL(e, NE,
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
double grad[max_Q1D][max_Q1D][max_Q1D][3];
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 < D1D; ++dz)
{
double gradXY[max_Q1D][max_Q1D][3];
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 < D1D; ++dy)
{
double gradX[max_Q1D][2];
for (int qx = 0; qx < Q1D; ++qx)
{
gradX[qx][0] = 0.0;
gradX[qx][1] = 0.0;
}
for (int dx = 0; dx < D1D; ++dx)
{
const double s = x(dx,dy,dz,e);
for (int qx = 0; qx < Q1D; ++qx)
{
gradX[qx][0] += s * B(qx,dx);
gradX[qx][1] += s * G(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)
{
const double wx = gradX[qx][0];
const double wDx = gradX[qx][1];
gradXY[qy][qx][0] += wDx * wy;
gradXY[qy][qx][1] += wx * wDy;
gradXY[qy][qx][2] += wx * 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;
}
}
}
}
// Calculate Dxyz, xDyz, xyDz 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 O11 = op(q,0,e);
const double O12 = op(q,1,e);
const double O13 = op(q,2,e);
const double O22 = op(q,3,e);
const double O23 = op(q,4,e);
const double O33 = op(q,5,e);
const double gradX = grad[qz][qy][qx][0];
const double gradY = grad[qz][qy][qx][1];
const double gradZ = grad[qz][qy][qx][2];
grad[qz][qy][qx][0] = (O11*gradX)+(O12*gradY)+(O13*gradZ);
grad[qz][qy][qx][1] = (O12*gradX)+(O22*gradY)+(O23*gradZ);
grad[qz][qy][qx][2] = (O13*gradX)+(O23*gradY)+(O33*gradZ);
}
}
}
for (int qz = 0; qz < Q1D; ++qz)
{
double gradXY[max_D1D][max_D1D][3];
for (int dy = 0; dy < D1D; ++dy)
{
for (int dx = 0; dx < D1D; ++dx)
{
gradXY[dy][dx][0] = 0;
gradXY[dy][dx][1] = 0;
gradXY[dy][dx][2] = 0;
}
}
for (int qy = 0; qy < Q1D; ++qy)
{
double gradX[max_D1D][3];
for (int dx = 0; dx < D1D; ++dx)
{
gradX[dx][0] = 0;
gradX[dx][1] = 0;
gradX[dx][2] = 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 < 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 < D1D; ++dy)
{
const double wy = Bt(dy,qy);
const double wDy = Gt(dy,qy);
for (int dx = 0; dx < 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 < D1D; ++dz)
{
const double wz = Bt(dz,qz);
const double wDz = Gt(dz,qz);
for (int dy = 0; dy < D1D; ++dy)
{
for (int dx = 0; dx < D1D; ++dx)
{
y(dx,dy,dz,e) +=
((gradXY[dy][dx][0] * wz) +
(gradXY[dy][dx][1] * wz) +
(gradXY[dy][dx][2] * wDz));
}
}
}
}
});
}
// Shared memory PA Diffusion Apply 3D kernel
template<const int T_D1D = 0,
const int T_Q1D = 0>
static void SmemPADiffusionApply3D(const int NE,
const Array<double> &_b,
const Array<double> &_g,
const Array<double> &_bt,
const Array<double> &_gt,
const Vector &_op,
const Vector &_x,
Vector &_y,
const int d1d = 0,
const int q1d = 0)
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
MFEM_VERIFY(D1D <= MD1, "");
MFEM_VERIFY(Q1D <= MQ1, "");
auto b = Reshape(_b.Read(), Q1D, D1D);
auto g = Reshape(_g.Read(), Q1D, D1D);
auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 6, NE);
auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
{
const int tidz = MFEM_THREAD_ID(z);
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
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);
double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
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 (*QQD1)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+1);
double (*QQD2)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+2);
double (*QDD0)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+0);
double (*QDD1)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+1);
double (*QDD2)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+2);
MFEM_FOREACH_THREAD(dz,z,D1D)
{
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
X[dz][dy][dx] = x(dx,dy,dz,e);
}
}
}
if (tidz == 0)
{
MFEM_FOREACH_THREAD(d,y,D1D)
{
MFEM_FOREACH_THREAD(q,x,Q1D)
{
B[q][d] = b(q,d);
G[q][d] = g(q,d);
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(dz,z,D1D)
{
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(qx,x,Q1D)
{
double u = 0.0;
double v = 0.0;
for (int dx = 0; dx < D1D; ++dx)
{
const double coords = X[dz][dy][dx];
u += coords * B[qx][dx];
v += coords * G[qx][dx];
}
DDQ0[dz][dy][qx] = u;
DDQ1[dz][dy][qx] = v;
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(dz,z,D1D)
{
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 < D1D; ++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 < D1D; ++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*Q1D) + (qz*Q1D*Q1D));
const double O11 = op(q,0,e);
const double O12 = op(q,1,e);
const double O13 = op(q,2,e);
const double O22 = op(q,3,e);
const double O23 = op(q,4,e);
const double O33 = op(q,5,e);
const double gX = QQQ0[qz][qy][qx];
const double gY = QQQ1[qz][qy][qx];
const double gZ = QQQ2[qz][qy][qx];
QQQ0[qz][qy][qx] = (O11*gX) + (O12*gY) + (O13*gZ);
QQQ1[qz][qy][qx] = (O12*gX) + (O22*gY) + (O23*gZ);
QQQ2[qz][qy][qx] = (O13*gX) + (O23*gY) + (O33*gZ);
}
}
}
MFEM_SYNC_THREAD;
if (tidz == 0)
{
MFEM_FOREACH_THREAD(d,y,D1D)
{
MFEM_FOREACH_THREAD(q,x,Q1D)
{
Bt[d][q] = b(q,d);
Gt[d][q] = g(q,d);
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(qz,z,Q1D)
{
MFEM_FOREACH_THREAD(qy,y,Q1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
double u = 0.0;
double v = 0.0;
double w = 0.0;
for (int qx = 0; qx < Q1D; ++qx)
{
u += QQQ0[qz][qy][qx] * Gt[dx][qx];
v += QQQ1[qz][qy][qx] * Bt[dx][qx];
w += QQQ2[qz][qy][qx] * Bt[dx][qx];
}
QQD0[qz][qy][dx] = u;
QQD1[qz][qy][dx] = v;
QQD2[qz][qy][dx] = w;
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(qz,z,Q1D)
{
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
double u = 0.0;
double v = 0.0;
double w = 0.0;
for (int qy = 0; qy < Q1D; ++qy)
{
u += QQD0[qz][qy][dx] * Bt[dy][qy];
v += QQD1[qz][qy][dx] * Gt[dy][qy];
w += QQD2[qz][qy][dx] * Bt[dy][qy];
}
QDD0[qz][dy][dx] = u;
QDD1[qz][dy][dx] = v;
QDD2[qz][dy][dx] = w;
}
}
}
MFEM_SYNC_THREAD;
MFEM_FOREACH_THREAD(dz,z,D1D)
{
MFEM_FOREACH_THREAD(dy,y,D1D)
{
MFEM_FOREACH_THREAD(dx,x,D1D)
{
double u = 0.0;
double v = 0.0;
double w = 0.0;
for (int qz = 0; qz < Q1D; ++qz)
{
u += QDD0[qz][dy][dx] * Bt[dz][qz];
v += QDD1[qz][dy][dx] * Bt[dz][qz];
w += QDD2[qz][dy][dx] * Gt[dz][qz];
}
y(dx,dy,dz,e) += (u + v + w);
}
}
}
});
}
static void PADiffusionApply(const int dim,
const int D1D,
const int Q1D,
const int NE,
const Array<double> &B,
const Array<double> &G,
const Array<double> &Bt,
const Array<double> &Gt,
const Vector &op,
const Vector &x,
Vector &y)
{
#ifdef MFEM_USE_OCCA
if (DeviceCanUseOcca())
{
if (dim == 2)
{
OccaPADiffusionApply2D(D1D, Q1D, NE, B, G, Bt, Gt, op, x, y);
return;
}
if (dim == 3)
{
OccaPADiffusionApply3D(D1D, Q1D, NE, B, G, Bt, Gt, op, x, y);
return;
}
MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
}
#endif // MFEM_USE_OCCA
if (dim == 2)
{
switch ((D1D << 4 ) | Q1D)
{
case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,Bt,Gt,op,x,y);
case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,Bt,Gt,op,x,y);
case 0x44: return SmemPADiffusionApply2D<4,4,8>(NE,B,G,Bt,Gt,op,x,y);
case 0x55: return SmemPADiffusionApply2D<5,5,8>(NE,B,G,Bt,Gt,op,x,y);
case 0x66: return SmemPADiffusionApply2D<6,6,4>(NE,B,G,Bt,Gt,op,x,y);
case 0x77: return SmemPADiffusionApply2D<7,7,4>(NE,B,G,Bt,Gt,op,x,y);
case 0x88: return SmemPADiffusionApply2D<8,8,2>(NE,B,G,Bt,Gt,op,x,y);
case 0x99: return SmemPADiffusionApply2D<9,9,2>(NE,B,G,Bt,Gt,op,x,y);
default: return PADiffusionApply2D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
}
}
else if (dim == 3)
{
switch ((D1D << 4 ) | Q1D)
{
case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,Bt,Gt,op,x,y);
case 0x45: return SmemPADiffusionApply3D<4,5>(NE,B,G,Bt,Gt,op,x,y);
case 0x56: return SmemPADiffusionApply3D<5,6>(NE,B,G,Bt,Gt,op,x,y);
case 0x67: return SmemPADiffusionApply3D<6,7>(NE,B,G,Bt,Gt,op,x,y);
case 0x78: return SmemPADiffusionApply3D<7,8>(NE,B,G,Bt,Gt,op,x,y);
case 0x89: return SmemPADiffusionApply3D<8,9>(NE,B,G,Bt,Gt,op,x,y);
default: return PADiffusionApply3D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
}
}
MFEM_ABORT("Unknown kernel.");
}
// PA Diffusion Apply kernel
void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
{
PADiffusionApply(dim, dofs1D, quad1D, ne,
maps->B, maps->G, maps->Bt, maps->Gt,
pa_data, x, y);
}
} // namespace mfem