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mfem/fem/bilininteg_vecdiffusion.cpp
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// 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 Vector Diffusion Integrator
// PA Diffusion Assemble 2D kernel
static void PAVectorDiffusionSetup2D(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, 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 c_detJ = W[q] * COEFF / ((J11*J22)-(J21*J12));
y(q,0,e) = c_detJ * (J12*J12 + J22*J22); // 1,1
y(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
y(q,2,e) = c_detJ * (J11*J11 + J21*J21); // 2,2
}
});
}
// PA Diffusion Assemble 3D kernel
static void PAVectorDiffusionSetup3D(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, 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 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
y(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
y(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
y(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
y(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
y(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
y(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
}
});
}
static void PAVectorDiffusionSetup(const int dim,
const int Q1D,
const int NE,
const Array<double> &W,
const Vector &J,
const double COEFF,
Vector &op)
{
if (!(dim == 2 || dim == 3))
{
MFEM_ABORT("Dimension not supported.");
}
if (dim == 2)
{
PAVectorDiffusionSetup2D(Q1D, NE, W, J, COEFF, op);
}
if (dim == 3)
{
PAVectorDiffusionSetup3D(Q1D, NE, W, J, COEFF, op);
}
}
void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
{
// Assumes tensor-product elements
Mesh *mesh = fes.GetMesh();
const FiniteElement &el = *fes.GetFE(0);
const IntegrationRule *ir
= IntRule ? IntRule : &DiffusionIntegrator::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();
sdim = mesh->SpaceDimension();
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::GetDeviceMemoryType());
double coeff = 1.0;
if (Q)
{
ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient*>(Q);
MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
coeff = cQ->constant;
}
const Array<double> &w = ir->GetWeights();
const Vector &j = geom->J;
Vector &d = pa_data;
if (dim == 1) { MFEM_ABORT("dim==1 not supported in PAVectorDiffusionSetup"); }
if (dim == 2 && sdim == 3)
{
constexpr int DIM = 2;
constexpr int SDIM = 3;
const int NQ = quad1D*quad1D;
auto W = w.Read();
auto J = Reshape(j.Read(), NQ, SDIM, DIM, ne);
auto D = Reshape(d.Write(), NQ, SDIM, ne);
MFEM_FORALL(e, ne,
{
for (int q = 0; q < NQ; ++q)
{
const double wq = W[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 E = J11*J11 + J21*J21 + J31*J31;
const double G = J12*J12 + J22*J22 + J32*J32;
const double F = J11*J12 + J21*J22 + J31*J32;
const double iw = 1.0 / sqrt(E*G - F*F);
const double alpha = wq * coeff * iw;
D(q,0,e) = alpha * G; // 1,1
D(q,1,e) = -alpha * F; // 1,2
D(q,2,e) = alpha * E; // 2,2
}
});
}
else
{
PAVectorDiffusionSetup(dim, quad1D, ne, w, j, coeff, d);
}
}
// PA Diffusion Apply 2D kernel
template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0> static
void PAVectorDiffusionApply2D(const int NE,
const Array<double> &b,
const Array<double> &g,
const Array<double> &bt,
const Array<double> &gt,
const Vector &d_,
const Vector &x_,
Vector &y_,
const int d1d = 0,
const int q1d = 0,
const int vdim = 0)
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
const int VDIM = T_VDIM ? T_VDIM : vdim;
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 D = Reshape(d_.Read(), Q1D*Q1D, 3, NE);
auto x = Reshape(x_.Read(), D1D, D1D, VDIM, NE);
auto y = Reshape(y_.ReadWrite(), D1D, D1D, VDIM, NE);
MFEM_FORALL(e, NE,
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
const int VDIM = T_VDIM ? T_VDIM : vdim;
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 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 < 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,c,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 = D(q,0,e);
const double O12 = D(q,1,e);
const double O22 = D(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] = 0.0;
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 < 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,c,e) += ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
}
}
}
}
});
}
// PA Diffusion Apply 3D kernel
template<const int T_D1D = 0,
const int T_Q1D = 0> static
void PAVectorDiffusionApply3D(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;
constexpr int VDIM = 3;
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, VDIM, NE);
auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, VDIM, 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;
for (int c = 0; c < VDIM; ++ c)
{
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,c,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,c,e) +=
((gradXY[dy][dx][0] * wz) +
(gradXY[dy][dx][1] * wz) +
(gradXY[dy][dx][2] * wDz));
}
}
}
}
}
});
}
// PA Diffusion Apply kernel
void VectorDiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
{
const int D1D = dofs1D;
const int Q1D = quad1D;
const Array<double> &B = maps->B;
const Array<double> &G = maps->G;
const Array<double> &Bt = maps->Bt;
const Array<double> &Gt = maps->Gt;
const Vector &D = pa_data;
if (dim == 2 && sdim == 3)
{
switch ((dofs1D << 4 ) | quad1D)
{
case 0x22: return PAVectorDiffusionApply2D<2,2,3>(ne,B,G,Bt,Gt,D,x,y);
case 0x33: return PAVectorDiffusionApply2D<3,3,3>(ne,B,G,Bt,Gt,D,x,y);
case 0x44: return PAVectorDiffusionApply2D<4,4,3>(ne,B,G,Bt,Gt,D,x,y);
case 0x55: return PAVectorDiffusionApply2D<5,5,3>(ne,B,G,Bt,Gt,D,x,y);
default:
return PAVectorDiffusionApply2D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D,sdim);
}
}
if (dim == 2 && sdim == 2)
{ return PAVectorDiffusionApply2D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D,sdim); }
if (dim == 3 && sdim == 3)
{ return PAVectorDiffusionApply3D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D); }
MFEM_ABORT("Unknown kernel.");
}
template<int T_D1D = 0, int T_Q1D = 0>
static void PAVectorDiffusionDiagonal2D(const int NE,
const Array<double> &b,
const Array<double> &g,
const Vector &d,
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);
// note the different shape for D, this is a (symmetric) matrix so we only
// store necessary entries
auto D = Reshape(d.Read(), Q1D*Q1D, 3, NE);
auto Y = Reshape(y.ReadWrite(), D1D, D1D, 2, NE);
MFEM_FORALL(e, NE,
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
// gradphi \cdot Q \gradphi has four terms
double QD0[MQ1][MD1];
double QD1[MQ1][MD1];
double QD2[MQ1][MD1];
for (int qx = 0; qx < Q1D; ++qx)
{
for (int dy = 0; dy < D1D; ++dy)
{
QD0[qx][dy] = 0.0;
QD1[qx][dy] = 0.0;
QD2[qx][dy] = 0.0;
for (int qy = 0; qy < Q1D; ++qy)
{
const int q = qx + qy * Q1D;
const double D0 = D(q,0,e);
const double D1 = D(q,1,e);
const double D2 = D(q,2,e);
QD0[qx][dy] += B(qy, dy) * B(qy, dy) * D0;
QD1[qx][dy] += B(qy, dy) * G(qy, dy) * D1;
QD2[qx][dy] += G(qy, dy) * G(qy, dy) * D2;
}
}
}
for (int dy = 0; dy < D1D; ++dy)
{
for (int dx = 0; dx < D1D; ++dx)
{
double temp = 0.0;
for (int qx = 0; qx < Q1D; ++qx)
{
temp += G(qx, dx) * G(qx, dx) * QD0[qx][dy];
temp += G(qx, dx) * B(qx, dx) * QD1[qx][dy];
temp += B(qx, dx) * G(qx, dx) * QD1[qx][dy];
temp += B(qx, dx) * B(qx, dx) * QD2[qx][dy];
}
Y(dx,dy,0,e) += temp;
Y(dx,dy,1,e) += temp;
}
}
});
}
template<int T_D1D = 0, int T_Q1D = 0>
static void PAVectorDiffusionDiagonal3D(const int NE,
const Array<double> &b,
const Array<double> &g,
const Vector &d,
Vector &y,
const int d1d = 0,
const int q1d = 0)
{
constexpr int DIM = 3;
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 Q = Reshape(d.Read(), Q1D*Q1D*Q1D, 6, NE);
auto Y = Reshape(y.ReadWrite(), D1D, D1D, D1D, 3, NE);
MFEM_FORALL(e, NE,
{
const int D1D = T_D1D ? T_D1D : d1d;
const int Q1D = T_Q1D ? T_Q1D : q1d;
constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
double QQD[MQ1][MQ1][MD1];
double QDD[MQ1][MD1][MD1];
for (int i = 0; i < DIM; ++i)
{
for (int j = 0; j < DIM; ++j)
{
// first tensor contraction, along z direction
for (int qx = 0; qx < Q1D; ++qx)
{
for (int qy = 0; qy < Q1D; ++qy)
{
for (int dz = 0; dz < D1D; ++dz)
{
QQD[qx][qy][dz] = 0.0;
for (int qz = 0; qz < Q1D; ++qz)
{
const int q = qx + (qy + qz * Q1D) * Q1D;
const int k = j >= i ?
3 - (3-i)*(2-i)/2 + j:
3 - (3-j)*(2-j)/2 + i;
const double O = Q(q,k,e);
const double Bz = B(qz,dz);
const double Gz = G(qz,dz);
const double L = i==2 ? Gz : Bz;
const double R = j==2 ? Gz : Bz;
QQD[qx][qy][dz] += L * O * R;
}
}
}
}
// second tensor contraction, along y direction
for (int qx = 0; qx < Q1D; ++qx)
{
for (int dz = 0; dz < D1D; ++dz)
{
for (int dy = 0; dy < D1D; ++dy)
{
QDD[qx][dy][dz] = 0.0;
for (int qy = 0; qy < Q1D; ++qy)
{
const double By = B(qy,dy);
const double Gy = G(qy,dy);
const double L = i==1 ? Gy : By;
const double R = j==1 ? Gy : By;
QDD[qx][dy][dz] += L * QQD[qx][qy][dz] * R;
}
}
}
}
// third tensor contraction, along x direction
for (int dz = 0; dz < D1D; ++dz)
{
for (int dy = 0; dy < D1D; ++dy)
{
for (int dx = 0; dx < D1D; ++dx)
{
double temp = 0.0;
for (int qx = 0; qx < Q1D; ++qx)
{
const double Bx = B(qx,dx);
const double Gx = G(qx,dx);
const double L = i==0 ? Gx : Bx;
const double R = j==0 ? Gx : Bx;
temp += L * QDD[qx][dy][dz] * R;
}
Y(dx, dy, dz, 0, e) += temp;
Y(dx, dy, dz, 1, e) += temp;
Y(dx, dy, dz, 2, e) += temp;
}
}
}
}
}
});
}
static void PAVectorDiffusionAssembleDiagonal(const int dim,
const int D1D,
const int Q1D,
const int NE,
const Array<double> &B,
const Array<double> &G,
const Vector &op,
Vector &y)
{
if (dim == 2)
{
return PAVectorDiffusionDiagonal2D(NE, B, G, op, y, D1D, Q1D);
}
else if (dim == 3)
{
return PAVectorDiffusionDiagonal3D(NE, B, G, op, y, D1D, Q1D);
}
MFEM_ABORT("Dimension not implemented.");
}
void VectorDiffusionIntegrator::AssembleDiagonalPA(Vector &diag)
{
PAVectorDiffusionAssembleDiagonal(dim,
dofs1D,
quad1D,
ne,
maps->B,
maps->G,
pa_data,
diag);
}
} // namespace mfem
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