void RBSCMConstruction::compute_SCM_bounding_box()
{
START_LOG("compute_SCM_bounding_box()", "RBSCMConstruction");
// Resize the bounding box vectors
rb_scm_eval->B_min.resize(get_rb_theta_expansion().get_n_A_terms());
rb_scm_eval->B_max.resize(get_rb_theta_expansion().get_n_A_terms());
for(unsigned int q=0; q<get_rb_theta_expansion().get_n_A_terms(); q++)
{
matrix_A->zero();
add_scaled_symm_Aq(q, 1.);
// Compute B_min(q)
eigen_solver->set_position_of_spectrum(SMALLEST_REAL);
set_eigensolver_properties(q);
solve();
unsigned int nconv = get_n_converged();
if (nconv != 0)
{
std::pair<Real, Real> eval = get_eigenpair(0);
// ensure that the eigenvalue is real
libmesh_assert_less (eval.second, TOLERANCE);
rb_scm_eval->set_B_min(q, eval.first);
libMesh::out << std::endl << "B_min("<<q<<") = " << rb_scm_eval->get_B_min(q) << std::endl;
}
else
{
libMesh::err << "Eigen solver for computing B_min did not converge" << std::endl;
libmesh_error();
}
// Compute B_max(q)
eigen_solver->set_position_of_spectrum(LARGEST_REAL);
set_eigensolver_properties(q);
solve();
nconv = get_n_converged();
if (nconv != 0)
{
std::pair<Real, Real> eval = get_eigenpair(0);
// ensure that the eigenvalue is real
libmesh_assert_less (eval.second, TOLERANCE);
rb_scm_eval->set_B_max(q,eval.first);
libMesh::out << "B_max("<<q<<") = " << rb_scm_eval->get_B_max(q) << std::endl;
}
else
{
libMesh::err << "Eigen solver for computing B_max did not converge" << std::endl;
libmesh_error();
}
}
STOP_LOG("compute_SCM_bounding_box()", "RBSCMConstruction");
}
void RBSCMConstruction::evaluate_stability_constant()
{
START_LOG("evaluate_stability_constant()", "RBSCMConstruction");
// Get current index of C_J
const unsigned int j = rb_scm_eval->C_J.size()-1;
eigen_solver->set_position_of_spectrum(SMALLEST_REAL);
// We assume B is set in system assembly
// For coercive problems, B is set to the inner product matrix
// For non-coercive time-dependent problems, B is set to the mass matrix
// Set matrix A corresponding to mu_star
matrix_A->zero();
for(unsigned int q=0; q<get_rb_theta_expansion().get_n_A_terms(); q++)
{
add_scaled_symm_Aq(q, get_rb_theta_expansion().eval_A_theta(q,get_parameters()));
}
set_eigensolver_properties(-1);
solve();
unsigned int nconv = get_n_converged();
if (nconv != 0)
{
std::pair<Real, Real> eval = get_eigenpair(0);
// ensure that the eigenvalue is real
libmesh_assert_less (eval.second, TOLERANCE);
// Store the coercivity constant corresponding to mu_star
rb_scm_eval->set_C_J_stability_constraint(j,eval.first);
libMesh::out << std::endl << "Stability constant for C_J("<<j<<") = "
<< rb_scm_eval->get_C_J_stability_constraint(j) << std::endl << std::endl;
// Compute and store the vector y = (y_1, \ldots, y_Q) for the
// eigenvector currently stored in eigen_system.solution.
// We use this later to compute the SCM upper bounds.
Real norm_B2 = libmesh_real( B_inner_product(*solution, *solution) );
for(unsigned int q=0; q<get_rb_theta_expansion().get_n_A_terms(); q++)
{
Real norm_Aq2 = libmesh_real( Aq_inner_product(q, *solution, *solution) );
rb_scm_eval->set_SCM_UB_vector(j,q,norm_Aq2/norm_B2);
}
}
else
{
libMesh::err << "Error: Eigensolver did not converge in evaluate_stability_constant"
<< std::endl;
libmesh_error();
}
STOP_LOG("evaluate_stability_constant()", "RBSCMConstruction");
}
Number RBSCMConstruction::Aq_inner_product(unsigned int q,
const NumericVector<Number>& v,
const NumericVector<Number>& w)
{
if(q >= get_rb_theta_expansion().get_n_A_terms())
libmesh_error_msg("Error: We must have q < Q_a in Aq_inner_product.");
matrix_A->zero();
add_scaled_symm_Aq(q, 1.);
matrix_A->vector_mult(*inner_product_storage_vector, w);
return v.dot(*inner_product_storage_vector);
}
