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; }