Hello Wolfgang,
thanks for your reply.
I wonder whether the stiffness matrix could be converted to a matrix with
rows = cell_numbers and columns = cell_numbers.
I tried to write the gradient with rows = degree_of_freedom into with rows
= cell_numbers.
###################
for (unsigned int i = 0; i < solid_3d.solution_n.size(); ++i) {
solver_vector(i) = solid_3d.solution_n[i];
obj_det(i)= solid_3d.solution_n[i];
norm2_value+=std::pow(solid_3d.solution_n[i],2);
}
norm2_value=std::sqrt(norm2_value);
Eigen::VectorXd
solver_gradient=-1*(obj_det/norm2_value).transpose()*inv_dense_matrix*solver_vector*solver_vector.transpose()*100;
// the length of rows and columns in solver_gradient is respectively
equal to the number of degree of freedom
/*---------------------new update on degree of finite into
cells---------------- */
//change the length of rows and column into the number of cells//
Eigen::VectorXd
cell_gradients_solid(solid_3d.triangulation.n_active_cells());
FE_Q<dim> fe_tmp(parameters.poly_degree);
const QGauss<dim> qf_cell(parameters.quad_order);
const UpdateFlags uf_cell(update_gradients | update_JxW_values);
FEValues<dim> fe_values_ref_tmp(fe_tmp, qf_cell, uf_cell);
unsigned int cell_index_solid = 0;
double dof_value = 0;
double gradient_tmp = 0;
std::cout<<"***************************************"<<std::endl;
for (auto cell = solid_3d.dof_handler_ref.begin_active(); cell !=
solid_3d.dof_handler_ref.end(); ++cell) {
if (cell->is_locally_owned()) {
fe_values_ref_tmp.reinit(cell);
std::vector<dealii::types::global_dof_index>
local_dof_indices(solid_3d.dofs_per_cell) ;
cell->get_dof_indices(local_dof_indices);
for (unsigned int i = 0; i < local_dof_indices.size(); ++i) {
dealii::types::global_dof_index global_index =
local_dof_indices[i];
dof_value = solver_gradient(global_index);
gradient_tmp += dof_value;
dof_value=0;
}
cell_gradients_solid(cell_index_solid) = gradient_tmp;
gradient_tmp=0;
++cell_index_solid;
}
}
//change the length of rows and column into the number of cells
std::cout<<cell_gradients_solid<<std::endl;
###################
If the gradient could be converted from degree of freedom into a
cell_numbers, may I know if the stiffness matrix with length of degree of
freedom could be converted to a stiffness matrix with rows = cell_numbers
and columns = cell_numbers.
But I am not quite sure if the idea about converting from degree of freedom
into cell_numbers is mathematically correct.
If I have a wrong thought, please kindly provide hint and suggestions.
Best regards
Lance
Wolfgang Bangerth <[email protected]> 于2023年10月31日周二 01:32写道：
>
> On 10/30/23 15:54, Lance Zhang wrote:
> >
> > may I know how the stiffness matrix in global degrees of freedom could
> > be converted into stiffness matrix in global cells?
>
> Lance:
> How do you define "stiffness matrix in global cells" mathematically?
>
> Best
> W.
>
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