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mfem/fem/pbilinearform.cpp
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// Copyright (c) 2010-2024, 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 "../config/config.hpp"
#ifdef MFEM_USE_MPI
#include "fem.hpp"
#include "../general/sort_pairs.hpp"
namespace mfem
{
void ParBilinearForm::pAllocMat()
{
int nbr_size = pfes->GetFaceNbrVSize();
if (precompute_sparsity == 0 || fes->GetVDim() > 1)
{
if (keep_nbr_block)
{
mat = new SparseMatrix(height + nbr_size, width + nbr_size);
}
else
{
mat = new SparseMatrix(height, width + nbr_size);
}
return;
}
// the sparsity pattern is defined from the map: face->element->dof
const Table &lelem_ldof = fes->GetElementToDofTable(); // <-- dofs
const Table &nelem_ndof = pfes->face_nbr_element_dof; // <-- vdofs
Table elem_dof; // element + nbr-element <---> dof
if (nbr_size > 0)
{
// merge lelem_ldof and nelem_ndof into elem_dof
int s1 = lelem_ldof.Size(), s2 = nelem_ndof.Size();
const int *I1 = lelem_ldof.GetI(), *J1 = lelem_ldof.GetJ();
const int *I2 = nelem_ndof.GetI(), *J2 = nelem_ndof.GetJ();
const int nnz1 = I1[s1], nnz2 = I2[s2];
elem_dof.SetDims(s1 + s2, nnz1 + nnz2);
int *I = elem_dof.GetI(), *J = elem_dof.GetJ();
for (int i = 0; i <= s1; i++)
{
I[i] = I1[i];
}
for (int j = 0; j < nnz1; j++)
{
J[j] = J1[j];
}
for (int i = 0; i <= s2; i++)
{
I[s1+i] = I2[i] + nnz1;
}
for (int j = 0; j < nnz2; j++)
{
J[nnz1+j] = J2[j] + height;
}
}
// dof_elem x elem_face x face_elem x elem_dof (keep_nbr_block = true)
// ldof_lelem x lelem_face x face_elem x elem_dof (keep_nbr_block = false)
Table dof_dof;
{
Table face_dof; // face_elem x elem_dof
{
Table *face_elem = pfes->GetParMesh()->GetFaceToAllElementTable();
if (nbr_size > 0)
{
mfem::Mult(*face_elem, elem_dof, face_dof);
}
else
{
mfem::Mult(*face_elem, lelem_ldof, face_dof);
}
delete face_elem;
if (nbr_size > 0)
{
elem_dof.Clear();
}
}
if (keep_nbr_block)
{
Table dof_face;
Transpose(face_dof, dof_face, height + nbr_size);
mfem::Mult(dof_face, face_dof, dof_dof);
}
else
{
Table ldof_face;
{
Table face_ldof;
Table *face_lelem = fes->GetMesh()->GetFaceToElementTable();
mfem::Mult(*face_lelem, lelem_ldof, face_ldof);
delete face_lelem;
Transpose(face_ldof, ldof_face, height);
}
mfem::Mult(ldof_face, face_dof, dof_dof);
}
}
int *I = dof_dof.GetI();
int *J = dof_dof.GetJ();
int nrows = dof_dof.Size();
real_t *data = Memory<real_t>(I[nrows]);
mat = new SparseMatrix(I, J, data, nrows, height + nbr_size);
*mat = 0.0;
dof_dof.LoseData();
}
void ParBilinearForm::ParallelRAP(SparseMatrix &loc_A, OperatorHandle &A,
bool steal_loc_A)
{
ParFiniteElementSpace &pfespace = *ParFESpace();
// Create a block diagonal parallel matrix
OperatorHandle A_diag(Operator::Hypre_ParCSR);
A_diag.MakeSquareBlockDiag(pfespace.GetComm(),
pfespace.GlobalVSize(),
pfespace.GetDofOffsets(),
&loc_A);
// Parallel matrix assembly using P^t A P (if needed)
if (IsIdentityProlongation(pfespace.GetProlongationMatrix()))
{
A_diag.SetOperatorOwner(false);
A.Reset(A_diag.As<HypreParMatrix>());
if (steal_loc_A)
{
HypreStealOwnership(*A.As<HypreParMatrix>(), loc_A);
}
}
else
{
OperatorHandle P(Operator::Hypre_ParCSR);
P.ConvertFrom(pfespace.Dof_TrueDof_Matrix());
A.MakePtAP(A_diag, P);
}
}
void ParBilinearForm::ParallelAssemble(OperatorHandle &A, SparseMatrix *A_local)
{
A.Clear();
if (A_local == NULL) { return; }
MFEM_VERIFY(A_local->Finalized(), "the local matrix must be finalized");
OperatorHandle dA(A.Type()), Ph(A.Type()), hdA;
if (interior_face_integs.Size() == 0)
{
// construct a parallel block-diagonal matrix 'A' based on 'a'
dA.MakeSquareBlockDiag(pfes->GetComm(), pfes->GlobalVSize(),
pfes->GetDofOffsets(), A_local);
}
else
{
// handle the case when 'a' contains off-diagonal
int lvsize = pfes->GetVSize();
const HYPRE_BigInt *face_nbr_glob_ldof = pfes->GetFaceNbrGlobalDofMap();
HYPRE_BigInt ldof_offset = pfes->GetMyDofOffset();
Array<HYPRE_BigInt> glob_J(A_local->NumNonZeroElems());
int *J = A_local->GetJ();
for (int i = 0; i < glob_J.Size(); i++)
{
if (J[i] < lvsize)
{
glob_J[i] = J[i] + ldof_offset;
}
else
{
glob_J[i] = face_nbr_glob_ldof[J[i] - lvsize];
}
}
// TODO - construct dA directly in the A format
hdA.Reset(
new HypreParMatrix(pfes->GetComm(), lvsize, pfes->GlobalVSize(),
pfes->GlobalVSize(), A_local->GetI(), glob_J,
A_local->GetData(), pfes->GetDofOffsets(),
pfes->GetDofOffsets()));
// - hdA owns the new HypreParMatrix
// - the above constructor copies all input arrays
glob_J.DeleteAll();
dA.ConvertFrom(hdA);
}
// TODO - assemble the Dof_TrueDof_Matrix directly in the required format?
Ph.ConvertFrom(pfes->Dof_TrueDof_Matrix());
// TODO: When Ph.Type() == Operator::ANY_TYPE we want to use the Operator
// returned by pfes->GetProlongationMatrix(), however that Operator is a
// const Operator, so we cannot store it in OperatorHandle. We need a const
// version of class OperatorHandle, e.g. ConstOperatorHandle.
A.MakePtAP(dA, Ph);
}
HypreParMatrix *ParBilinearForm::ParallelAssemble(SparseMatrix *m)
{
OperatorHandle Mh(Operator::Hypre_ParCSR);
ParallelAssemble(Mh, m);
Mh.SetOperatorOwner(false);
return Mh.As<HypreParMatrix>();
}
void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
{
ParMesh *pmesh = pfes->GetParMesh();
FaceElementTransformations *T;
Array<int> vdofs1, vdofs2, vdofs_all;
DenseMatrix elemmat;
int nfaces = pmesh->GetNSharedFaces();
for (int i = 0; i < nfaces; i++)
{
T = pmesh->GetSharedFaceTransformations(i);
int Elem2NbrNo = T->Elem2No - pmesh->GetNE();
pfes->GetElementVDofs(T->Elem1No, vdofs1);
pfes->GetFaceNbrElementVDofs(Elem2NbrNo, vdofs2);
vdofs1.Copy(vdofs_all);
for (int j = 0; j < vdofs2.Size(); j++)
{
if (vdofs2[j] >= 0)
{
vdofs2[j] += height;
}
else
{
vdofs2[j] -= height;
}
}
vdofs_all.Append(vdofs2);
for (int k = 0; k < interior_face_integs.Size(); k++)
{
interior_face_integs[k]->
AssembleFaceMatrix(*pfes->GetFE(T->Elem1No),
*pfes->GetFaceNbrFE(Elem2NbrNo),
*T, elemmat);
if (keep_nbr_block)
{
mat->AddSubMatrix(vdofs_all, vdofs_all, elemmat, skip_zeros);
}
else
{
mat->AddSubMatrix(vdofs1, vdofs_all, elemmat, skip_zeros);
}
}
}
}
void ParBilinearForm::Assemble(int skip_zeros)
{
if (interior_face_integs.Size())
{
pfes->ExchangeFaceNbrData();
if (!ext && mat == NULL)
{
pAllocMat();
}
}
BilinearForm::Assemble(skip_zeros);
if (!ext && interior_face_integs.Size() > 0)
{
AssembleSharedFaces(skip_zeros);
}
}
void ParBilinearForm::AssembleDiagonal(Vector &diag) const
{
MFEM_ASSERT(diag.Size() == fes->GetTrueVSize(),
"Vector for holding diagonal has wrong size!");
const Operator *P = fes->GetProlongationMatrix();
if (!ext)
{
MFEM_ASSERT(p_mat.Ptr(), "the ParBilinearForm is not assembled!");
p_mat->AssembleDiagonal(diag); // TODO: add support for PETSc matrices
return;
}
// Here, we have extension, ext.
if (IsIdentityProlongation(P))
{
ext->AssembleDiagonal(diag);
return;
}
// Here, we have extension, ext, and parallel/conforming prolongation, P.
Vector local_diag(P->Height());
ext->AssembleDiagonal(local_diag);
if (fes->Conforming())
{
P->MultTranspose(local_diag, diag);
return;
}
// For an AMR mesh, a convergent diagonal is assembled with |P^T| d_l,
// where |P^T| has the entry-wise absolute values of the conforming
// prolongation transpose operator.
const HypreParMatrix *HP = dynamic_cast<const HypreParMatrix*>(P);
if (HP)
{
HP->AbsMultTranspose(1.0, local_diag, 0.0, diag);
}
else
{
MFEM_ABORT("unsupported prolongation matrix type.");
}
}
void ParBilinearForm
::ParallelEliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
HypreParMatrix &A, const HypreParVector &X,
HypreParVector &B) const
{
Array<int> dof_list;
pfes->GetEssentialTrueDofs(bdr_attr_is_ess, dof_list);
// do the parallel elimination
A.EliminateRowsCols(dof_list, X, B);
}
HypreParMatrix *ParBilinearForm::
ParallelEliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
HypreParMatrix &A) const
{
Array<int> dof_list;
pfes->GetEssentialTrueDofs(bdr_attr_is_ess, dof_list);
return A.EliminateRowsCols(dof_list);
}
void ParBilinearForm::TrueAddMult(const Vector &x, Vector &y, const real_t a)
const
{
const Operator *P = pfes->GetProlongationMatrix();
Xaux.SetSize(P->Height());
Yaux.SetSize(P->Height());
Ytmp.SetSize(P->Width());
P->Mult(x, Xaux);
if (ext)
{
ext->Mult(Xaux, Yaux);
}
else
{
MFEM_VERIFY(interior_face_integs.Size() == 0,
"the case of interior face integrators is not"
" implemented");
mat->Mult(Xaux, Yaux);
}
P->MultTranspose(Yaux, Ytmp);
y.Add(a, Ytmp);
}
real_t ParBilinearForm::ParInnerProduct(const ParGridFunction &x,
const ParGridFunction &y) const
{
MFEM_ASSERT(mat != NULL, "local matrix must be assembled");
real_t loc = InnerProduct(x, y);
real_t glob = 0.;
MPI_Allreduce(&loc, &glob, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
pfes->GetComm());
return glob;
}
real_t ParBilinearForm::TrueInnerProduct(const ParGridFunction &x,
const ParGridFunction &y) const
{
MFEM_ASSERT(x.ParFESpace() == pfes, "the parallel spaces must match");
MFEM_ASSERT(y.ParFESpace() == pfes, "the parallel spaces must match");
HypreParVector *x_p = x.ParallelProject();
HypreParVector *y_p = y.ParallelProject();
real_t res = TrueInnerProduct(*x_p, *y_p);
delete x_p;
delete y_p;
return res;
}
real_t ParBilinearForm::TrueInnerProduct(HypreParVector &x,
HypreParVector &y) const
{
MFEM_VERIFY(p_mat.Ptr() != NULL, "parallel matrix must be assembled");
if (p_mat->GetType() != Operator::Hypre_ParCSR)
{
return TrueInnerProduct((const Vector&)x, (const Vector&)y);
}
HypreParVector *Ax = new HypreParVector(pfes);
HypreParMatrix *A = p_mat.As<HypreParMatrix>();
A->Mult(x, *Ax);
real_t res = mfem::InnerProduct(y, *Ax);
delete Ax;
return res;
}
real_t ParBilinearForm::TrueInnerProduct(const Vector &x,
const Vector &y) const
{
MFEM_VERIFY(p_mat.Ptr() != NULL, "parallel matrix must be assembled");
Vector Ax(pfes->GetTrueVSize());
p_mat->Mult(x, Ax);
real_t res = mfem::InnerProduct(pfes->GetComm(), y, Ax);
return res;
}
void ParBilinearForm::FormLinearSystem(
const Array<int> &ess_tdof_list, Vector &x, Vector &b,
OperatorHandle &A, Vector &X, Vector &B, int copy_interior)
{
if (ext)
{
ext->FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
return;
}
// Finish the matrix assembly and perform BC elimination, storing the
// eliminated part of the matrix.
FormSystemMatrix(ess_tdof_list, A);
const Operator &P = *pfes->GetProlongationMatrix();
const SparseMatrix &R = *pfes->GetRestrictionMatrix();
// Transform the system and perform the elimination in B, based on the
// essential BC values from x. Restrict the BC part of x in X, and set the
// non-BC part to zero. Since there is no good initial guess for the Lagrange
// multipliers, set X = 0.0 for hybridization.
if (static_cond)
{
// Schur complement reduction to the exposed dofs
static_cond->ReduceSystem(x, b, X, B, copy_interior);
}
else if (hybridization)
{
// Reduction to the Lagrange multipliers system
HypreParVector true_X(pfes), true_B(pfes);
P.MultTranspose(b, true_B);
R.Mult(x, true_X);
p_mat.EliminateBC(p_mat_e, ess_tdof_list, true_X, true_B);
R.MultTranspose(true_B, b);
hybridization->ReduceRHS(true_B, B);
X.SetSize(B.Size());
X = 0.0;
}
else
{
// Variational restriction with P
X.SetSize(P.Width());
B.SetSize(X.Size());
P.MultTranspose(b, B);
R.Mult(x, X);
p_mat.EliminateBC(p_mat_e, ess_tdof_list, X, B);
if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
}
}
void ParBilinearForm::EliminateVDofsInRHS(
const Array<int> &vdofs, const Vector &x, Vector &b)
{
p_mat.EliminateBC(p_mat_e, vdofs, x, b);
}
void ParBilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
OperatorHandle &A)
{
if (ext)
{
ext->FormSystemMatrix(ess_tdof_list, A);
return;
}
// Finish the matrix assembly and perform BC elimination, storing the
// eliminated part of the matrix.
if (static_cond)
{
if (!static_cond->HasEliminatedBC())
{
static_cond->SetEssentialTrueDofs(ess_tdof_list);
static_cond->Finalize();
static_cond->EliminateReducedTrueDofs(Matrix::DIAG_ONE);
}
static_cond->GetParallelMatrix(A);
}
else
{
if (mat)
{
const int remove_zeros = 0;
Finalize(remove_zeros);
MFEM_VERIFY(p_mat.Ptr() == NULL && p_mat_e.Ptr() == NULL,
"The ParBilinearForm must be updated with Update() before "
"re-assembling the ParBilinearForm.");
ParallelAssemble(p_mat, mat);
delete mat;
mat = NULL;
delete mat_e;
mat_e = NULL;
p_mat_e.EliminateRowsCols(p_mat, ess_tdof_list);
}
if (hybridization)
{
hybridization->GetParallelMatrix(A);
}
else
{
A = p_mat;
}
}
}
void ParBilinearForm::RecoverFEMSolution(
const Vector &X, const Vector &b, Vector &x)
{
if (ext)
{
ext->RecoverFEMSolution(X, b, x);
return;
}
const Operator &P = *pfes->GetProlongationMatrix();
if (static_cond)
{
// Private dofs back solve
static_cond->ComputeSolution(b, X, x);
}
else if (hybridization)
{
// Primal unknowns recovery
HypreParVector true_X(pfes), true_B(pfes);
P.MultTranspose(b, true_B);
const SparseMatrix &R = *pfes->GetRestrictionMatrix();
R.Mult(x, true_X); // get essential b.c. from x
hybridization->ComputeSolution(true_B, X, true_X);
x.SetSize(P.Height());
P.Mult(true_X, x);
}
else
{
// Apply conforming prolongation
x.SetSize(P.Height(), GetHypreMemoryType());
P.Mult(X, x);
}
}
void ParBilinearForm::Update(FiniteElementSpace *nfes)
{
BilinearForm::Update(nfes);
if (nfes)
{
pfes = dynamic_cast<ParFiniteElementSpace *>(nfes);
MFEM_VERIFY(pfes != NULL, "nfes must be a ParFiniteElementSpace!");
}
p_mat.Clear();
p_mat_e.Clear();
}
HypreParMatrix *ParMixedBilinearForm::ParallelAssemble()
{
// construct the block-diagonal matrix A
HypreParMatrix *A =
new HypreParMatrix(trial_pfes->GetComm(),
test_pfes->GlobalVSize(),
trial_pfes->GlobalVSize(),
test_pfes->GetDofOffsets(),
trial_pfes->GetDofOffsets(),
mat);
HypreParMatrix *rap = RAP(test_pfes->Dof_TrueDof_Matrix(), A,
trial_pfes->Dof_TrueDof_Matrix());
delete A;
return rap;
}
void ParMixedBilinearForm::ParallelAssemble(OperatorHandle &A)
{
// construct the rectangular block-diagonal matrix dA
OperatorHandle dA(A.Type());
dA.MakeRectangularBlockDiag(trial_pfes->GetComm(),
test_pfes->GlobalVSize(),
trial_pfes->GlobalVSize(),
test_pfes->GetDofOffsets(),
trial_pfes->GetDofOffsets(),
mat);
OperatorHandle P_test(A.Type()), P_trial(A.Type());
// TODO - construct the Dof_TrueDof_Matrix directly in the required format.
P_test.ConvertFrom(test_pfes->Dof_TrueDof_Matrix());
P_trial.ConvertFrom(trial_pfes->Dof_TrueDof_Matrix());
A.MakeRAP(P_test, dA, P_trial);
}
/// Compute y += a (P^t A P) x, where x and y are vectors on the true dofs
void ParMixedBilinearForm::TrueAddMult(const Vector &x, Vector &y,
const real_t a) const
{
if (Xaux.ParFESpace() != trial_pfes)
{
Xaux.SetSpace(trial_pfes);
Yaux.SetSpace(test_pfes);
}
Xaux.Distribute(&x);
mat->Mult(Xaux, Yaux);
test_pfes->Dof_TrueDof_Matrix()->MultTranspose(a, Yaux, 1.0, y);
}
void ParMixedBilinearForm::FormRectangularSystemMatrix(
const Array<int>
&trial_tdof_list,
const Array<int> &test_tdof_list,
OperatorHandle &A)
{
if (ext)
{
ext->FormRectangularSystemOperator(trial_tdof_list, test_tdof_list, A);
return;
}
if (mat)
{
Finalize();
ParallelAssemble(p_mat);
delete mat;
mat = NULL;
delete mat_e;
mat_e = NULL;
HypreParMatrix *temp =
p_mat.As<HypreParMatrix>()->EliminateCols(trial_tdof_list);
p_mat.As<HypreParMatrix>()->EliminateRows(test_tdof_list);
p_mat_e.Reset(temp, true);
}
A = p_mat;
}
void ParMixedBilinearForm::FormRectangularLinearSystem(
const Array<int>
&trial_tdof_list,
const Array<int> &test_tdof_list, Vector &x,
Vector &b, OperatorHandle &A, Vector &X,
Vector &B)
{
if (ext)
{
ext->FormRectangularLinearSystem(trial_tdof_list, test_tdof_list,
x, b, A, X, B);
return;
}
FormRectangularSystemMatrix(trial_tdof_list, test_tdof_list, A);
const Operator *test_P = test_pfes->GetProlongationMatrix();
const SparseMatrix *trial_R = trial_pfes->GetRestrictionMatrix();
X.SetSize(trial_pfes->TrueVSize());
B.SetSize(test_pfes->TrueVSize());
test_P->MultTranspose(b, B);
trial_R->Mult(x, X);
p_mat_e.As<HypreParMatrix>()->Mult(-1.0, X, 1.0, B);
B.SetSubVector(test_tdof_list, 0.0);
}
HypreParMatrix* ParDiscreteLinearOperator::ParallelAssemble() const
{
MFEM_ASSERT(mat, "Matrix is not assembled");
MFEM_ASSERT(mat->Finalized(), "Matrix is not finalized");
SparseMatrix* RA = mfem::Mult(*range_fes->GetRestrictionMatrix(), *mat);
HypreParMatrix* P = domain_fes->Dof_TrueDof_Matrix();
HypreParMatrix* RAP = P->LeftDiagMult(*RA, range_fes->GetTrueDofOffsets());
delete RA;
return RAP;
}
void ParDiscreteLinearOperator::ParallelAssemble(OperatorHandle &A)
{
// construct the rectangular block-diagonal matrix dA
OperatorHandle dA(A.Type());
dA.MakeRectangularBlockDiag(domain_fes->GetComm(),
range_fes->GlobalVSize(),
domain_fes->GlobalVSize(),
range_fes->GetDofOffsets(),
domain_fes->GetDofOffsets(),
mat);
SparseMatrix *Rt = Transpose(*range_fes->GetRestrictionMatrix());
OperatorHandle R_test_transpose(A.Type());
R_test_transpose.MakeRectangularBlockDiag(range_fes->GetComm(),
range_fes->GlobalVSize(),
range_fes->GlobalTrueVSize(),
range_fes->GetDofOffsets(),
range_fes->GetTrueDofOffsets(),
Rt);
// TODO - construct the Dof_TrueDof_Matrix directly in the required format.
OperatorHandle P_trial(A.Type());
P_trial.ConvertFrom(domain_fes->Dof_TrueDof_Matrix());
A.MakeRAP(R_test_transpose, dA, P_trial);
delete Rt;
}
void ParDiscreteLinearOperator::FormRectangularSystemMatrix(OperatorHandle &A)
{
if (ext)
{
Array<int> empty;
ext->FormRectangularSystemOperator(empty, empty, A);
return;
}
mfem_error("not implemented!");
}
void ParDiscreteLinearOperator::GetParBlocks(Array2D<HypreParMatrix *> &blocks)
const
{
MFEM_VERIFY(mat->Finalized(), "Local matrix needs to be finalized for "
"GetParBlocks");
HypreParMatrix* RLP = ParallelAssemble();
blocks.SetSize(range_fes->GetVDim(), domain_fes->GetVDim());
RLP->GetBlocks(blocks,
range_fes->GetOrdering() == Ordering::byVDIM,
domain_fes->GetOrdering() == Ordering::byVDIM);
delete RLP;
}
}
#endif