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laghos_assembly.cpp
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// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project (17-SC-20-SC)
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.
#include "laghos_assembly.hpp"
#ifdef MFEM_USE_MPI
using namespace std;
namespace mfem
{
namespace hydrodynamics
{
const Tensors1D *tensors1D = NULL;
const FastEvaluator *evaluator = NULL;
Tensors1D::Tensors1D(int H1order, int L2order, int nqp1D)
: HQshape1D(H1order + 1, nqp1D),
HQgrad1D(H1order + 1, nqp1D),
LQshape1D(L2order + 1, nqp1D)
{
// In this miniapp we assume:
// - Gauss-Legendre quadrature points.
// - Gauss-Lobatto continuous kinematic basis.
// - Bernstein discontinuous thermodynamic basis.
const double *quad1D_pos = poly1d.GetPoints(nqp1D - 1,
Quadrature1D::GaussLegendre);
Poly_1D::Basis &basisH1 = poly1d.GetBasis(H1order,
Quadrature1D::GaussLobatto);
Vector col, grad_col;
for (int q = 0; q < nqp1D; q++)
{
HQshape1D.GetColumnReference(q, col);
HQgrad1D.GetColumnReference(q, grad_col);
basisH1.Eval(quad1D_pos[q], col, grad_col);
}
for (int q = 0; q < nqp1D; q++)
{
LQshape1D.GetColumnReference(q, col);
poly1d.CalcBernstein(L2order, quad1D_pos[q], col);
}
}
void FastEvaluator::GetL2Values(const Vector &vecL2, Vector &vecQ) const
{
const int nL2dof1D = tensors1D->LQshape1D.Height(),
nqp1D = tensors1D->LQshape1D.Width();
if (dim == 2)
{
DenseMatrix E(vecL2.GetData(), nL2dof1D, nL2dof1D);
DenseMatrix LQ(nL2dof1D, nqp1D);
vecQ.SetSize(nqp1D * nqp1D);
DenseMatrix QQ(vecQ.GetData(), nqp1D, nqp1D);
// LQ_j2_k1 = E_j1_j2 LQs_j1_k1 -- contract in x direction.
// QQ_k1_k2 = LQ_j2_k1 LQs_j2_k2 -- contract in y direction.
MultAtB(E, tensors1D->LQshape1D, LQ);
MultAtB(LQ, tensors1D->LQshape1D, QQ);
}
else
{
DenseMatrix E(vecL2.GetData(), nL2dof1D*nL2dof1D, nL2dof1D);
DenseMatrix LL_Q(nL2dof1D * nL2dof1D, nqp1D),
L_LQ(LL_Q.GetData(), nL2dof1D, nL2dof1D*nqp1D),
Q_LQ(nqp1D, nL2dof1D*nqp1D);
vecQ.SetSize(nqp1D * nqp1D * nqp1D);
DenseMatrix QQ_Q(vecQ.GetData(), nqp1D * nqp1D, nqp1D);
// LLQ_j1_j2_k3 = E_j1_j2_j3 LQs_j3_k3 -- contract in z direction.
// QLQ_k1_j2_k3 = LQs_j1_k1 LLQ_j1_j2_k3 -- contract in x direction.
// QQQ_k1_k2_k3 = QLQ_k1_j2_k3 LQs_j2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(E, tensors1D->LQshape1D, LL_Q);
MultAtB(tensors1D->LQshape1D, L_LQ, Q_LQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Q(k1 + nqp1D*k2, k3) = 0.0;
for (int j2 = 0; j2 < nL2dof1D; j2++)
{
QQ_Q(k1 + nqp1D*k2, k3) +=
Q_LQ(k1, j2 + k3*nL2dof1D) * tensors1D->LQshape1D(j2, k2);
}
}
}
}
}
}
void FastEvaluator::GetVectorGrad(const DenseMatrix &vec, DenseTensor &J) const
{
const int nH1dof1D = tensors1D->HQshape1D.Height(),
nqp1D = tensors1D->LQshape1D.Width();
DenseMatrix X;
if (dim == 2)
{
const int nH1dof = nH1dof1D * nH1dof1D;
DenseMatrix HQ(nH1dof1D, nqp1D), QQ(nqp1D, nqp1D);
Vector x(nH1dof);
const H1_QuadrilateralElement *fe =
dynamic_cast<const H1_QuadrilateralElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
for (int c = 0; c < 2; c++)
{
// Transfer from the mfem's H1 local numbering to the tensor structure
// numbering.
for (int j = 0; j < nH1dof; j++) { x[j] = vec(dof_map[j], c); }
X.UseExternalData(x.GetData(), nH1dof1D, nH1dof1D);
// HQ_i2_k1 = X_i1_i2 HQg_i1_k1 -- gradients in x direction.
// QQ_k1_k2 = HQ_i2_k1 HQs_i2_k2 -- contract in y direction.
MultAtB(X, tensors1D->HQgrad1D, HQ);
MultAtB(HQ, tensors1D->HQshape1D, QQ);
// Set the (c,0) component of the Jacobians at all quadrature points.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
const int idx = k2 * nqp1D + k1;
J(idx)(c, 0) = QQ(k1, k2);
}
}
// HQ_i2_k1 = X_i1_i2 HQs_i1_k1 -- contract in x direction.
// QQ_k1_k2 = HQ_i2_k1 HQg_i2_k2 -- gradients in y direction.
MultAtB(X, tensors1D->HQshape1D, HQ);
MultAtB(HQ, tensors1D->HQgrad1D, QQ);
// Set the (c,1) component of the Jacobians at all quadrature points.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
const int idx = k2 * nqp1D + k1;
J(idx)(c, 1) = QQ(k1, k2);
}
}
}
}
else
{
const int nH1dof = nH1dof1D * nH1dof1D * nH1dof1D;
DenseMatrix HH_Q(nH1dof1D * nH1dof1D, nqp1D),
H_HQ(HH_Q.GetData(), nH1dof1D, nH1dof1D * nqp1D),
Q_HQ(nqp1D, nH1dof1D*nqp1D), QQ_Q(nqp1D * nqp1D, nqp1D);
Vector x(nH1dof);
const H1_HexahedronElement *fe =
dynamic_cast<const H1_HexahedronElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
for (int c = 0; c < 3; c++)
{
// Transfer from the mfem's H1 local numbering to the tensor structure
// numbering.
for (int j = 0; j < nH1dof; j++) { x[j] = vec(dof_map[j], c); }
X.UseExternalData(x.GetData(), nH1dof1D * nH1dof1D, nH1dof1D);
// HHQ_i1_i2_k3 = X_i1_i2_i3 HQs_i3_k3 -- contract in z direction.
// QHQ_k1_i2_k3 = HQg_i1_k1 HHQ_i1_i2_k3 -- gradients in x direction.
// QQQ_k1_k2_k3 = QHQ_k1_i2_k3 HQs_i2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(X, tensors1D->HQshape1D, HH_Q);
MultAtB(tensors1D->HQgrad1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Q(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Q(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQshape1D(i2, k2);
}
}
}
}
// Set the (c,0) component of the Jacobians at all quadrature points.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
const int idx = k3*nqp1D*nqp1D + k2*nqp1D + k1;
J(idx)(c, 0) = QQ_Q(k1 + k2*nqp1D, k3);
}
}
}
// HHQ_i1_i2_k3 = X_i1_i2_i3 HQs_i3_k3 -- contract in z direction.
// QHQ_k1_i2_k3 = HQs_i1_k1 HHQ_i1_i2_k3 -- contract in x direction.
// QQQ_k1_k2_k3 = QHQ_k1_i2_k3 HQg_i2_k2 -- gradients in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(X, tensors1D->HQshape1D, HH_Q);
MultAtB(tensors1D->HQshape1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Q(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Q(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQgrad1D(i2, k2);
}
}
}
}
// Set the (c,1) component of the Jacobians at all quadrature points.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
const int idx = k3*nqp1D*nqp1D + k2*nqp1D + k1;
J(idx)(c, 1) = QQ_Q(k1 + k2*nqp1D, k3);
}
}
}
// HHQ_i1_i2_k3 = X_i1_i2_i3 HQg_i3_k3 -- gradients in z direction.
// QHQ_k1_i2_k3 = HQs_i1_k1 HHQ_i1_i2_k3 -- contract in x direction.
// QQQ_k1_k2_k3 = QHQ_k1_i2_k3 HQs_i2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(X, tensors1D->HQgrad1D, HH_Q);
MultAtB(tensors1D->HQshape1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Q(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Q(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQshape1D(i2, k2);
}
}
}
}
// Set the (c,2) component of the Jacobians at all quadrature points.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
const int idx = k3*nqp1D*nqp1D + k2*nqp1D + k1;
J(idx)(c, 2) = QQ_Q(k1 + k2*nqp1D, k3);
}
}
}
}
}
}
void DensityIntegrator::AssembleRHSElementVect(const FiniteElement &fe,
ElementTransformation &Tr,
Vector &elvect)
{
const int ip_cnt = IntRule->GetNPoints();
Vector shape(fe.GetDof());
elvect.SetSize(fe.GetDof());
elvect = 0.0;
for (int q = 0; q < ip_cnt; q++)
{
fe.CalcShape(IntRule->IntPoint(q), shape);
// Note that rhoDetJ = rho0DetJ0.
shape *= quad_data.rho0DetJ0w(Tr.ElementNo*ip_cnt + q);
elvect += shape;
}
}
void ForceIntegrator::AssembleElementMatrix2(const FiniteElement &trial_fe,
const FiniteElement &test_fe,
ElementTransformation &Trans,
DenseMatrix &elmat)
{
const int nqp = IntRule->GetNPoints();
const int dim = trial_fe.GetDim();
const int zone_id = Trans.ElementNo;
const int h1dofs_cnt = test_fe.GetDof();
const int l2dofs_cnt = trial_fe.GetDof();
elmat.SetSize(h1dofs_cnt*dim, l2dofs_cnt);
elmat = 0.0;
DenseMatrix vshape(h1dofs_cnt, dim), loc_force(h1dofs_cnt, dim);
Vector shape(l2dofs_cnt), Vloc_force(loc_force.Data(), h1dofs_cnt*dim);
for (int q = 0; q < nqp; q++)
{
const IntegrationPoint &ip = IntRule->IntPoint(q);
// Form stress:grad_shape at the current point.
test_fe.CalcDShape(ip, vshape);
for (int i = 0; i < h1dofs_cnt; i++)
{
for (int vd = 0; vd < dim; vd++) // Velocity components.
{
loc_force(i, vd) = 0.0;
for (int gd = 0; gd < dim; gd++) // Gradient components.
{
loc_force(i, vd) +=
quad_data.stressJinvT(vd)(zone_id*nqp + q, gd) * vshape(i,gd);
}
}
}
trial_fe.CalcShape(ip, shape);
AddMultVWt(Vloc_force, shape, elmat);
}
}
void ForcePAOperator::Mult(const Vector &vecL2, Vector &vecH1) const
{
if (dim == 2) { MultQuad(vecL2, vecH1); }
else if (dim == 3) { MultHex(vecL2, vecH1); }
else { MFEM_ABORT("Unsupported dimension"); }
}
void ForcePAOperator::MultTranspose(const Vector &vecH1, Vector &vecL2) const
{
if (dim == 2) { MultTransposeQuad(vecH1, vecL2); }
else if (dim == 3) { MultTransposeHex(vecH1, vecL2); }
else { MFEM_ABORT("Unsupported dimension"); }
}
// Force matrix action on quadrilateral elements in 2D.
void ForcePAOperator::MultQuad(const Vector &vecL2, Vector &vecH1) const
{
const int nH1dof1D = tensors1D->HQshape1D.Height(),
nL2dof1D = tensors1D->LQshape1D.Height(),
nqp1D = tensors1D->HQshape1D.Width(),
nqp = nqp1D * nqp1D,
nH1dof = nH1dof1D * nH1dof1D;
Array<int> h1dofs, l2dofs;
Vector e(nL2dof1D * nL2dof1D);
DenseMatrix E(e.GetData(), nL2dof1D, nL2dof1D);
DenseMatrix LQ(nL2dof1D, nqp1D), HQ(nH1dof1D, nqp1D), QQ(nqp1D, nqp1D),
HHx(nH1dof1D, nH1dof1D), HHy(nH1dof1D, nH1dof1D);
// Quadrature data for a specific direction.
DenseMatrix QQd(nqp1D, nqp1D);
double *data_qd = QQd.GetData(), *data_q = QQ.GetData();
const H1_QuadrilateralElement *fe =
dynamic_cast<const H1_QuadrilateralElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
vecH1 = 0.0;
for (int z = 0; z < nzones; z++)
{
// Note that the local numbering for L2 is the tensor numbering.
L2FESpace.GetElementDofs(z, l2dofs);
vecL2.GetSubVector(l2dofs, e);
// LQ_j2_k1 = E_j1_j2 LQs_j1_k1 -- contract in x direction.
// QQ_k1_k2 = LQ_j2_k1 LQs_j2_k2 -- contract in y direction.
MultAtB(E, tensors1D->LQshape1D, LQ);
MultAtB(LQ, tensors1D->LQshape1D, QQ);
// Iterate over the components (x and y) of the result.
for (int c = 0; c < 2; c++)
{
// QQd_k1_k2 *= stress_k1_k2(c,0) -- stress that scales d[v_c]_dx.
// HQ_i2_k1 = HQs_i2_k2 QQ_k1_k2 -- contract in y direction.
// HHx_i1_i2 = HQg_i1_k1 HQ_i2_k1 -- gradients in x direction.
double *d = quad_data->stressJinvT(c).GetData() + z*nqp;
for (int q = 0; q < nqp; q++) { data_qd[q] = data_q[q] * d[q]; }
MultABt(tensors1D->HQshape1D, QQd, HQ);
MultABt(tensors1D->HQgrad1D, HQ, HHx);
// QQd_k1_k2 *= stress_k1_k2(c,1) -- stress that scales d[v_c]_dy.
// HQ_i2_k1 = HQg_i2_k2 QQ_k1_k2 -- gradients in y direction.
// HHy_i1_i2 = HQ_i1_k1 HQ_i2_k1 -- contract in x direction.
d = quad_data->stressJinvT(c).GetData() + 1*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { data_qd[q] = data_q[q] * d[q]; }
MultABt(tensors1D->HQgrad1D, QQd, HQ);
MultABt(tensors1D->HQshape1D, HQ, HHy);
// Set the c-component of the result.
H1FESpace.GetElementVDofs(z, h1dofs);
for (int i1 = 0; i1 < nH1dof1D; i1++)
{
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
// Transfer from the mfem's H1 local numbering to the tensor
// structure numbering.
const int idx = i2 * nH1dof1D + i1;
vecH1[h1dofs[c*nH1dof + dof_map[idx]]] +=
HHx(i1, i2) + HHy(i1, i2);
}
}
}
}
}
// Force matrix action on hexahedral elements in 3D.
void ForcePAOperator::MultHex(const Vector &vecL2, Vector &vecH1) const
{
const int nH1dof1D = tensors1D->HQshape1D.Height(),
nL2dof1D = tensors1D->LQshape1D.Height(),
nqp1D = tensors1D->HQshape1D.Width(),
nqp = nqp1D * nqp1D * nqp1D,
nH1dof = nH1dof1D * nH1dof1D * nH1dof1D;
Array<int> h1dofs, l2dofs;
Vector e(nL2dof1D * nL2dof1D * nL2dof1D);
DenseMatrix E(e.GetData(), nL2dof1D*nL2dof1D, nL2dof1D);
DenseMatrix HH_Q(nH1dof1D * nH1dof1D, nqp1D),
H_HQ(HH_Q.GetData(), nH1dof1D, nH1dof1D*nqp1D),
Q_HQ(nqp1D, nH1dof1D*nqp1D);
DenseMatrix LL_Q(nL2dof1D * nL2dof1D, nqp1D),
L_LQ(LL_Q.GetData(), nL2dof1D, nL2dof1D*nqp1D),
Q_LQ(nqp1D, nL2dof1D*nqp1D);
DenseMatrix QQ_Q(nqp1D * nqp1D, nqp1D), QQ_Qc(nqp1D * nqp1D, nqp1D);
double *qqq = QQ_Q.GetData(), *qqqc = QQ_Qc.GetData();
DenseMatrix HHHx(nH1dof1D * nH1dof1D, nH1dof1D),
HHHy(nH1dof1D * nH1dof1D, nH1dof1D),
HHHz(nH1dof1D * nH1dof1D, nH1dof1D);
const H1_HexahedronElement *fe =
dynamic_cast<const H1_HexahedronElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
vecH1 = 0.0;
for (int z = 0; z < nzones; z++)
{
// Note that the local numbering for L2 is the tensor numbering.
L2FESpace.GetElementDofs(z, l2dofs);
vecL2.GetSubVector(l2dofs, e);
// LLQ_j1_j2_k3 = E_j1_j2_j3 LQs_j3_k3 -- contract in z direction.
// QLQ_k1_j2_k3 = LQs_j1_k1 LLQ_j1_j2_k3 -- contract in x direction.
// QQQ_k1_k2_k3 = QLQ_k1_j2_k3 LQs_j2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(E, tensors1D->LQshape1D, LL_Q);
MultAtB(tensors1D->LQshape1D, L_LQ, Q_LQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Q(k1 + nqp1D*k2, k3) = 0.0;
for (int j2 = 0; j2 < nL2dof1D; j2++)
{
QQ_Q(k1 + nqp1D*k2, k3) +=
Q_LQ(k1, j2 + k3*nL2dof1D) * tensors1D->LQshape1D(j2, k2);
}
}
}
}
// Iterate over the components (x, y, z) of the result.
for (int c = 0; c < 3; c++)
{
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,0) -- stress scaling d[v_c]_dx.
double *d = quad_data->stressJinvT(c).GetData() + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] = qqq[q] * d[q]; }
// QHQ_k1_i2_k3 = QQQc_k1_k2_k3 HQs_i2_k2 -- contract in y direction.
// The first step does some reordering (it's not product of matrices).
// HHQ_i1_i2_k3 = HQg_i1_k1 QHQ_k1_i2_k3 -- gradients in x direction.
// HHHx_i1_i2_i3 = HHQ_i1_i2_k3 HQs_i3_k3 -- contract in z direction.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) = 0.0;
for (int k2 = 0; k2 < nqp1D; k2++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) +=
QQ_Qc(k1 + nqp1D*k2, k3) * tensors1D->HQshape1D(i2, k2);
}
}
}
}
mfem::Mult(tensors1D->HQgrad1D, Q_HQ, H_HQ);
MultABt(HH_Q, tensors1D->HQshape1D, HHHx);
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,1) -- stress scaling d[v_c]_dy.
d = quad_data->stressJinvT(c).GetData() + 1*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] = qqq[q] * d[q]; }
// QHQ_k1_i2_k3 = QQQc_k1_k2_k3 HQg_i2_k2 -- gradients in y direction.
// The first step does some reordering (it's not product of matrices).
// HHQ_i1_i2_k3 = HQs_i1_k1 QHQ_k1_i2_k3 -- contract in x direction.
// HHHy_i1_i2_i3 = HHQ_i1_i2_k3 HQs_i3_k3 -- contract in z direction.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) = 0.0;
for (int k2 = 0; k2 < nqp1D; k2++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) +=
QQ_Qc(k1 + nqp1D*k2, k3) * tensors1D->HQgrad1D(i2, k2);
}
}
}
}
mfem::Mult(tensors1D->HQshape1D, Q_HQ, H_HQ);
MultABt(HH_Q, tensors1D->HQshape1D, HHHy);
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,2) -- stress scaling d[v_c]_dz.
d = quad_data->stressJinvT(c).GetData() + 2*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] = qqq[q] * d[q]; }
// QHQ_k1_i2_k3 = QQQc_k1_k2_k3 HQg_i2_k2 -- contract in y direction.
// The first step does some reordering (it's not product of matrices).
// HHQ_i1_i2_k3 = HQs_i1_k1 QHQ_k1_i2_k3 -- contract in x direction.
// HHHz_i1_i2_i3 = HHQ_i1_i2_k3 HQs_i3_k3 -- gradients in z direction.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) = 0.0;
for (int k2 = 0; k2 < nqp1D; k2++)
{
Q_HQ(k1, i2 + nH1dof1D*k3) +=
QQ_Qc(k1 + nqp1D*k2, k3) * tensors1D->HQshape1D(i2, k2);
}
}
}
}
mfem::Mult(tensors1D->HQshape1D, Q_HQ, H_HQ);
MultABt(HH_Q, tensors1D->HQgrad1D, HHHz);
// Set the c-component of the result.
H1FESpace.GetElementVDofs(z, h1dofs);
for (int i1 = 0; i1 < nH1dof1D; i1++)
{
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
for (int i3 = 0; i3 < nH1dof1D; i3++)
{
// Transfer from the mfem's H1 local numbering to the tensor
// structure numbering.
const int idx = i3*nH1dof1D*nH1dof1D + i2*nH1dof1D + i1;
vecH1[h1dofs[c*nH1dof + dof_map[idx]]] +=
HHHx(i1 + i2*nH1dof1D, i3) +
HHHy(i1 + i2*nH1dof1D, i3) +
HHHz(i1 + i2*nH1dof1D, i3);
}
}
}
}
}
}
// Transpose force matrix action on quadrilateral elements in 2D.
void ForcePAOperator::MultTransposeQuad(const Vector &vecH1,
Vector &vecL2) const
{
const int nH1dof1D = tensors1D->HQshape1D.Height(),
nL2dof1D = tensors1D->LQshape1D.Height(),
nqp1D = tensors1D->HQshape1D.Width(),
nqp = nqp1D * nqp1D,
nH1dof = nH1dof1D * nH1dof1D;
Array<int> h1dofs, l2dofs;
Vector v(nH1dof * 2), e(nL2dof1D * nL2dof1D);
DenseMatrix V, E(e.GetData(), nL2dof1D, nL2dof1D);
DenseMatrix HQ(nH1dof1D, nqp1D), LQ(nL2dof1D, nqp1D),
QQc(nqp1D, nqp1D), QQ(nqp1D, nqp1D);
double *qqc = QQc.GetData();
const H1_QuadrilateralElement *fe =
dynamic_cast<const H1_QuadrilateralElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
for (int z = 0; z < nzones; z++)
{
H1FESpace.GetElementVDofs(z, h1dofs);
// Form (stress:grad_v) at all quadrature points.
QQ = 0.0;
for (int c = 0; c < 2; c++)
{
// Transfer from the mfem's H1 local numbering to the tensor structure
// numbering.
for (int j = 0; j < nH1dof; j++)
{
v[c*nH1dof + j] = vecH1[h1dofs[c*nH1dof + dof_map[j]]];
}
// Connect to [v_c], i.e., the c-component of v.
V.UseExternalData(v.GetData() + c*nH1dof, nH1dof1D, nH1dof1D);
// HQ_i2_k1 = V_i1_i2 HQg_i1_k1 -- gradients in x direction.
// QQc_k1_k2 = HQ_i2_k1 HQs_i2_k2 -- contract in y direction.
// QQc_k1_k2 *= stress_k1_k2(c,0) -- stress that scales d[v_c]_dx.
MultAtB(V, tensors1D->HQgrad1D, HQ);
MultAtB(HQ, tensors1D->HQshape1D, QQc);
double *d = quad_data->stressJinvT(c).GetData() + z*nqp;
for (int q = 0; q < nqp; q++) { qqc[q] *= d[q]; }
// Add the (stress(c,0) * d[v_c]_dx) part of (stress:grad_v).
QQ += QQc;
// HQ_i2_k1 = V_i1_i2 HQs_i1_k1 -- contract in x direction.
// QQc_k1_k2 = HQ_i2_k1 HQg_i2_k2 -- gradients in y direction.
// QQc_k1_k2 *= stress_k1_k2(c,1) -- stress that scales d[v_c]_dy.
MultAtB(V, tensors1D->HQshape1D, HQ);
MultAtB(HQ, tensors1D->HQgrad1D, QQc);
d = quad_data->stressJinvT(c).GetData() + 1*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { qqc[q] *= d[q]; }
// Add the (stress(c,1) * d[v_c]_dy) part of (stress:grad_v).
QQ += QQc;
}
// LQ_j1_k2 = LQs_j1_k1 QQ_k1_k2 -- contract in x direction.
// E_j1_j2 = LQ_j1_k2 LQs_j2_k2 -- contract in y direction.
mfem::Mult(tensors1D->LQshape1D, QQ, LQ);
MultABt(LQ, tensors1D->LQshape1D, E);
L2FESpace.GetElementDofs(z, l2dofs);
vecL2.SetSubVector(l2dofs, e);
}
}
// Transpose force matrix action on hexahedral elements in 3D.
void ForcePAOperator::MultTransposeHex(const Vector &vecH1, Vector &vecL2) const
{
const int nH1dof1D = tensors1D->HQshape1D.Height(),
nL2dof1D = tensors1D->LQshape1D.Height(),
nqp1D = tensors1D->HQshape1D.Width(),
nqp = nqp1D * nqp1D * nqp1D,
nH1dof = nH1dof1D * nH1dof1D * nH1dof1D;
Array<int> h1dofs, l2dofs;
Vector v(nH1dof * 3), e(nL2dof1D * nL2dof1D * nL2dof1D);
DenseMatrix V, E(e.GetData(), nL2dof1D * nL2dof1D, nL2dof1D);
DenseMatrix HH_Q(nH1dof1D * nH1dof1D, nqp1D),
H_HQ(HH_Q.GetData(), nH1dof1D, nH1dof1D * nqp1D),
Q_HQ(nqp1D, nH1dof1D*nqp1D);
DenseMatrix LL_Q(nL2dof1D * nL2dof1D, nqp1D),
L_LQ(LL_Q.GetData(), nL2dof1D, nL2dof1D * nqp1D),
Q_LQ(nqp1D, nL2dof1D*nqp1D);
DenseMatrix QQ_Q(nqp1D * nqp1D, nqp1D), QQ_Qc(nqp1D * nqp1D, nqp1D);
double *qqqc = QQ_Qc.GetData();
const H1_HexahedronElement *fe =
dynamic_cast<const H1_HexahedronElement *>(H1FESpace.GetFE(0));
const Array<int> &dof_map = fe->GetDofMap();
for (int z = 0; z < nzones; z++)
{
H1FESpace.GetElementVDofs(z, h1dofs);
// Form (stress:grad_v) at all quadrature points.
QQ_Q = 0.0;
for (int c = 0; c < 3; c++)
{
// Transfer from the mfem's H1 local numbering to the tensor structure
// numbering.
for (int j = 0; j < nH1dof; j++)
{
v[c*nH1dof + j] = vecH1[h1dofs[c*nH1dof + dof_map[j]]];
}
// Connect to [v_c], i.e., the c-component of v.
V.UseExternalData(v.GetData() + c*nH1dof, nH1dof1D*nH1dof1D, nH1dof1D);
// HHQ_i1_i2_k3 = V_i1_i2_i3 HQs_i3_k3 -- contract in z direction.
// QHQ_k1_i2_k3 = HQg_i1_k1 HHQ_i1_i2_k3 -- gradients in x direction.
// QQQc_k1_k2_k3 = QHQ_k1_i2_k3 HQs_i2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(V, tensors1D->HQshape1D, HH_Q);
MultAtB(tensors1D->HQgrad1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Qc(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Qc(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQshape1D(i2, k2);
}
}
}
}
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,0) -- stress scaling d[v_c]_dx.
double *d = quad_data->stressJinvT(c).GetData() + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] *= d[q]; }
// Add the (stress(c,0) * d[v_c]_dx) part of (stress:grad_v).
QQ_Q += QQ_Qc;
// HHQ_i1_i2_k3 = V_i1_i2_i3 HQs_i3_k3 -- contract in z direction.
// QHQ_k1_i2_k3 = HQs_i1_k1 HHQ_i1_i2_k3 -- contract in x direction.
// QQQc_k1_k2_k3 = QHQ_k1_i2_k3 HQg_i2_k2 -- gradients in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(V, tensors1D->HQshape1D, HH_Q);
MultAtB(tensors1D->HQshape1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Qc(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Qc(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQgrad1D(i2, k2);
}
}
}
}
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,1) -- stress scaling d[v_c]_dy.
d = quad_data->stressJinvT(c).GetData() + 1*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] *= d[q]; }
// Add the (stress(c,1) * d[v_c]_dy) part of (stress:grad_v).
QQ_Q += QQ_Qc;
// HHQ_i1_i2_k3 = V_i1_i2_i3 HQg_i3_k3 -- gradients in z direction.
// QHQ_k1_i2_k3 = HQs_i1_k1 HHQ_i1_i2_k3 -- contract in x direction.
// QQQc_k1_k2_k3 = QHQ_k1_i2_k3 HQs_i2_k2 -- contract in y direction.
// The last step does some reordering (it's not product of matrices).
mfem::Mult(V, tensors1D->HQgrad1D, HH_Q);
MultAtB(tensors1D->HQshape1D, H_HQ, Q_HQ);
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int k2 = 0; k2 < nqp1D; k2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
QQ_Qc(k1 + nqp1D*k2, k3) = 0.0;
for (int i2 = 0; i2 < nH1dof1D; i2++)
{
QQ_Qc(k1 + nqp1D*k2, k3) += Q_HQ(k1, i2 + k3*nH1dof1D) *
tensors1D->HQshape1D(i2, k2);
}
}
}
}
// QQQc_k1_k2_k3 *= stress_k1_k2_k3(c,2) -- stress scaling d[v_c]_dz.
d = quad_data->stressJinvT(c).GetData() + 2*nzones*nqp + z*nqp;
for (int q = 0; q < nqp; q++) { qqqc[q] *= d[q]; }
// Add the (stress(c,2) * d[v_c]_dz) part of (stress:grad_v).
QQ_Q += QQ_Qc;
}
// QLQ_k1_j2_k3 = QQQ_k1_k2_k3 LQs_j2_k2 -- contract in y direction.
// The first step does some reordering (it's not product of matrices).
// LLQ_j1_j2_k3 = LQs_j1_k1 QLQ_k1_j2_k3 -- contract in x direction.
// E_j1_j2_i3 = LLQ_j1_j2_k3 LQs_j3_k3 -- contract in z direction.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int j2 = 0; j2 < nL2dof1D; j2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
Q_LQ(k1, j2 + nL2dof1D*k3) = 0.0;
for (int k2 = 0; k2 < nqp1D; k2++)
{
Q_LQ(k1, j2 + nL2dof1D*k3) +=
QQ_Q(k1 + nqp1D*k2, k3) * tensors1D->LQshape1D(j2, k2);
}
}
}
}
mfem::Mult(tensors1D->LQshape1D, Q_LQ, L_LQ);
MultABt(LL_Q, tensors1D->LQshape1D, E);
L2FESpace.GetElementDofs(z, l2dofs);
vecL2.SetSubVector(l2dofs, e);
}
}
void MassPAOperator::ComputeDiagonal2D(Vector &diag) const
{
const H1_QuadrilateralElement *fe_H1 =
dynamic_cast<const H1_QuadrilateralElement *>(FESpace.GetFE(0));
const Array<int> &dof_map = fe_H1->GetDofMap();
const DenseMatrix &HQs = tensors1D->HQshape1D;
const int ndof1D = HQs.Height(), nqp1D = HQs.Width(), nqp = nqp1D * nqp1D;
Vector dz(ndof1D * ndof1D);
DenseMatrix HQ(ndof1D, nqp1D), D(dz.GetData(), ndof1D, ndof1D);
Array<int> dofs;
diag.SetSize(height);
diag = 0.0;
// Squares of the shape functions at all quadrature points.
DenseMatrix HQs_sq(ndof1D, nqp1D);
for (int i = 0; i < ndof1D; i++)
{
for (int k = 0; k < nqp1D; k++)
{
HQs_sq(i, k) = HQs(i, k) * HQs(i, k);
}
}
for (int z = 0; z < nzones; z++)
{
DenseMatrix QQ(quad_data->rho0DetJ0w.GetData() + z*nqp, nqp1D, nqp1D);
// HQ_i1_k2 = HQs_i1_k1^2 QQ_k1_k2 -- contract in x direction.
// Y_i1_i2 = HQ_i1_k2 HQs_i2_k2^2 -- contract in y direction.
mfem::Mult(HQs_sq, QQ, HQ);
MultABt(HQ, HQs_sq, D);
// Transfer from the tensor structure numbering to mfem's H1 numbering.
FESpace.GetElementDofs(z, dofs);
for (int j = 0; j < dz.Size(); j++)
{
diag[dofs[dof_map[j]]] += dz[j];
}
}
for (int i = 0; i < height / 2; i++)
{
diag(i + height / 2) = diag(i);
}
}
void MassPAOperator::ComputeDiagonal3D(Vector &diag) const
{
const H1_HexahedronElement *fe_H1 =
dynamic_cast<const H1_HexahedronElement *>(FESpace.GetFE(0));
const Array<int> &dof_map = fe_H1->GetDofMap();
const DenseMatrix &HQs = tensors1D->HQshape1D;
const int ndof1D = HQs.Height(), nqp1D = HQs.Width(),
nqp = nqp1D * nqp1D * nqp1D;
DenseMatrix HH_Q(ndof1D * ndof1D, nqp1D), Q_HQ(nqp1D, ndof1D*nqp1D);
DenseMatrix H_HQ(HH_Q.GetData(), ndof1D, ndof1D*nqp1D);
Vector dz(ndof1D * ndof1D * ndof1D);
DenseMatrix D(dz.GetData(), ndof1D*ndof1D, ndof1D);
Array<int> dofs;
diag.SetSize(height);
diag = 0.0;
// Squares of the shape functions at all quadrature points.
DenseMatrix HQs_sq(ndof1D, nqp1D);
for (int i = 0; i < ndof1D; i++)
{
for (int k = 0; k < nqp1D; k++)
{
HQs_sq(i, k) = HQs(i, k) * HQs(i, k);
}
}
for (int z = 0; z < nzones; z++)
{
DenseMatrix QQ_Q(quad_data->rho0DetJ0w.GetData() + z*nqp,
nqp1D * nqp1D, nqp1D);
// QHQ_k1_i2_k3 = QQQ_k1_k2_k3 HQs_i2_k2^2 -- contract in y direction.
// The first step does some reordering (it's not product of matrices).
// HHQ_i1_i2_k3 = HQs_i1_k1^2 QHQ_k1_i2_k3 -- contract in x direction.
// D_i1_i2_i3 = HHQ_i1_i2_k3 HQs_i3_k3^2 -- contract in z direction.
for (int k1 = 0; k1 < nqp1D; k1++)
{
for (int i2 = 0; i2 < ndof1D; i2++)
{
for (int k3 = 0; k3 < nqp1D; k3++)
{
Q_HQ(k1, i2 + ndof1D*k3) = 0.0;
for (int k2 = 0; k2 < nqp1D; k2++)
{
Q_HQ(k1, i2 + ndof1D*k3) +=
QQ_Q(k1 + nqp1D*k2, k3) * HQs_sq(i2, k2);
}
}
}
}
mfem::Mult(HQs_sq, Q_HQ, H_HQ);
MultABt(HH_Q, HQs_sq, D);
// Transfer from the tensor structure numbering to mfem's H1 numbering.
FESpace.GetElementDofs(z, dofs);
for (int j = 0; j < dz.Size(); j++)
{
diag[dofs[dof_map[j]]] += dz[j];
}
}
for (int i = 0; i < height / 3; i++)
{
diag(i + height / 3) = diag(i);
diag(i + 2 * height / 3) = diag(i);
}
}
void MassPAOperator::Mult(const Vector &x, Vector &y) const
{
const int comp_size = FESpace.GetNDofs();
for (int c = 0; c < dim; c++)
{
Vector x_comp(x.GetData() + c * comp_size, comp_size),
y_comp(y.GetData() + c * comp_size, comp_size);
if (dim == 2) { MultQuad(x_comp, y_comp); }
else if (dim == 3) { MultHex(x_comp, y_comp); }
else { MFEM_ABORT("Unsupported dimension"); }
}
}
// Mass matrix action on quadrilateral elements in 2D.
void MassPAOperator::MultQuad(const Vector &x, Vector &y) const
{
const H1_QuadrilateralElement *fe_H1 =
dynamic_cast<const H1_QuadrilateralElement *>(FESpace.GetFE(0));
const DenseMatrix &HQs = tensors1D->HQshape1D;
const int ndof1D = HQs.Height(), nqp1D = HQs.Width();
DenseMatrix HQ(ndof1D, nqp1D), QQ(nqp1D, nqp1D);
Vector xz(ndof1D * ndof1D), yz(ndof1D * ndof1D);
DenseMatrix X(xz.GetData(), ndof1D, ndof1D),
Y(yz.GetData(), ndof1D, ndof1D);
Array<int> dofs;
double *qq = QQ.GetData();
const int nqp = nqp1D * nqp1D;
y.SetSize(x.Size());
y = 0.0;
for (int z = 0; z < nzones; z++)
{
FESpace.GetElementDofs(z, dofs);
// Transfer from the mfem's H1 local numbering to the tensor structure
// numbering.
const Array<int> &dof_map = fe_H1->GetDofMap();
for (int j = 0; j < xz.Size(); j++)
{
xz[j] = x[dofs[dof_map[j]]];
}
// HQ_i1_k2 = X_i1_i2 HQs_i2_k2 -- contract in y direction.
// QQ_k1_k2 = HQs_i1_k1 HQ_i1_k2 -- contract in x direction.
mfem::Mult(X, HQs, HQ);
MultAtB(HQs, HQ, QQ);
// QQ_k1_k2 *= quad_data_k1_k2 -- scaling with quadrature values.
double *d = quad_data->rho0DetJ0w.GetData() + z*nqp;
for (int q = 0; q < nqp; q++) { qq[q] *= d[q]; }
// HQ_i1_k2 = HQs_i1_k1 QQ_k1_k2 -- contract in x direction.
// Y_i1_i2 = HQ_i1_k2 HQs_i2_k2 -- contract in y direction.
mfem::Mult(HQs, QQ, HQ);
MultABt(HQ, HQs, Y);
for (int j = 0; j < yz.Size(); j++)
{
y[dofs[dof_map[j]]] += yz[j];
}
}
}
// Mass matrix action on hexahedral elements in 3D.
void MassPAOperator::MultHex(const Vector &x, Vector &y) const
{
const H1_HexahedronElement *fe_H1 =
dynamic_cast<const H1_HexahedronElement *>(FESpace.GetFE(0));
const DenseMatrix &HQs = tensors1D->HQshape1D;