value_array_type create_b_vector(
idx nv,
idx_array_type kok_xadj,
idx_edge_array_type kok_adj,
value_array_type kok_mtx_vals,
value_array_type x_vector){
value_array_type b_vector ("B VECTOR", nv);
Kokkos::parallel_for (Kokkos::RangePolicy<MyExecSpace> (0, nv) ,
SPMV(
kok_xadj,
kok_adj,
kok_mtx_vals,
x_vector,
b_vector));
return b_vector;
}
TEUCHOS_UNIT_TEST( MCSA, one_step_solve_test)
{
int N = 100;
int problem_size = N*N;
// Build the diffusion operator.
double bc_val = 10.0;
double dx = 0.01;
double dy = 0.01;
double dt = 0.01;
double alpha = 0.01;
HMCSA::DiffusionOperator diffusion_operator( 5,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
bc_val, bc_val, bc_val, bc_val,
N, N,
dx, dy, dt, alpha );
Teuchos::RCP<Epetra_CrsMatrix> A = diffusion_operator.getCrsMatrix();
Epetra_Map map = A->RowMap();
// Solution Vectors.
std::vector<double> x_vector( problem_size );
Epetra_Vector x( View, map, &x_vector[0] );
std::vector<double> x_aztec_vector( problem_size );
Epetra_Vector x_aztec( View, map, &x_aztec_vector[0] );
// Build source - set intial and Dirichlet boundary conditions.
std::vector<double> b_vector( problem_size, 1.0 );
int idx;
for ( int j = 1; j < N-1; ++j )
{
int i = 0;
idx = i + j*N;
b_vector[idx] = bc_val;
}
for ( int j = 1; j < N-1; ++j )
{
int i = N-1;
idx = i + j*N;
b_vector[idx] = bc_val;
}
for ( int i = 0; i < N; ++i )
{
int j = 0;
idx = i + j*N;
b_vector[idx] = bc_val;
}
for ( int i = 0; i < N; ++i )
{
int j = N-1;
idx = i + j*N;
b_vector[idx] = bc_val;
}
Epetra_Vector b( View, map, &b_vector[0] );
// MCSA Linear problem.
Teuchos::RCP<Epetra_LinearProblem> linear_problem = Teuchos::rcp(
new Epetra_LinearProblem( A.getRawPtr(), &x, &b ) );
// MCSA Jacobi precondition.
Teuchos::RCP<Epetra_CrsMatrix> H = buildH( A );
double spec_rad_H = HMCSA::OperatorTools::spectralRadius( H );
std::cout << std::endl << std::endl
<< "---------------------" << std::endl
<< "Iteration matrix spectral radius: "
<< spec_rad_H << std::endl;
HMCSA::JacobiPreconditioner preconditioner( linear_problem );
preconditioner.precondition();
H = buildH( preconditioner.getOperator() );
double spec_rad_precond_H =
HMCSA::OperatorTools::spectralRadius( H );
std::cout << "Preconditioned iteration matrix spectral radius: "
<< spec_rad_precond_H << std::endl
<< "---------------------" << std::endl;
}
//---------------------------------------------------------------------------//
int main( int argc, char** argv )
{
// Problem parameters.
int xN = 201;
int yN = 201;
int problem_size = xN*yN;
double x_min = 0.0;
double x_max = 2.0;
double y_min = 0.0;
double y_max = 2.0;
double ic_val = 0.0;
double bc_val_xmin = 0.0;
double bc_val_xmax = 0.0;
double bc_val_ymin = 10.0;
double bc_val_ymax = 10.0;
int num_steps = 1;
double T = 0.01;
double dx = (x_max-x_min)/(xN-1);
double dy = (y_max-y_min)/(yN-1);
double dt = T / num_steps;
double alpha = 0.01;
int max_iters = 1000;
double tolerance = 1.0e-8;
int num_histories = 40000;
double weight_cutoff = 1.0e-12;
// Setup up a VTK mesh for output.
HMCSA::VtkWriter vtk_writer( x_min, x_max, y_min, y_max,
dx, dy, xN, yN );
// Build the Diffusion operator.
HMCSA::DiffusionOperator diffusion_operator(
5,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
HMCSA::HMCSA_DIRICHLET,
bc_val_xmin, bc_val_xmax, bc_val_ymin, bc_val_ymax,
xN, yN,
dx, dy, dt, alpha );
Teuchos::RCP<Epetra_CrsMatrix> A = diffusion_operator.getCrsMatrix();
Epetra_Map map = A->RowMap();
// Solution Vector.
std::vector<double> x_vector( problem_size );
Epetra_Vector x( View, map, &x_vector[0] );
// Build source - set intial and Dirichlet boundary conditions.
std::vector<double> b_vector( problem_size, ic_val );
buildIC( b_vector, xN, yN,
bc_val_xmin, bc_val_xmax, bc_val_ymin, bc_val_ymax );
Epetra_Vector b( View, map, &b_vector[0] );
// Linear problem.
Teuchos::RCP<Epetra_LinearProblem> linear_problem = Teuchos::rcp(
new Epetra_LinearProblem( A.getRawPtr(), &x, &b ) );
// Time step.
HMCSA::TimeIntegrator time_integrator( linear_problem, vtk_writer );
time_integrator.integrate( true, num_steps, max_iters,
tolerance, num_histories,
weight_cutoff );
return 0;
}
TEUCHOS_UNIT_TEST( MCSA, MCSA_test)
{
int problem_size = 16;
Epetra_SerialComm comm;
Epetra_Map map( problem_size, 0, comm );
std::vector<double> x_vector( problem_size );
Epetra_Vector x( View, map, &x_vector[0] );
std::vector<double> x_aztec_vector( problem_size );
Epetra_Vector x_aztec( View, map, &x_aztec_vector[0] );
std::vector<double> b_vector( problem_size, 0.4 );
Epetra_Vector b( View, map, &b_vector[0] );
Teuchos::RCP<Epetra_CrsMatrix> A =
Teuchos::rcp( new Epetra_CrsMatrix( Copy, map, problem_size ) );
double lower_diag = -0.1;
double diag = 2.4;
double upper_diag = -0.1;
int global_row = 0;
int lower_row = 0;
int upper_row = 0;
for ( int i = 0; i < problem_size; ++i )
{
global_row = A->GRID(i);
lower_row = i-1;
upper_row = i+1;
if ( lower_row > -1 )
{
A->InsertGlobalValues( global_row, 1, &lower_diag, &lower_row );
}
A->InsertGlobalValues( global_row, 1, &diag, &global_row );
if ( upper_row < problem_size )
{
A->InsertGlobalValues( global_row, 1, &upper_diag, &upper_row );
}
}
A->FillComplete();
double spec_rad_A = HMCSA::OperatorTools::spectralRadius( A );
std::cout << std::endl <<
"Operator spectral radius: " << spec_rad_A << std::endl;
Teuchos::RCP<Epetra_LinearProblem> linear_problem = Teuchos::rcp(
new Epetra_LinearProblem( A.getRawPtr(), &x, &b ) );
HMCSA::JacobiPreconditioner preconditioner( linear_problem );
preconditioner.precondition();
HMCSA::MCSA mcsa_solver( linear_problem );
mcsa_solver.iterate( 100, 1.0e-8, 100, 1.0e-8 );
std::cout << "MCSA ITERS: " << mcsa_solver.getNumIters() << std::endl;
Epetra_LinearProblem aztec_linear_problem( A.getRawPtr(), &x_aztec, &b );
AztecOO aztec_solver( aztec_linear_problem );
aztec_solver.SetAztecOption( AZ_solver, AZ_gmres );
aztec_solver.Iterate( 100, 1.0e-8 );
std::vector<double> error_vector( problem_size );
Epetra_Vector error( View, map, &error_vector[0] );
for (int i = 0; i < problem_size; ++i)
{
error[i] = x[i] - x_aztec[i];
}
double error_norm;
error.Norm2( &error_norm );
std::cout << std::endl <<
"Aztec GMRES vs. MCSA absolute error L2 norm: " <<
error_norm << std::endl;
}
