Hello all,
I am trying to project a solution in FE_DGP(sol_dg) to FE_Q (sol_cg), but I
only know the gradients of sol_dg and its values at some vertices, so I
want to fix values of sol_cg at the same vertices after the projection.
The first method I tried is quite straightforward, but the resulting global
matirx is very ill-conditioned. I set the corresponding row to zero except
the diagonal entry, and then change the right hand size.
for( ; cell_c!= endc;++cell_dg, ++cell_c ){
const unit active_index = cell_dg->active_cell_index();
if(interface_flag[active_index] == 1){
fe_values_continuous.reinit(cell_c);
fe_values_v_dg.reinit(cell_dg);
fe_values_v_dg.get_function_values(solution, solu_dg);
cell_c->get_dof_indices(local_dof_indices_c);
for(unit vert=0; vert<4; ++vert){
// local_dof_indices_c[vert] global index
const unit index_i = local_dof_indices_c[vert];
ls_rhs_continuous(index_i) = solu_dg[vert]* aver_diag;
for(unit i=0; i<size_m; ++i)
ls_matrix_continuous.set(local_dof_indices_c[vert], i, 0.);
ls_matrix_continuous.set(index_i, index_i, aver_diag);
}
}
}
so I want to use constraint matrix to do the same thing, but cannot get the
right answer.
for( ; cell_c!= endc;++cell_dg, ++cell_c ){
const unit active_index = cell_dg->active_cell_index();
if(interface_flag[active_index] == 1){
fe_values_continuous.reinit(cell_c);
fe_values_v_dg.reinit(cell_dg);
fe_values_v_dg.get_function_values(solution, solu_dg);
cell_c->get_dof_indices(local_dof_indices_c);
for(unit vert=0; vert<4; ++vert){
// local_dof_indices_c[vert] global index
const unit index_i = local_dof_indices_c[vert];
constraints.add_line(index_i);
constraints.set_inhomogeneity(index_i, solu_dg[vert]);
}
}
}
constraints.close();
cell_c = dof_handler_continuous.begin_active();
cell_dg = dof_handler.begin_active();
for( ; cell_c!=endc; ++cell_c, ++cell_dg){
fe_values_dg.reinit(cell_dg);
fe_values_dg.get_function_gradients(solution, grad_dg);
ls_matrix = 0;
ls_rhs = 0;
fe_values_continuous.reinit(cell_c);
for(unit q=0; q<n_q_points; ++q){
for(unit i=0; i<dofs_per_cell_continuous; ++i){
ls_rhs(i) += fe_values_continuous.shape_grad(i,q)
* fe_values_continuous.JxW(q)
* grad_dg[q];
for(unit j=0; j<dofs_per_cell_continuous; ++j)
ls_matrix(i,j) += fe_values_continuous.shape_grad(i,q)
* fe_values_continuous.shape_grad(j,q)
* fe_values_continuous.JxW(q);
}
}
cell_c->get_dof_indices(local_dof_indices_c);
constraints.distribute_local_to_global (ls_matrix, ls_rhs,
local_dof_indices_c,
ls_matrix_continuous,
ls_rhs_continuous);
Any help would be appreciated
Thanks,
Jiaqi
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