Thank you for your helpful information.
I was wondering if there would be any difficulties for parallelization of
the code when using block matrices and vectors. would you please let me
know if you have paralleled your code.
Thanks,
Hamed
On Wednesday, June 8, 2016 at 4:48:49 AM UTC-5, ha.ba...@gmail.com wrote:
>
>
> I have solve a thermoelastic problem using block matrices and block
> vectors and a same dofhandler for the displacement and temperature fields.
>
> Fully coupled thermal-stress analysis is needed when the stress analysis
> is dependent on the temperature distribution and the temperature
> distribution depends on the stress solution. For example, metalworking
> problems may include significant heating due to inelastic deformation of
> the material which, in turn, changes the material properties. Some
> problems require a fully coupled analysis in the sense that the mechanical
> and thermal solutions evolve simultaneously, but with a weak coupling
> between the two solutions. In other words, the components in the
> off-diagonal submatrices are small compared to the components in the
> diagonal submatrices. For the thermoelastic problem the off-diagonal terms
> are zero and solution is straight and stable. You can solve the block
> systems simultaneously or using staggered solution technique.
>
>
> Setup system as follow:
>
>
> dof_handler.distribute_dofs (fe);
>
> DoFRenumbering::Cuthill_McKee(dof_handler);
>
> BlockDynamicSparsityPattern dsp(2, 2);
>
> std::vector<*unsigned* *int*> block_component(3, 0);
>
> block_component[*dim*] = 1; // temperature
>
> DoFRenumbering::component_wise(dof_handler, block_component);
>
> DoFTools::count_dofs_per_block(dof_handler, dofs_per_block
> ,block_component);
>
> *const* types::global_dof_index n_dofs_u = dofs_per_block[0];
>
> // determine number of temperature DOFs if requested.
>
> types::global_dof_index n_dofs_temp;
>
> n_dofs_temp = dofs_per_block[1];
>
> dsp.block(0, 0).*reinit*(n_dofs_u, n_dofs_u);
>
> dsp.block(0, 1).*reinit*(n_dofs_u, n_dofs_temp);
>
> dsp.block(1, 0).*reinit*(n_dofs_temp, n_dofs_u);
>
> dsp.block(1, 1).*reinit*(n_dofs_temp, n_dofs_temp);
>
> dsp.collect_sizes();
>
> ...
>
>
> use the following approach for system matrix and RHS:
>
> *for* (*unsigned* *int* q=0; q<n_q_points; ++q)
>
> {
>
> // extract temperature gradient and value
>
> *for* (*unsigned* *int* k = 0; k < dofs_per_cell; ++k){
>
> temp_grads_N[k] = fe_values[temp_fe].gradient (k, q);
>
> temp_N[k] = fe_values[temp_fe].value (k, q);
>
> }
>
> *for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
>
> *for* (*unsigned* *int* j=0; j<dofs_per_cell; ++j)
>
> {
>
> *const* *unsigned* *int* comp_j = fe.system_to_component_index(j).first;
>
> *if* (comp_j < *dim*){
>
>
> cell_matrix(i,j) += determine block(0,0)
>
> }*else* *if* (comp_j == *dim*){
>
> // temperature
>
> cell_matrix(i,j) += determine block(1,1)
>
> }
>
> }
>
> }
>
> cell->get_dof_indices (local_dof_indices);
>
> *for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
>
> {
>
> *for* (*unsigned* *int* j=0; j<dofs_per_cell; ++j)
>
> system_matrix.add (local_dof_indices[i],local_dof_indices[j],
>
> cell_matrix(i,j));
>
> }
>
>
>
>
> for rhs:
>
>
>
> loop over cells:
>
>
> PointHistory<*dim*> *local_quadrature_points_data
>
> = *reinterpret_cast*<PointHistory<*dim*>*>(cell->user_pointer());
>
>
> // extract nodal total and incremental displacement
>
> // will be used for strain and delta_strain calculation
>
> fe_values[u_fe].get_function_gradients (solution_delta,
> displacement_increment_grads);
>
> fe_values[u_fe].get_function_gradients (solution, displacement_grads);
>
> // extract temperature values and gradients
>
> *if*(parameters.is_temperature){
>
> fe_values[temp_fe].get_function_values (solution, temp_value);
>
> fe_values[temp_fe].get_function_values (solution_n, temp_n_value);
>
> fe_values[temp_fe].get_function_gradients (solution, temp_grads);
>
> }
>
> // Then we can loop over all degrees of freedom on this cell and
>
> // compute local contributions to the right hand side:
>
> *for* (*unsigned* *int* q=0; q<n_q_points; ++q)
>
> {
>
> *for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i){
>
> *const* *unsigned* *int* comp_i = fe.system_to_component_index(i).first;
>
> *if* ((comp_i < *dim*) ){
>
> cell_rhs(i) +=
>
> }*else* *if* (comp_i == *dim*)
>
> {
>
> // temperature
>
> cell_rhs(i) +=
>
> }
>
> }
>
> }
>
> cell->get_dof_indices (local_dof_indices);
>
> *for* (*unsigned* *int* i=0; i<dofs_per_cell; ++i)
>
> system_rhs(local_dof_indices[i]) += cell_rhs(i);
>
>
>
> On Tuesday, August 26, 2014 at 5:51:25 PM UTC+4:30, Lisa Collins wrote:
>>
>> Hi,
>>
>> I want to start deal.ii and model a thermoelastic problem in 2D & 3D.
>>
>> Can you please guide me which steps I should study.
>> Which step should be considered as the base of my work and by modifying
>> it I can model a thermoelastic problem?
>>
>> Best regards
>> Lisa
>>
>
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