PetscErrorCode FEMAssembleTotal2DLaplace(MPI_Comm comm, Mesh *mesh, Mat &A,
Vec &b, PetscReal(*f)(Point), PetscReal(*K)(Point)) {
PetscErrorCode ierr;
PetscInt rank;
MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
PetscInt size = mesh->vetrices.size();
ierr
= MatCreateMPIAIJ(comm, size, size, PETSC_DECIDE, PETSC_DECIDE, 7, PETSC_NULL, 0, PETSC_NULL, &A);
CHKERRQ(ierr);
ierr = VecCreateMPI(comm, size, PETSC_DECIDE, &b);
CHKERRQ(ierr);
for (std::map<PetscInt, Element*>::iterator e = mesh->elements.begin(); e
!= mesh->elements.end(); e++) {
PetscScalar bl[3];
PetscScalar Al[9];
PetscReal R[4];
PetscInt elSize = e->second->numVetrices;
Point *vetrices = new Point[elSize];
PetscInt ixs[elSize];
for (int j = 0; j < elSize; j++) {
ixs[j] = e->second->vetrices[j];
vetrices[j] = *(mesh->vetrices[ixs[j]]);
}
R[0] = vetrices[1].x - vetrices[0].x;
R[2] = vetrices[1].y - vetrices[0].y;
R[1] = vetrices[2].x - vetrices[0].x;
R[3] = vetrices[2].y - vetrices[0].y;
Point center = getCenterOfSet(vetrices, elSize);
bLoc(R, bl, f(center));
ALoc(R, Al, K(center));
ierr = VecSetValues(b, elSize, ixs, bl, ADD_VALUES);
CHKERRQ(ierr);
ierr = MatSetValues(A, elSize, ixs, elSize, ixs, Al, ADD_VALUES);
CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(b);
CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
return ierr;
}
void RLS
( const DistSparseMatrix<Real>& A,
const DistMultiVec<Real>& b,
Real rho,
DistMultiVec<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
mpi::Comm comm = A.Comm();
DistMultiVec<Int> orders(comm), firstInds(comm);
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
{
const Int localHeight = orders.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = orders.GlobalRow(iLoc);
if( i < m+1 )
{
orders.SetLocal( iLoc, 0, m+1 );
firstInds.SetLocal( iLoc, 0, 0 );
}
else
{
orders.SetLocal( iLoc, 0, n+2 );
firstInds.SetLocal( iLoc, 0, m+1 );
}
}
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
DistSparseMatrix<Real> G(comm);
{
Zeros( G, m+n+3, n+2 );
// Count the number of entries of G to reserve
// -------------------------------------------
Int numLocalUpdates = 0;
const Int localHeight = G.LocalHeight();
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 || i == m+1 || (i>m+1 && i<m+n+2) )
++numLocalUpdates;
}
const Int numEntriesA = A.NumLocalEntries();
G.Reserve( numLocalUpdates+numEntriesA, numEntriesA );
// Queue the local updates
// -----------------------
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const Int i = G.GlobalRow(iLoc);
if( i == 0 )
G.QueueLocalUpdate( iLoc, 0, -1 );
else if( i == m+1 )
G.QueueLocalUpdate( iLoc, 1, -1 );
else if( i > m+1 && i < m+n+2 )
G.QueueLocalUpdate( iLoc, i-m, -1 );
}
// Queue the remote updates
// ------------------------
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
DistMultiVec<Real> h(comm);
Zeros( h, m+n+3, 1 );
auto& bLoc = b.LockedMatrix();
{
const Int bLocalHeight = b.LocalHeight();
h.Reserve( bLocalHeight );
for( Int iLoc=0; iLoc<bLocalHeight; ++iLoc )
h.QueueUpdate( b.GlobalRow(iLoc)+1, 0, bLoc(iLoc) );
h.ProcessQueues();
}
h.Set( END, 0, 1 );
// c := [1; rho; 0]
DistMultiVec<Real> c(comm);
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
DistSparseMatrix<Real> AHat(comm);
Zeros( AHat, 0, n+2 );
DistMultiVec<Real> bHat(comm);
Zeros( bHat, 0, 1 );
DistMultiVec<Real> xHat(comm), y(comm), z(comm), s(comm);
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
PetscErrorCode FEMAssemble2DLaplace(MPI_Comm comm, Mesh *mesh, Mat &A, Vec &b,
PetscReal(*f)(Point), PetscReal(*K)(Point)) {
PetscErrorCode ierr;
PetscInt rank;
MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
PetscInt size = mesh->vetrices.size();
ierr
= MatCreateMPIAIJ(comm, size, size, PETSC_DECIDE, PETSC_DECIDE, 7, PETSC_NULL, 0, PETSC_NULL, &A);
CHKERRQ(ierr);
ierr = VecCreateMPI(comm, size, PETSC_DECIDE, &b);
CHKERRQ(ierr);
std::set<PetscInt> indDirchlet;
for (std::set<PetscInt>::iterator i = mesh->borderEdges.begin(); i
!= mesh->borderEdges.end(); i++) {
for (int j = 0; j < 2; j++) {
indDirchlet.insert(mesh->edges[*i]->vetrices[j]);
}
}
for (std::map<PetscInt, Element*>::iterator e = mesh->elements.begin(); e
!= mesh->elements.end(); e++) {
PetscScalar bl[3];
PetscScalar Al[9];
PetscReal R[4];
PetscInt elSize = e->second->numVetrices;
Point *vetrices = new Point[elSize];
PetscInt ixs[elSize];
for (int j = 0; j < elSize; j++) {
ixs[j] = e->second->vetrices[j];
vetrices[j] = *(mesh->vetrices[ixs[j]]);
}
R[0] = vetrices[1].x - vetrices[0].x;
R[2] = vetrices[1].y - vetrices[0].y;
R[1] = vetrices[2].x - vetrices[0].x;
R[3] = vetrices[2].y - vetrices[0].y;
Point center = getCenterOfSet(vetrices, elSize);
bLoc(R, bl, f(center));
ALoc(R, Al, K(center));
//Enforce Dirchlet condition
for (int j = 0; j < 3; j++) {
if (indDirchlet.count(ixs[j]) > 0) {
for (int k = 0; k < 3; k++) {
Al[j * 3 + k] = 0;
Al[k * 3 + j] = 0;
}
Al[j * 3 + j] = 1;
bl[j] = 0;
}
}
ierr = VecSetValues(b, elSize, ixs, bl, ADD_VALUES);
CHKERRQ(ierr);
ierr = MatSetValues(A, elSize, ixs, elSize, ixs, Al, ADD_VALUES);
CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(b);
CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);
CHKERRQ(ierr);
ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
return ierr;
}
