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Commit 6ef1e048 authored by Thomas Witkowski's avatar Thomas Witkowski
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Some work on nested schur complement approach.

parent b640da9e
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Showing with 410 additions and 73 deletions
AMDiS/src/AMDiS.h
View file @ 6ef1e048
......@@ -136,7 +136,7 @@
#if HAVE_PARALLEL_MTL4
#include "parallel/Mtl4Solver.h"
#else
#include "parallel/PetscSolver.h"
#include "parallel/PetscProblemStat.h"
#endif
#endif
......
AMDiS/src/ProblemVec.cc
View file @ 6ef1e048
......@@ -1545,6 +1545,11 @@ namespace AMDiS {
BoundaryType *bound =
useGetBound ? new BoundaryType[basisFcts->getNumber()] : NULL;
if (matrix)
matrix->startInsertion(matrix->getNnz());
if (vector)
vector->set(0.0);
// == Traverse mesh and assemble. ==
......
AMDiS/src/Serializer.h
View file @ 6ef1e048
......@@ -23,6 +23,10 @@
#ifndef AMDIS_SERIALIZER_H
#define AMDIS_SERIALIZER_H
#if HAVE_PARALLEL_DOMAIN_AMDIS
#include <mpi.h>
#endif
#include <map>
#include "boost/lexical_cast.hpp"
......
AMDiS/src/parallel/MeshDistributor.cc
View file @ 6ef1e048
......@@ -1702,35 +1702,26 @@ namespace AMDiS {
}
// === Get starting position for global rank DOF ordering. ====
// Get displacment for global rank DOF ordering and global DOF number.
nRankDofs = rankDofs.size();
mpiComm.Scan(&nRankDofs, &rstart, 1, MPI_INT, MPI_SUM);
rstart -= nRankDofs;
mpi::getDofNumbering(mpiComm, nRankDofs, rstart, nOverallDofs);
// === Stores for all rank owned DOFs a new global index. ===
// Stores for all rank owned DOFs a new global index.
DofIndexMap rankDofsNewGlobalIndex;
for (int i = 0; i < nRankDofs; i++)
rankDofsNewGlobalIndex[rankDofs[i]] = i + rstart;
// === Calculate number of overall DOFs of all partitions. ===
nOverallDofs = 0;
mpiComm.Allreduce(&nRankDofs, &nOverallDofs, 1, MPI_INT, MPI_SUM);
// === Send and receive new DOF indices. ===
#if (DEBUG != 0)
ParallelDebug::testDofContainerCommunication(*this, sendDofs, recvDofs);
#endif
int i = 0;
StdMpi<vector<DegreeOfFreedom> > stdMpi(mpiComm, false);
for (RankToDofContainer::iterator sendIt = sendDofs.begin();
sendIt != sendDofs.end(); ++sendIt, i++) {
sendIt != sendDofs.end(); ++sendIt) {
stdMpi.getSendData(sendIt->first).resize(0);
stdMpi.getSendData(sendIt->first).reserve(sendIt->second.size());
for (DofContainer::iterator dofIt = sendIt->second.begin();
......@@ -1751,10 +1742,10 @@ namespace AMDiS {
for (RankToDofContainer::iterator recvIt = recvDofs.begin();
recvIt != recvDofs.end(); ++recvIt) {
int j = 0;
int i = 0;
for (DofContainer::iterator dofIt = recvIt->second.begin();
dofIt != recvIt->second.end(); ++dofIt) {
rankDofsNewGlobalIndex[*dofIt] = stdMpi.getRecvData(recvIt->first)[j++];
rankDofsNewGlobalIndex[*dofIt] = stdMpi.getRecvData(recvIt->first)[i++];
isRankDof[**dofIt] = false;
}
}
......
AMDiS/src/parallel/MeshPartitioner.h
View file @ 6ef1e048
......@@ -25,6 +25,8 @@
#include <map>
#include <set>
#include <mpi.h>
#include "AMDiS_fwd.h"
#include "Mesh.h"
......
AMDiS/src/parallel/MpiHelper.h
View file @ 6ef1e048
......@@ -48,6 +48,31 @@ namespace AMDiS {
{
srand(time(NULL) * (MPI::COMM_WORLD.Get_rank() + 1));
}
/** \brief
* In many situations a rank computes a number of local DOFs. Then all
* ranks want to know the number of global DOFs and the starting
* displacment number of the DOF numbering in each rank.
*
* \param[in] mpiComm The MPI communicator.
* \param[in] nRankDofs The number of local DOFs.
* \param[out] rStartDofs Displacment of the DOF numbering. On rank n
* this is the sum of all local DOF numbers in
* ranks 0 to n - 1.
* \param[out] nOverallDofs Global sum of nRankDofs. Is equal on all
* ranks.
*/
inline void getDofNumbering(MPI::Intracomm& mpiComm,
int nRankDofs,
int& rStartDofs,
int& nOverallDofs)
{
rStartDofs = 0;
nOverallDofs = 0;
mpiComm.Scan(&nRankDofs, &rStartDofs, 1, MPI_INT, MPI_SUM);
rStartDofs -= nRankDofs;
mpiComm.Allreduce(&nRankDofs, &nOverallDofs, 1, MPI_INT, MPI_SUM);
}
}
}
......
AMDiS/src/parallel/PetscProblemStat.cc
View file @ 6ef1e048
......@@ -29,6 +29,7 @@ namespace AMDiS {
double wtime = MPI::Wtime();
petscSolver->setMeshDistributor(meshDistributor);
petscSolver->fillPetscMatrix(systemMatrix, rhs);
petscSolver->solvePetscMatrix(*solution, adaptInfo);
......
AMDiS/src/parallel/PetscProblemStat.h
View file @ 6ef1e048
......@@ -42,12 +42,12 @@ namespace AMDiS {
if (name == "petsc-schur") {
#ifdef HAVE_PETSC_DEV
petscSolver = new PetscSolverSchur(meshDistributor);
petscSolver = new PetscSolverSchur();
#else
ERROR_EXIT("Petsc schur complement solver is only supported when petsc-dev is used!\n");
#endif
} else if (name == "petsc" || name == "") {
petscSolver = new PetscSolverGlobalMatrix(meshDistributor);
petscSolver = new PetscSolverGlobalMatrix();
} else {
ERROR_EXIT("No parallel solver %s available!\n", name.c_str());
}
......
AMDiS/src/parallel/PetscSolver.cc
View file @ 6ef1e048
......@@ -12,6 +12,7 @@
#include "parallel/PetscSolver.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"
namespace AMDiS {
......@@ -30,6 +31,10 @@ namespace AMDiS {
{
FUNCNAME("PetscSolverGlobalMatrix::fillPetscMatrix()");
TEST_EXIT_DBG(meshDistributor)("No mesh distributor object defined!\n");
TEST_EXIT_DBG(mat)("No DOF matrix defined!\n");
TEST_EXIT_DBG(vec)("NO DOF vector defined!\n");
double wtime = MPI::Wtime();
int nComponents = mat->getNumRows();
int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
......@@ -233,9 +238,9 @@ namespace AMDiS {
for (cursor_type cursor = begin<row>(mat->getBaseMatrix()),
cend = end<row>(mat->getBaseMatrix()); cursor != cend; ++cursor) {
// Global index of the current row dof.
// Global index of the current row DOF.
int globalRowDof = meshDistributor->mapLocalToGlobal(*cursor);
// Test if the current row dof is a periodic dof.
// Test if the current row DOF is a periodic DOF.
bool periodicRow = meshDistributor->isPeriodicDof(globalRowDof);
if (!periodicRow) {
......@@ -264,7 +269,7 @@ namespace AMDiS {
if (!periodicCol) {
// Calculate the exact position of the column index in the PETSc matrix.
cols.push_back(globalColDof * dispMult + dispAddCol);
cols.push_back(colIndex);
values.push_back(value(*icursor));
} else {
// === Row index is not periodic, but column index is. ===
......@@ -434,10 +439,10 @@ namespace AMDiS {
if (rankOnly && !meshDistributor->getIsRankDof(dofIt.getDOFIndex()))
continue;
// Calculate global row index of the dof.
// Calculate global row index of the DOF.
DegreeOfFreedom globalRowDof =
meshDistributor->mapLocalToGlobal(dofIt.getDOFIndex());
// Calculate PETSc index of the row dof.
// Calculate PETSc index of the row DOF.
int index = globalRowDof * dispMult + dispAdd;
if (meshDistributor->isPeriodicDof(globalRowDof)) {
......@@ -451,7 +456,7 @@ namespace AMDiS {
VecSetValues(petscVec, 1, &mappedIndex, &value, ADD_VALUES);
}
} else {
// The dof index is not periodic.
// The DOF index is not periodic.
double value = *dofIt;
VecSetValues(petscVec, 1, &index, &value, ADD_VALUES);
}
......@@ -652,33 +657,42 @@ namespace AMDiS {
}
#ifdef HAVE_PETSC_DEV
void PetscSolverSchur::fillPetscMatrix(Matrix<DOFMatrix*> *mat, SystemVector *vec)
#ifdef HAVE_PETSC_DEV
void PetscSolverSchur::updateDofData()
{
FUNCNAME("PetscSolverSchur::fillPetscMatrix()");
FUNCNAME("PetscSolverSchur::updateDofData()");
int nComponents = mat->getNumRows();
TEST_EXIT_DBG(meshDistributor)("No mesh distributor object defined!\n");
MPI::Intracomm& mpiComm = meshDistributor->getMpiComm();
typedef map<int, DofContainer> RankToDofContainer;
typedef map<DegreeOfFreedom, bool> DofIndexToBool;
std::set<DegreeOfFreedom> boundaryDofsSet;
boundaryDofs.clear();
std::set<DegreeOfFreedom> boundaryLocalDofs;
RankToDofContainer& sendDofs = meshDistributor->getSendDofs();
for (RankToDofContainer::iterator rankIt = sendDofs.begin();
rankIt != sendDofs.end(); ++rankIt)
rankIt != sendDofs.end(); ++rankIt) {
for (DofContainer::iterator dofIt = rankIt->second.begin();
dofIt != rankIt->second.end(); ++dofIt) {
boundaryLocalDofs.insert(**dofIt);
for (int i = 0; i < nComponents; i++)
boundaryDofsSet.insert(meshDistributor->mapLocalToGlobal(**dofIt) * nComponents + i);
boundaryDofs.insert(meshDistributor->mapLocalToGlobal(**dofIt));
}
}
boundaryDofs.clear();
boundaryDofs.insert(boundaryDofs.begin(),
boundaryDofsSet.begin(), boundaryDofsSet.end());
nBoundaryDofs = boundaryDofs.size();
mpi::getDofNumbering(mpiComm, nBoundaryDofs,
rStartBoundaryDofs, nOverallBoundaryDofs);
int counter = rStartBoundaryDofs;
for (std::set<DegreeOfFreedom>::iterator it = boundaryDofs.begin();
it != boundaryDofs.end(); ++it)
mapGlobalBoundaryDof[*it] = counter++;
std::set<DegreeOfFreedom> otherBoundaryLocalDofs;
RankToDofContainer& recvDofs = meshDistributor->getRecvDofs();
for (RankToDofContainer::iterator rankIt = recvDofs.begin();
......@@ -687,19 +701,153 @@ namespace AMDiS {
dofIt != rankIt->second.end(); ++dofIt)
otherBoundaryLocalDofs.insert(**dofIt);
std::set<DegreeOfFreedom> interiorDofsSet;
interiorDofs.clear();
DofIndexToBool& isRankDof = meshDistributor->getIsRankDof();
for (DofIndexToBool::iterator dofIt = isRankDof.begin();
dofIt != isRankDof.end(); ++dofIt)
dofIt != isRankDof.end(); ++dofIt) {
if (dofIt->second &&
boundaryLocalDofs.count(dofIt->first) == 0 &&
otherBoundaryLocalDofs.count(dofIt->first) == 0)
for (int i = 0; i < nComponents; i++)
interiorDofsSet.insert(meshDistributor->mapLocalToGlobal(dofIt->first) * nComponents + i);
interiorDofs.insert(meshDistributor->mapLocalToGlobal(dofIt->first));
}
interiorDofs.clear();
interiorDofs.insert(interiorDofs.begin(),
interiorDofsSet.begin(), interiorDofsSet.end());
nInteriorDofs = interiorDofs.size();
mpi::getDofNumbering(mpiComm, nInteriorDofs,
rStartInteriorDofs, nOverallInteriorDofs);
counter = rStartInteriorDofs;
for (std::set<DegreeOfFreedom>::iterator it = interiorDofs.begin();
it != interiorDofs.end(); ++it)
mapGlobalInteriorDof[*it] = counter++;
TEST_EXIT_DBG(nInteriorDofs > 0)("Should not happen!\n");
StdMpi<vector<DegreeOfFreedom> > stdMpi(mpiComm, false);
for (RankToDofContainer::iterator sendIt = meshDistributor->getSendDofs().begin();
sendIt != meshDistributor->getSendDofs().end(); ++sendIt) {
stdMpi.getSendData(sendIt->first).resize(0);
stdMpi.getSendData(sendIt->first).reserve(sendIt->second.size());
for (DofContainer::iterator dofIt = sendIt->second.begin();
dofIt != sendIt->second.end(); ++dofIt) {
int globalSendDof = meshDistributor->mapLocalToGlobal(**dofIt);
TEST_EXIT_DBG(mapGlobalBoundaryDof.count(globalSendDof))
("No mapping for boundary DOF %d!\n", globalSendDof);
stdMpi.getSendData(sendIt->first).push_back(mapGlobalBoundaryDof[globalSendDof]);
}
}
stdMpi.updateSendDataSize();
stdMpi.recv(meshDistributor->getRecvDofs());
stdMpi.startCommunication();
for (RankToDofContainer::iterator recvIt = meshDistributor->getRecvDofs().begin();
recvIt != meshDistributor->getRecvDofs().end(); ++recvIt) {
int i = 0;
for (DofContainer::iterator dofIt = recvIt->second.begin();
dofIt != recvIt->second.end(); ++dofIt) {
int globalRecvDof = meshDistributor->mapLocalToGlobal(**dofIt);
mapGlobalBoundaryDof[globalRecvDof] = stdMpi.getRecvData(recvIt->first)[i++];
}
}
}
void PetscSolverSchur::fillPetscMatrix(Matrix<DOFMatrix*> *mat, SystemVector *vec)
{
FUNCNAME("PetscSolverSchur::fillPetscMatrix()");
updateDofData();
int nComponents = mat->getNumRows();
int nInteriorRows = nInteriorDofs * nComponents;
int nOverallInteriorRows = nOverallInteriorDofs * nComponents;
int nBoundaryRows = nBoundaryDofs * nComponents;
int nOverallBoundaryRows = nOverallBoundaryDofs * nComponents;
MSG("INTERIOR LOCAL MAT: %d x %d\n", nInteriorRows, nInteriorRows);
MSG("INTERIOR GLOBAL MAT: %d x %d\n", nOverallInteriorRows, nOverallInteriorRows);
MSG("BOUNDARY LOCAL MAT: %d x %d\n", nBoundaryRows, nBoundaryRows);
MSG("BOUNDARY GLOBAL MAT: %d x %d\n", nOverallBoundaryRows, nOverallBoundaryRows);
MatCreateMPIAIJ(PETSC_COMM_WORLD,
nInteriorRows, nInteriorRows,
nOverallInteriorRows, nOverallInteriorRows,
100, PETSC_NULL, 100, PETSC_NULL, &matA11);
MatCreateMPIAIJ(PETSC_COMM_WORLD,
nBoundaryRows, nBoundaryRows,
nOverallBoundaryRows, nOverallBoundaryRows,
100, PETSC_NULL, 100, PETSC_NULL, &matA22);
MatCreateMPIAIJ(PETSC_COMM_WORLD,
nInteriorRows, nBoundaryRows,
nOverallInteriorRows, nOverallBoundaryRows,
100, PETSC_NULL, 100, PETSC_NULL, &matA12);
MatCreateMPIAIJ(PETSC_COMM_WORLD,
nBoundaryRows, nInteriorRows,
nOverallBoundaryRows, nOverallInteriorRows,
100, PETSC_NULL, 100, PETSC_NULL, &matA21);
for (int i = 0; i < nComponents; i++)
for (int j = 0; j < nComponents; j++)
if ((*mat)[i][j])
setDofMatrix((*mat)[i][j], nComponents, i, j);
MatAssemblyBegin(matA11, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(matA11, MAT_FINAL_ASSEMBLY);
MatAssemblyBegin(matA12, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(matA12, MAT_FINAL_ASSEMBLY);
MatAssemblyBegin(matA21, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(matA21, MAT_FINAL_ASSEMBLY);
MatAssemblyBegin(matA22, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(matA22, MAT_FINAL_ASSEMBLY);
Mat tmpMat[2][2];
tmpMat[0][0] = matA11;
tmpMat[0][1] = matA12;
tmpMat[1][0] = matA21;
tmpMat[1][1] = matA22;
MatCreateNest(PETSC_COMM_WORLD, 2, PETSC_NULL, 2, PETSC_NULL,
&tmpMat[0][0], &petscMatrix);
MatNestSetVecType(petscMatrix, VECNEST);
MatAssemblyBegin(petscMatrix, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(petscMatrix, MAT_FINAL_ASSEMBLY);
MatGetVecs(matA12, &petscRhsVec2, &petscRhsVec1);
MatGetVecs(matA12, &petscSolVec2, &petscSolVec1);
for (int i = 0; i < nComponents; i++)
setDofVector(petscRhsVec, vec->getDOFVector(i), nComponents, i);
Vec tmpVec[2];
tmpVec[0] = petscRhsVec1;
tmpVec[1] = petscRhsVec2;
VecCreateNest(PETSC_COMM_WORLD, 2, PETSC_NULL, tmpVec, &petscRhsVec);
tmpVec[0] = petscSolVec1;
tmpVec[1] = petscSolVec2;
VecCreateNest(PETSC_COMM_WORLD, 2, PETSC_NULL, tmpVec, &petscSolVec);
VecAssemblyBegin(petscRhsVec1);
VecAssemblyEnd(petscRhsVec1);
VecAssemblyBegin(petscRhsVec2);
VecAssemblyEnd(petscRhsVec2);
VecAssemblyBegin(petscRhsVec);
VecAssemblyEnd(petscRhsVec);
}
......@@ -711,23 +859,138 @@ namespace AMDiS {
PC pc;
KSPCreate(PETSC_COMM_WORLD, &solver);
KSPGetPC(solver, &pc);
PCSetType(pc, PCFIELDSPLIT);
IS interiorIs;
ISCreateGeneral(PETSC_COMM_WORLD, interiorDofs.size(), &(interiorDofs[0]),
PETSC_COPY_VALUES, &interiorIs);
PCFieldSplitSetIS(pc, "interior", interiorIs);
IS boundaryIs;
ISCreateGeneral(PETSC_COMM_WORLD, boundaryDofs.size(), &(boundaryDofs[0]),
PETSC_COPY_VALUES, &boundaryIs);
PCFieldSplitSetIS(pc, "boundary", boundaryIs);
// KSPSetOperators(solver, petscMatrix, petscMatrix, SAME_NONZERO_PATTERN);
// PCSetType(pc, PCFIELDSPLIT);
const PetscInt interiorField[1] = {0};
const PetscInt boundaryField[1] = {1};
PCFieldSplitSetFields(pc, "interior", 1, interiorField);
PCFieldSplitSetFields(pc, "boundary", 1, boundaryField);
KSPSetOperators(solver, petscMatrix, petscMatrix, SAME_NONZERO_PATTERN);
KSPSetTolerances(solver, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
KSPSetFromOptions(solver);
PCSetFromOptions(pc);
KSPSolve(solver, petscRhsVec, petscSolVec);
KSPDestroy(solver);
VecDestroy(petscRhsVec1);
VecDestroy(petscRhsVec2);
VecDestroy(petscRhsVec);
VecDestroy(petscSolVec1);
VecDestroy(petscSolVec2);
VecDestroy(petscSolVec);
MatDestroy(matA11);
MatDestroy(matA12);
MatDestroy(matA21);
MatDestroy(matA22);
MatDestroy(petscMatrix);
MSG("SOLVED IT!\n");
exit(0);
}
void PetscSolverSchur::setDofMatrix(DOFMatrix* mat, int dispMult,
int dispAddRow, int dispAddCol)
{
FUNCNAME("PetscSolverSchur::setDofMatrix()");
TEST_EXIT(mat)("No DOFMatrix!\n");
using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
namespace traits= mtl::traits;
typedef DOFMatrix::base_matrix_type Matrix;
traits::col<Matrix>::type col(mat->getBaseMatrix());
traits::const_value<Matrix>::type value(mat->getBaseMatrix());
typedef traits::range_generator<row, Matrix>::type cursor_type;
typedef traits::range_generator<nz, cursor_type>::type icursor_type;
vector<int> colsBoundary, colsInterior;
vector<double> valuesBoundary, valuesInterior;
colsBoundary.reserve(300);
colsInterior.reserve(300);
valuesBoundary.reserve(300);
valuesInterior.reserve(300);
for (cursor_type cursor = begin<row>(mat->getBaseMatrix()),
cend = end<row>(mat->getBaseMatrix()); cursor != cend; ++cursor) {
// Global index of the current row DOF.
int globalRowDof = meshDistributor->mapLocalToGlobal(*cursor);
colsBoundary.clear();
colsInterior.clear();
valuesBoundary.clear();
valuesInterior.clear();
for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor);
icursor != icend; ++icursor) {
int globalColDof = meshDistributor->mapLocalToGlobal(col(*icursor));
if (boundaryDofs.count(globalColDof)) {
int colIndex =
mapGlobalBoundaryDof[globalColDof] * dispMult + dispAddCol;
colsBoundary.push_back(colIndex);
valuesBoundary.push_back(value(*icursor));
} else {
int colIndex =
mapGlobalInteriorDof[globalColDof] * dispMult + dispAddCol;
colsInterior.push_back(colIndex);
valuesInterior.push_back(value(*icursor));
}
}
if (boundaryDofs.count(globalRowDof)) {
int rowIndex =
mapGlobalBoundaryDof[globalRowDof] * dispMult + dispAddRow;
MatSetValues(matA22, 1, &rowIndex, colsBoundary.size(),
&(colsBoundary[0]), &(valuesBoundary[0]), ADD_VALUES);
MatSetValues(matA21, 1, &rowIndex, colsInterior.size(),
&(colsInterior[0]), &(valuesInterior[0]), ADD_VALUES);
} else {
int rowIndex =
mapGlobalInteriorDof[globalRowDof] * dispMult + dispAddRow;
MatSetValues(matA11, 1, &rowIndex, colsInterior.size(),
&(colsInterior[0]), &(valuesInterior[0]), ADD_VALUES);
MatSetValues(matA12, 1, &rowIndex, colsBoundary.size(),
&(colsBoundary[0]), &(valuesBoundary[0]), ADD_VALUES);
}
}
}
void PetscSolverSchur::setDofVector(Vec& petscVec, DOFVector<double>* vec,
int dispMult, int dispAdd, bool rankOnly)
{
DOFVector<double>::Iterator dofIt(vec, USED_DOFS);
for (dofIt.reset(); !dofIt.end(); ++dofIt) {
if (rankOnly && !meshDistributor->getIsRankDof(dofIt.getDOFIndex()))
continue;
// Calculate global row index of the dof.
DegreeOfFreedom globalRowDof =
meshDistributor->mapLocalToGlobal(dofIt.getDOFIndex());
double value = *dofIt;
if (boundaryDofs.count(globalRowDof)) {
int index = mapGlobalBoundaryDof[globalRowDof] * dispMult + dispAdd;
VecSetValues(petscRhsVec2, 1, &index, &value, ADD_VALUES);
} else {
int index = mapGlobalInteriorDof[globalRowDof] * dispMult + dispAdd;
VecSetValues(petscRhsVec1, 1, &index, &value, ADD_VALUES);
}
}
}
#endif
......
AMDiS/src/parallel/PetscSolver.h
View file @ 6ef1e048
......@@ -23,15 +23,19 @@
#ifndef AMDIS_PETSC_SOLVER_H
#define AMDIS_PETSC_SOLVER_H
#include <set>
#include <map>
#include <mpi.h>
#include "AMDiS_fwd.h"
#include "Global.h"
#include "Parameters.h"
#include "DOFMatrix.h"