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mfem/fem/hybridization.cpp
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2020-03-09 15:36:41 -07:00

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26 KiB
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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 "hybridization.hpp"
#include "gridfunc.hpp"
#ifdef MFEM_USE_MPI
#include "pfespace.hpp"
#endif
#include <map>
// uncomment next line for debugging: write C and P to file
// #define MFEM_DEBUG_HYBRIDIZATION_CP
#ifdef MFEM_DEBUG_HYBRIDIZATION_CP
#include <fstream>
#endif
namespace mfem
{
Hybridization::Hybridization(FiniteElementSpace *fespace,
FiniteElementSpace *c_fespace)
: fes(fespace), c_fes(c_fespace), c_bfi(NULL), Ct(NULL), H(NULL),
Af_data(NULL), Af_ipiv(NULL)
{
#ifdef MFEM_USE_MPI
pC = P_pc = NULL;
pH.SetType(Operator::Hypre_ParCSR);
#endif
}
Hybridization::~Hybridization()
{
#ifdef MFEM_USE_MPI
delete P_pc;
delete pC;
#endif
delete [] Af_ipiv;
delete [] Af_data;
delete H;
delete Ct;
delete c_bfi;
}
void Hybridization::ConstructC()
{
const int NE = fes->GetNE();
int num_hat_dofs = hat_offsets[NE];
Array<int> vdofs, c_vdofs;
int c_num_face_nbr_dofs = 0;
#ifdef MFEM_USE_MPI
ParFiniteElementSpace *c_pfes = dynamic_cast<ParFiniteElementSpace*>(c_fes);
ParMesh *pmesh = c_pfes ? c_pfes->GetParMesh() : NULL;
HYPRE_Int num_shared_slave_faces = 0, glob_num_shared_slave_faces = 0;
if (c_pfes)
{
if (pmesh->Nonconforming())
{
const int dim = pmesh->Dimension();
const NCMesh::NCList &shared = pmesh->pncmesh->GetSharedList(dim-1);
num_shared_slave_faces = (HYPRE_Int)shared.slaves.size();
MPI_Allreduce(&num_shared_slave_faces, &glob_num_shared_slave_faces, 1,
HYPRE_MPI_INT, MPI_SUM, pmesh->GetComm());
MFEM_ASSERT(glob_num_shared_slave_faces%2 == 0, "");
glob_num_shared_slave_faces /= 2;
if (glob_num_shared_slave_faces)
{
c_pfes->ExchangeFaceNbrData();
c_num_face_nbr_dofs = c_pfes->GetFaceNbrVSize();
}
#ifdef MFEM_DEBUG_HERE
MFEM_WARNING('[' << c_pfes->GetMyRank() <<
"] num_shared_slave_faces = " << num_shared_slave_faces
<< ", glob_num_shared_slave_faces = "
<< glob_num_shared_slave_faces
<< "\n num_face_nbr_dofs = " << c_num_face_nbr_dofs
<< ", num_shared_faces = " << pmesh->GetNSharedFaces());
#undef MFEM_DEBUG_HERE
#endif
}
}
#endif
const int c_vsize = c_fes->GetVSize();
Ct = new SparseMatrix(num_hat_dofs, c_vsize + c_num_face_nbr_dofs);
if (c_bfi)
{
const int skip_zeros = 1;
DenseMatrix elmat;
FaceElementTransformations *FTr;
Mesh *mesh = fes->GetMesh();
int num_faces = mesh->GetNumFaces();
for (int i = 0; i < num_faces; i++)
{
FTr = mesh->GetInteriorFaceTransformations(i);
if (!FTr) { continue; }
int o1 = hat_offsets[FTr->Elem1No];
int s1 = hat_offsets[FTr->Elem1No+1] - o1;
int o2 = hat_offsets[FTr->Elem2No];
int s2 = hat_offsets[FTr->Elem2No+1] - o2;
vdofs.SetSize(s1 + s2);
for (int j = 0; j < s1; j++)
{
vdofs[j] = o1 + j;
}
for (int j = 0; j < s2; j++)
{
vdofs[s1+j] = o2 + j;
}
c_fes->GetFaceVDofs(i, c_vdofs);
c_bfi->AssembleFaceMatrix(*c_fes->GetFaceElement(i),
*fes->GetFE(FTr->Elem1No),
*fes->GetFE(FTr->Elem2No),
*FTr, elmat);
// zero-out small elements in elmat
elmat.Threshold(1e-12 * elmat.MaxMaxNorm());
Ct->AddSubMatrix(vdofs, c_vdofs, elmat, skip_zeros);
}
#ifdef MFEM_USE_MPI
if (pmesh)
{
// Assemble local contribution to Ct from shared faces
const int num_shared_faces = pmesh->GetNSharedFaces();
for (int i = 0; i < num_shared_faces; i++)
{
const int face_no = pmesh->GetSharedFace(i);
const bool ghost_sface = (face_no >= num_faces);
const FiniteElement *fe, *face_fe;
if (!ghost_sface)
{
FTr = pmesh->GetFaceElementTransformations(face_no);
MFEM_ASSERT(FTr->Elem2No < 0, "");
face_fe = c_fes->GetFaceElement(face_no);
c_fes->GetFaceVDofs(face_no, c_vdofs);
}
else
{
const int fill2 = false; // only need side "1" data
FTr = pmesh->GetSharedFaceTransformations(i, fill2);
face_fe = c_pfes->GetFaceNbrFaceFE(face_no);
c_pfes->GetFaceNbrFaceVDofs(face_no, c_vdofs);
FiniteElementSpace::AdjustVDofs(c_vdofs);
for (int j = 0; j < c_vdofs.Size(); j++)
{
c_vdofs[j] += c_vsize;
}
}
int o1 = hat_offsets[FTr->Elem1No];
int s1 = hat_offsets[FTr->Elem1No+1] - o1;
vdofs.SetSize(s1);
for (int j = 0; j < s1; j++)
{
vdofs[j] = o1 + j;
}
fe = fes->GetFE(FTr->Elem1No);
c_bfi->AssembleFaceMatrix(*face_fe, *fe, *fe, *FTr, elmat);
// zero-out small elements in elmat
elmat.Threshold(1e-12 * elmat.MaxMaxNorm());
Ct->AddSubMatrix(vdofs, c_vdofs, elmat, skip_zeros);
}
if (glob_num_shared_slave_faces)
{
// Convert Ct to parallel and then transpose it:
Ct->Finalize(skip_zeros);
HYPRE_Int Ct_num_rows = Ct->Height();
Array<HYPRE_Int> Ct_rows, *offsets[1] = { &Ct_rows };
pmesh->GenerateOffsets(1, &Ct_num_rows, offsets);
Array<HYPRE_Int> Ct_J(Ct->NumNonZeroElems());
HYPRE_Int c_ldof_offset = c_pfes->GetMyDofOffset();
const HYPRE_Int *c_face_nbr_glob_ldof =
c_pfes->GetFaceNbrGlobalDofMap();
int *J = Ct->GetJ();
for (int i = 0; i < Ct_J.Size(); i++)
{
Ct_J[i] = J[i] < c_vsize ?
J[i] + c_ldof_offset :
c_face_nbr_glob_ldof[J[i] - c_vsize];
}
HypreParMatrix pCt(pmesh->GetComm(), Ct->Height(),
Ct_rows.Last(), c_pfes->GlobalVSize(),
Ct->GetI(), Ct_J.GetData(), Ct->GetData(),
Ct_rows, c_pfes->GetDofOffsets());
Ct_J.DeleteAll();
pC = pCt.Transpose();
}
if (pmesh->Nonconforming())
{
// TODO - Construct P_pc directly in the pH format
P_pc = c_pfes->GetPartialConformingInterpolation();
}
}
#endif
Ct->Finalize(skip_zeros);
}
else
{
// Check if c_fes is really needed here.
MFEM_ABORT("TODO: algebraic definition of C");
}
}
void Hybridization::Init(const Array<int> &ess_tdof_list)
{
if (Ct) { return; }
// count the number of dofs in the discontinuous version of fes:
const int NE = fes->GetNE();
Array<int> vdofs;
int num_hat_dofs = 0;
hat_offsets.SetSize(NE+1);
hat_offsets[0] = 0;
for (int i = 0; i < NE; i++)
{
fes->GetElementVDofs(i, vdofs);
num_hat_dofs += vdofs.Size();
hat_offsets[i+1] = num_hat_dofs;
}
// Assemble the constraint matrix C
ConstructC();
#ifdef MFEM_DEBUG_HYBRIDIZATION_CP
// Debug: write C and P to file
{
std::ofstream C_file("C_matrix.txt");
SparseMatrix *C = Transpose(*Ct);
C->PrintMatlab(C_file);
delete C;
const SparseMatrix *P = fes->GetConformingProlongation();
if (P)
{
std::ofstream P_file("P_matrix.txt");
P->PrintMatlab(P_file);
}
}
#endif
// Define the "free" (0) and "essential" (1) hat_dofs.
// The "essential" hat_dofs are those that depend only on essential cdofs;
// all other hat_dofs are "free".
hat_dofs_marker.SetSize(num_hat_dofs);
Array<int> free_tdof_marker;
#ifdef MFEM_USE_MPI
ParFiniteElementSpace *pfes = dynamic_cast<ParFiniteElementSpace*>(fes);
free_tdof_marker.SetSize(pfes ? pfes->TrueVSize() :
fes->GetConformingVSize());
#else
free_tdof_marker.SetSize(fes->GetConformingVSize());
#endif
free_tdof_marker = 1;
for (int i = 0; i < ess_tdof_list.Size(); i++)
{
free_tdof_marker[ess_tdof_list[i]] = 0;
}
Array<int> free_vdofs_marker;
#ifdef MFEM_USE_MPI
if (!pfes)
{
const SparseMatrix *cP = fes->GetConformingProlongation();
if (!cP)
{
free_vdofs_marker.MakeRef(free_tdof_marker);
}
else
{
free_vdofs_marker.SetSize(fes->GetVSize());
cP->BooleanMult(free_tdof_marker, free_vdofs_marker);
}
}
else
{
HypreParMatrix *P = pfes->Dof_TrueDof_Matrix();
free_vdofs_marker.SetSize(fes->GetVSize());
P->BooleanMult(1, free_tdof_marker, 0, free_vdofs_marker);
}
#else
const SparseMatrix *cP = fes->GetConformingProlongation();
if (!cP)
{
free_vdofs_marker.MakeRef(free_tdof_marker);
}
else
{
free_vdofs_marker.SetSize(fes->GetVSize());
cP->BooleanMult(free_tdof_marker, free_vdofs_marker);
}
#endif
for (int i = 0; i < NE; i++)
{
fes->GetElementVDofs(i, vdofs);
FiniteElementSpace::AdjustVDofs(vdofs);
for (int j = 0; j < vdofs.Size(); j++)
{
hat_dofs_marker[hat_offsets[i]+j] = ! free_vdofs_marker[vdofs[j]];
}
}
#ifndef MFEM_DEBUG
// In DEBUG mode this array is used below.
free_tdof_marker.DeleteAll();
#endif
free_vdofs_marker.DeleteAll();
// Split the "free" (0) hat_dofs into "internal" (0) or "boundary" (-1).
// The "internal" hat_dofs are those "free" hat_dofs for which the
// corresponding column in C is zero; otherwise the free hat_dof is
// "boundary".
for (int i = 0; i < num_hat_dofs; i++)
{
// skip "essential" hat_dofs and empty rows in Ct
if (hat_dofs_marker[i] != 1 && Ct->RowSize(i) > 0)
{
hat_dofs_marker[i] = -1; // mark this hat_dof as "boundary"
}
}
// Define Af_offsets and Af_f_offsets
Af_offsets.SetSize(NE+1);
Af_offsets[0] = 0;
Af_f_offsets.SetSize(NE+1);
Af_f_offsets[0] = 0;
// #define MFEM_DEBUG_HERE // uncomment to enable printing of hat dofs stats
#ifdef MFEM_DEBUG_HERE
int b_size = 0;
#endif
for (int i = 0; i < NE; i++)
{
int f_size = 0; // count the "free" hat_dofs in element i
for (int j = hat_offsets[i]; j < hat_offsets[i+1]; j++)
{
if (hat_dofs_marker[j] != 1) { f_size++; }
#ifdef MFEM_DEBUG_HERE
if (hat_dofs_marker[j] == -1) { b_size++; }
#endif
}
Af_offsets[i+1] = Af_offsets[i] + f_size*f_size;
Af_f_offsets[i+1] = Af_f_offsets[i] + f_size;
}
#ifdef MFEM_DEBUG_HERE
#ifndef MFEM_USE_MPI
int myid = 0;
#else
int myid = pmesh ? pmesh->GetMyRank() : 0;
#endif
int i_size = Af_f_offsets[NE] - b_size;
int e_size = num_hat_dofs - (i_size + b_size);
mfem::out << "\nHybridization::Init:"
<< " [" << myid << "] hat dofs - \"internal\": " << i_size
<< ", \"boundary\": " << b_size
<< ", \"essential\": " << e_size << '\n' << std::endl;
#undef MFEM_DEBUG_HERE
#endif
Af_data = new double[Af_offsets[NE]];
Af_ipiv = new int[Af_f_offsets[NE]];
#ifdef MFEM_DEBUG
// check that Ref = 0
const SparseMatrix *R = fes->GetRestrictionMatrix();
if (!R) { return; }
Array<int> vdof_marker(fes->GetVSize()); // 0 - f, 1 - e
vdof_marker = 0;
for (int i = 0; i < NE; i++)
{
fes->GetElementVDofs(i, vdofs);
FiniteElementSpace::AdjustVDofs(vdofs);
for (int j = 0; j < vdofs.Size(); j++)
{
if (hat_dofs_marker[hat_offsets[i]+j] == 1) // "essential" hat dof
{
vdof_marker[vdofs[j]] = 1;
}
}
}
for (int tdof = 0; tdof < R->Height(); tdof++)
{
if (free_tdof_marker[tdof]) { continue; }
const int ncols = R->RowSize(tdof);
const int *cols = R->GetRowColumns(tdof);
const double *vals = R->GetRowEntries(tdof);
for (int j = 0; j < ncols; j++)
{
if (std::abs(vals[j]) != 0.0 && vdof_marker[cols[j]] == 0)
{
MFEM_ABORT("Ref != 0");
}
}
}
#endif
}
void Hybridization::GetIBDofs(
int el, Array<int> &i_dofs, Array<int> &b_dofs) const
{
// returns local indices in i_dofs and b_dofs
int h_start, h_end;
h_start = hat_offsets[el];
h_end = hat_offsets[el+1];
i_dofs.Reserve(h_end-h_start);
i_dofs.SetSize(0);
b_dofs.Reserve(h_end-h_start);
b_dofs.SetSize(0);
for (int i = h_start; i < h_end; i++)
{
int mark = hat_dofs_marker[i];
if (mark == 0) { i_dofs.Append(i-h_start); }
else if (mark == -1) { b_dofs.Append(i-h_start); }
}
}
void Hybridization::GetBDofs(int el, int &num_idofs, Array<int> &b_dofs) const
{
// returns global indices in b_dofs
const int h_start = hat_offsets[el];
const int h_end = hat_offsets[el+1];
b_dofs.Reserve(h_end-h_start);
b_dofs.SetSize(0);
num_idofs = 0;
for (int i = h_start; i < h_end; i++)
{
int mark = hat_dofs_marker[i];
if (mark == 0) { num_idofs++; }
else if (mark == -1) { b_dofs.Append(i); }
}
}
void Hybridization::AssembleMatrix(int el, const DenseMatrix &A)
{
Array<int> i_dofs, b_dofs;
GetIBDofs(el, i_dofs, b_dofs);
DenseMatrix A_ii(Af_data + Af_offsets[el], i_dofs.Size(), i_dofs.Size());
DenseMatrix A_ib(A_ii.Data() + i_dofs.Size()*i_dofs.Size(),
i_dofs.Size(), b_dofs.Size());
DenseMatrix A_bi(A_ib.Data() + i_dofs.Size()*b_dofs.Size(),
b_dofs.Size(), i_dofs.Size());
DenseMatrix A_bb(A_bi.Data() + b_dofs.Size()*i_dofs.Size(),
b_dofs.Size(), b_dofs.Size());
for (int j = 0; j < i_dofs.Size(); j++)
{
int j_dof = i_dofs[j];
for (int i = 0; i < i_dofs.Size(); i++)
{
A_ii(i,j) = A(i_dofs[i],j_dof);
}
for (int i = 0; i < b_dofs.Size(); i++)
{
A_bi(i,j) = A(b_dofs[i],j_dof);
}
}
for (int j = 0; j < b_dofs.Size(); j++)
{
int j_dof = b_dofs[j];
for (int i = 0; i < i_dofs.Size(); i++)
{
A_ib(i,j) = A(i_dofs[i],j_dof);
}
for (int i = 0; i < b_dofs.Size(); i++)
{
A_bb(i,j) = A(b_dofs[i],j_dof);
}
}
}
void Hybridization::AssembleBdrMatrix(int bdr_el, const DenseMatrix &A)
{
// Not tested.
#ifdef MFEM_DEBUG
Array<int> vdofs, bvdofs;
fes->GetBdrElementVDofs(bdr_el, bvdofs);
#endif
int el;
DenseMatrix B(A);
Array<int> i_dofs, b_dofs, e2f;
{
int info, vdim = fes->GetVDim();
Array<int> lvdofs;
Mesh *mesh = fes->GetMesh();
mesh->GetBdrElementAdjacentElement(bdr_el, el, info);
e2f.SetSize(hat_offsets[el+1]-hat_offsets[el], -1);
lvdofs.Reserve(A.Height());
fes->FEColl()->SubDofOrder(mesh->GetElementBaseGeometry(el),
mesh->Dimension()-1, info, lvdofs);
// Convert local element dofs to local element vdofs.
Ordering::DofsToVDofs<Ordering::byNODES>(e2f.Size()/vdim, vdim, lvdofs);
MFEM_ASSERT(lvdofs.Size() == A.Height(), "internal error");
#ifdef MFEM_DEBUG
fes->GetElementVDofs(el, vdofs);
for (int i = 0; i < lvdofs.Size(); i++)
{
int bd = lvdofs[i];
bd = (bd >= 0) ? vdofs[bd] : -1-vdofs[-1-bd];
MFEM_ASSERT(bvdofs[i] == bd, "internal error");
}
#endif
B.AdjustDofDirection(lvdofs);
FiniteElementSpace::AdjustVDofs(lvdofs);
// Create a map from local element vdofs to local boundary (face) vdofs.
for (int i = 0; i < lvdofs.Size(); i++)
{
e2f[lvdofs[i]] = i;
}
}
GetIBDofs(el, i_dofs, b_dofs);
DenseMatrix A_ii(Af_data + Af_offsets[el], i_dofs.Size(), i_dofs.Size());
DenseMatrix A_ib(A_ii.Data() + i_dofs.Size()*i_dofs.Size(),
i_dofs.Size(), b_dofs.Size());
DenseMatrix A_bi(A_ib.Data() + i_dofs.Size()*b_dofs.Size(),
b_dofs.Size(), i_dofs.Size());
DenseMatrix A_bb(A_bi.Data() + b_dofs.Size()*i_dofs.Size(),
b_dofs.Size(), b_dofs.Size());
for (int j = 0; j < i_dofs.Size(); j++)
{
int j_f = e2f[i_dofs[j]];
if (j_f == -1) { continue; }
for (int i = 0; i < i_dofs.Size(); i++)
{
int i_f = e2f[i_dofs[i]];
if (i_f == -1) { continue; }
A_ii(i,j) += B(i_f,j_f);
}
for (int i = 0; i < b_dofs.Size(); i++)
{
int i_f = e2f[b_dofs[i]];
if (i_f == -1) { continue; }
A_bi(i,j) += B(i_f,j_f);
}
}
for (int j = 0; j < b_dofs.Size(); j++)
{
int j_f = e2f[b_dofs[j]];
if (j_f == -1) { continue; }
for (int i = 0; i < i_dofs.Size(); i++)
{
int i_f = e2f[i_dofs[i]];
if (i_f == -1) { continue; }
A_ib(i,j) += B(i_f,j_f);
}
for (int i = 0; i < b_dofs.Size(); i++)
{
int i_f = e2f[b_dofs[i]];
if (i_f == -1) { continue; }
A_bb(i,j) += B(i_f,j_f);
}
}
}
void Hybridization::ComputeH()
{
const int skip_zeros = 1;
Array<int> c_dof_marker(Ct->Width());
Array<int> b_dofs, c_dofs;
const int NE = fes->GetNE();
DenseMatrix Cb_t, Sb_inv_Cb_t, Hb;
#ifndef MFEM_USE_MPI
H = new SparseMatrix(Ct->Width());
#else
H = pC ? NULL : new SparseMatrix(Ct->Width());
// V = Sb^{-1} Cb^T, for parallel non-conforming meshes
SparseMatrix *V = pC ? new SparseMatrix(Ct->Height(), Ct->Width()) : NULL;
#endif
c_dof_marker = -1;
int c_mark_start = 0;
for (int el = 0; el < NE; el++)
{
int i_dofs_size;
GetBDofs(el, i_dofs_size, b_dofs);
LUFactors LU_ii(Af_data + Af_offsets[el], Af_ipiv + Af_f_offsets[el]);
double *A_ib_data = LU_ii.data + i_dofs_size*i_dofs_size;
double *A_bi_data = A_ib_data + i_dofs_size*b_dofs.Size();
LUFactors LU_bb(A_bi_data + i_dofs_size*b_dofs.Size(),
LU_ii.ipiv + i_dofs_size);
LU_ii.Factor(i_dofs_size);
LU_ii.BlockFactor(i_dofs_size, b_dofs.Size(),
A_ib_data, A_bi_data, LU_bb.data);
LU_bb.Factor(b_dofs.Size());
// Extract Cb_t from Ct, define c_dofs
c_dofs.SetSize(0);
for (int i = 0; i < b_dofs.Size(); i++)
{
const int row = b_dofs[i];
const int ncols = Ct->RowSize(row);
const int *cols = Ct->GetRowColumns(row);
for (int j = 0; j < ncols; j++)
{
const int c_dof = cols[j];
if (c_dof_marker[c_dof] < c_mark_start)
{
c_dof_marker[c_dof] = c_mark_start + c_dofs.Size();
c_dofs.Append(c_dof);
}
}
}
Cb_t.SetSize(b_dofs.Size(), c_dofs.Size());
Cb_t = 0.0;
for (int i = 0; i < b_dofs.Size(); i++)
{
const int row = b_dofs[i];
const int ncols = Ct->RowSize(row);
const int *cols = Ct->GetRowColumns(row);
const double *vals = Ct->GetRowEntries(row);
for (int j = 0; j < ncols; j++)
{
const int loc_j = c_dof_marker[cols[j]] - c_mark_start;
Cb_t(i,loc_j) = vals[j];
}
}
// Compute Hb = Cb Sb^{-1} Cb^t
Sb_inv_Cb_t = Cb_t;
LU_bb.Solve(Cb_t.Height(), Cb_t.Width(), Sb_inv_Cb_t.Data());
#ifdef MFEM_USE_MPI
if (!pC)
#endif
{
Hb.SetSize(Cb_t.Width());
MultAtB(Cb_t, Sb_inv_Cb_t, Hb);
// Assemble Hb into H
H->AddSubMatrix(c_dofs, c_dofs, Hb, skip_zeros);
}
#ifdef MFEM_USE_MPI
else
{
V->AddSubMatrix(b_dofs, c_dofs, Sb_inv_Cb_t, skip_zeros);
}
#endif
c_mark_start += c_dofs.Size();
MFEM_VERIFY(c_mark_start >= 0, "overflow"); // check for overflow
}
const bool fix_empty_rows = true;
#ifndef MFEM_USE_MPI
H->Finalize(skip_zeros, fix_empty_rows);
#else
ParFiniteElementSpace *c_pfes = dynamic_cast<ParFiniteElementSpace*>(c_fes);
if (!pC)
{
H->Finalize(skip_zeros, fix_empty_rows);
if (!c_pfes) { return; }
OperatorHandle pP(pH.Type()), dH(pH.Type());
// TODO - construct P_pc / Dof_TrueDof_Matrix directly in the pH format
pP.ConvertFrom(P_pc ? P_pc : c_pfes->Dof_TrueDof_Matrix());
dH.MakeSquareBlockDiag(c_pfes->GetComm(),c_pfes->GlobalVSize(),
c_pfes->GetDofOffsets(), H);
pH.MakePtAP(dH, pP);
delete H;
H = NULL;
}
else
{
// TODO: add ones on the diagonal of zero rows
V->Finalize();
Array<HYPRE_Int> V_J(V->NumNonZeroElems());
MFEM_ASSERT(c_pfes, "");
const int c_vsize = c_fes->GetVSize();
HYPRE_Int c_ldof_offset = c_pfes->GetMyDofOffset();
const HYPRE_Int *c_face_nbr_glob_ldof = c_pfes->GetFaceNbrGlobalDofMap();
int *J = V->GetJ();
for (int i = 0; i < V_J.Size(); i++)
{
V_J[i] = J[i] < c_vsize ?
J[i] + c_ldof_offset :
c_face_nbr_glob_ldof[J[i] - c_vsize];
}
// TODO - lpH directly in the pH format
HypreParMatrix *lpH;
{
HypreParMatrix pV(c_pfes->GetComm(), V->Height(),
pC->GetGlobalNumCols(), pC->GetGlobalNumRows(),
V->GetI(), V_J.GetData(), V->GetData(),
pC->ColPart(), pC->RowPart());
// The above constructor makes copies of all input arrays, so we can
// safely delete V_J and V:
V_J.DeleteAll();
delete V;
lpH = ParMult(pC, &pV);
}
OperatorHandle pP(pH.Type()), plpH(pH.Type());
// TODO - construct P_pc directly in the pH format
pP.ConvertFrom(P_pc);
plpH.ConvertFrom(lpH);
MFEM_VERIFY(pH.Type() != Operator::PETSC_MATIS, "To be implemented");
pH.MakePtAP(plpH, pP);
delete lpH;
}
#endif
}
void Hybridization::Finalize()
{
#ifndef MFEM_USE_MPI
if (!H) { ComputeH(); }
#else
if (!H && !pH.Ptr()) { ComputeH(); }
#endif
}
void Hybridization::MultAfInv(const Vector &b, const Vector &lambda, Vector &bf,
int mode) const
{
// b1 = Rf^t b (assuming that Ref = 0)
Vector b1;
const SparseMatrix *R = fes->GetRestrictionMatrix();
if (!R)
{
b1.SetDataAndSize(b.GetData(), b.Size());
}
else
{
b1.SetSize(fes->GetVSize());
R->MultTranspose(b, b1);
}
const int NE = fes->GetMesh()->GetNE();
Array<int> vdofs, i_dofs, b_dofs;
Vector el_vals, bf_i, i_vals, b_vals;
bf.SetSize(hat_offsets[NE]);
if (mode == 1)
{
#ifdef MFEM_USE_MPI
ParFiniteElementSpace *c_pfes =
dynamic_cast<ParFiniteElementSpace*>(c_fes);
if (!c_pfes)
{
Ct->Mult(lambda, bf);
}
else
{
Vector L(c_pfes->GetVSize());
(P_pc ? P_pc : c_pfes->GetProlongationMatrix())->Mult(lambda, L);
pC ? pC->MultTranspose(L, bf) : Ct->Mult(L, bf);
}
#else
Ct->Mult(lambda, bf);
#endif
}
// Apply Af^{-1}
Array<bool> vdof_marker(b1.Size());
vdof_marker = false;
for (int i = 0; i < NE; i++)
{
fes->GetElementVDofs(i, vdofs);
b1.GetSubVector(vdofs, el_vals);
for (int j = 0; j < vdofs.Size(); j++)
{
int vdof = vdofs[j];
if (vdof < 0) { vdof = -1 - vdof; }
if (vdof_marker[vdof]) { el_vals(j) = 0.0; }
else { vdof_marker[vdof] = true; }
}
bf_i.SetDataAndSize(&bf[hat_offsets[i]], vdofs.Size());
if (mode == 1)
{
el_vals -= bf_i;
}
GetIBDofs(i, i_dofs, b_dofs);
el_vals.GetSubVector(i_dofs, i_vals);
el_vals.GetSubVector(b_dofs, b_vals);
LUFactors LU_ii(Af_data + Af_offsets[i], Af_ipiv + Af_f_offsets[i]);
double *U_ib = LU_ii.data + i_dofs.Size()*i_dofs.Size();
double *L_bi = U_ib + i_dofs.Size()*b_dofs.Size();
LUFactors LU_bb(L_bi + b_dofs.Size()*i_dofs.Size(),
LU_ii.ipiv + i_dofs.Size());
LU_ii.BlockForwSolve(i_dofs.Size(), b_dofs.Size(), 1, L_bi,
i_vals.GetData(), b_vals.GetData());
LU_bb.Solve(b_dofs.Size(), 1, b_vals.GetData());
bf_i = 0.0;
if (mode == 1)
{
LU_ii.BlockBackSolve(i_dofs.Size(), b_dofs.Size(), 1, U_ib,
b_vals.GetData(), i_vals.GetData());
bf_i.SetSubVector(i_dofs, i_vals);
}
bf_i.SetSubVector(b_dofs, b_vals);
}
}
void Hybridization::ReduceRHS(const Vector &b, Vector &b_r) const
{
// bf = Af^{-1} Rf^t b
Vector bf;
MultAfInv(b, b, bf, 0);
// b_r = Cf bf
#ifdef MFEM_USE_MPI
ParFiniteElementSpace *c_pfes = dynamic_cast<ParFiniteElementSpace*>(c_fes);
if (!c_pfes)
{
b_r.SetSize(Ct->Width());
Ct->MultTranspose(bf, b_r);
}
else
{
Vector bl(pC ? pC->Height() : Ct->Width());
pC ? pC->Mult(bf, bl) : Ct->MultTranspose(bf, bl);
b_r.SetSize(pH.Ptr()->Height());
(P_pc ? P_pc : c_pfes->GetProlongationMatrix())->MultTranspose(bl, b_r);
}
#else
b_r.SetSize(Ct->Width());
Ct->MultTranspose(bf, b_r);
#endif
}
void Hybridization::ComputeSolution(const Vector &b, const Vector &sol_r,
Vector &sol) const
{
// bf = Af^{-1} ( Rf^t - Cf^t sol_r )
Vector bf;
MultAfInv(b, sol_r, bf, 1);
// sol = Rf bf
GridFunction s;
const SparseMatrix *R = fes->GetRestrictionMatrix();
if (!R)
{
MFEM_ASSERT(sol.Size() == fes->GetVSize(), "");
s.MakeRef(fes, sol, 0);
}
else
{
s.SetSpace(fes);
R->MultTranspose(sol, s);
}
const int NE = fes->GetMesh()->GetNE();
Array<int> vdofs;
for (int i = 0; i < NE; i++)
{
fes->GetElementVDofs(i, vdofs);
for (int j = hat_offsets[i]; j < hat_offsets[i+1]; j++)
{
if (hat_dofs_marker[j] == 1) { continue; } // skip essential b.c.
int vdof = vdofs[j-hat_offsets[i]];
if (vdof >= 0) { s(vdof) = bf(j); }
else { s(-1-vdof) = -bf(j); }
}
}
if (R)
{
R->Mult(s, sol); // assuming that Ref = 0
}
}
void Hybridization::Reset()
{
delete H;
H = NULL;
#ifdef MFEM_USE_MPI
pH.Clear();
#endif
}
}