Dear Alberto,
The correctness of my answer depends on the numbering assigned to the
degrees-of-freedom, which is something that you've not mentioned above. But
from what I can discern the 9th row relates to the pressure test function,
so K_{8,[0-7]} are the components from the coupling block K_{pu}, K_{88} is
K_{pp} and K_{89} is K_{pJ}. Since these degree's of freedom are not
constrained, this row should remain untouched after boundary values are
applied. So, to me, nothing necessarily appears amiss on row 9 (as you've
indicated).
Do you agree with this?
Kind regards,
Jean-Paul
On Tuesday, April 18, 2017 at 12:32:44 PM UTC+2, Alberto Salvadori wrote:
>
> Hi,
>
> sorry for asking your help again, that I really appreciated.
> Today's issue is about imposing boundary conditions for a three-fields
> formulation.
>
> In brief, I defined a 4 nodes square element, of type:
>
> fe(FE_Q<dim>(poly_degree), dim, // displacement
>
> FE_DGPMonomial<dim>(poly_degree - 1), 1, // pressure
>
> FE_DGPMonomial<dim>(poly_degree - 1), 1), // dilatation
>
> with poly_degree = 1.
>
> While debugging on a single element, which has 10 dofs in 2D ( 4x2
> displacements + 1 pressure + 1 dilatation), I aim at imposing Dirichlet
> boundary conditions on displacements, whereas body forces are zero.
>
> The cell matrix and the cell_rhs are the following.
>
> *Cell matrix = *
>
> *{ 0.7037, 0.0278, -0.2037, -0.4722, -0.1481, 0.4722, -0.3519,
> -0.0278, -1.0000, 0.0000}, *
>
> *{ 0.0278, 0.7037, 0.4722, -0.1481, -0.4722, -0.2037, -0.0278,
> -0.3519, -1.0000, 0.0000}, *
>
> *{ -0.2037, 0.4722, 0.7037, -0.0278, -0.3519, 0.0278, -0.1481,
> -0.4722, 1.0000, 0.0000}, *
>
> *{ -0.4722, -0.1481, -0.0278, 0.7037, 0.0278, -0.3519, 0.4722,
> -0.2037, -1.0000, 0.0000}, *
>
> *{ -0.1481, -0.4722, -0.3519, 0.0278, 0.7037, -0.0278, -0.2037,
> 0.4722, -1.0000, 0.0000}, *
>
> *{ 0.4722, -0.2037, 0.0278, -0.3519, -0.0278, 0.7037, -0.4722,
> -0.1481, 1.0000, 0.0000}, *
>
> *{ -0.3519, -0.0278, -0.1481, 0.4722, -0.2037, -0.4722, 0.7037,
> 0.0278, 1.0000, 0.0000}, *
>
> *{ -0.0278, -0.3519, -0.4722, -0.2037, 0.4722, -0.1481, 0.0278,
> 0.7037, 1.0000, 0.0000}, *
>
> *{ -1.0000, -1.0000, 1.0000, -1.0000, -1.0000, 1.0000, 1.0000,
> 1.0000, 0.0000, -4.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.0000, -4.0000, 6.6667}, *
>
> *Cell rhs =0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
> 0.000e+00 0.000e+00 0.000e+00 0.000e+00 *
>
> They seem to be correct. After calling
>
> system_matrix.compress(VectorOperation::add);
>
> system_rhs.compress(VectorOperation::add);
>
> the system matrix coincides with the cell matrix, the same for the rhs. To
> impose BCs I followed the scheme of step-18, as follows:
>
> std::map<types::global_dof_index,double> boundary_values;
>
>
> ComponentMask displacements_mask = fe.component_mask (displacements);
>
> VectorTools::interpolate_boundary_values (dof_handler,
>
> 0,
>
>
> IncrementalDirichletBoundaryValues<dim>( TIDM, NRit, GPDofs ),
>
> boundary_values,
>
> displacements_mask);
>
>
>
> PETScWrappers::MPI::Vector tmp (locally_owned_dofs,mpi_communicator);
>
> MatrixTools::apply_boundary_values (boundary_values,
>
> system_matrix,
>
> tmp,
>
> system_rhs,
>
> false);
>
> incremental_displacement = tmp;
>
> where the class IncrementalDirichletBoundaryValues implements the
> Dirichlet BC and GPDofs = 4.
> The boundary values after VectorTools::interpolate_boundary_values turn
> out to be:
>
> *boundary_values = -0.0500, -0.0500, -0.0500, 0.0500, 0.0500,
> -0.0500, 0.0500, 0.0500, 0.0000, 0.0000, *
>
> *tmp = -0.0500, -0.0500, -0.0500, 0.0500, 0.0500, -0.0500,
> 0.0500, 0.0500, 0.0000, 0.0000, *
>
> which are pretty much what I expected. However, after MatrixTools
> ::apply_boundary_values the system matrix and the rhs are as follows,
>
> * System matrix = *
>
> *{ 0.7037, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.7037, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.7037, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.7037, 0.0000, 0.0000, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.7037, 0.0000, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.7037, 0.0000,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.7037,
> 0.0000, 0.0000, 0.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.7037, 0.0000, 0.0000}, *
>
> *{ -1.0000, -1.0000, 1.0000, -1.0000, -1.0000, 1.0000, 1.0000,
> 1.0000, 0.0000, -4.0000}, *
>
> *{ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
> 0.0000, -4.0000, 6.6667}, *
>
> *System_rhs = -0.0352, -0.0352, -0.0352, 0.0352, 0.0352, -0.0352,
> 0.0352, 0.0352, 0.0000, 0.0000, *
>
> The* System_rhs *seems correct, but the matrix, particularly the 9th row,
> does not, but I am not sure why.
>
> Many thanks in advance,
> Alberto
>
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