Re: [deal.II] Poisson equation, implementation of boundary values, mixed finite element, semiconductor devices

[Konrad Wiśniewski]

Hi Konrad,

Thank you very much for your comment! I will try to go into the detail of 
it in next days. I must admit that to this point I've just used 
::make_zero_boundary_constraints with regard to the conditions on E field. 
I didn't have a better idea, and your solutions seem much more better. I 
will probably use the second option, but I need to read more about the 
first function that you mentioned. Anyway - it will help me for sure, 
thanks! We will see if I will be able to proceed without any further advice 
:). 

Best
Konrad



W dniu sobota, 7 września 2019 09:42:10 UTC+2 użytkownik Konrad napisał:
>
> Hi Konrad,
>
> I may add as a comment (without going into details): Your problem is - as 
> you correctly describe above - a mixed Poisson problem. You essentially 
> have two options to solve it and the way you choose influences the way you 
> need to treat the boundary conditions: in primal form and in mixed form. In 
> your formulation you have natural boundary conditions (Dirichlet) on Phi 
> which means that you need to prescribe them in the variational form. This 
> will lead to a boundary integral on the relevant part of the boundary and 
> result in an additional term on the right-hand side. The boundary condition 
> for E is a flux condition and in your mixed form this (Neumann) condition 
> is essential. This means that you need to enforce them on the 
> Raviart-Thomas space as a hard constraints. There are essentially two 
> options for this:
>
> 1. If you have given a vector field that describes E on the relevant part 
> of the boundary you can use the function
> *VectorTools::project_boundary_values_div_conforming. *This will project 
> the given vector field onto its normal component (since this is the one you 
> must describe with RT elements in H(div)) and use the projected value as 
> boundary condition for the normal flux of E
>
> 2. If you only are given the scalar value of the normal flux of E then you 
> may have to set the relevant dofs in the RT-space by hand. This you can do 
> through constraints that way:
>
> AffineConstraints   constraints;
>
> constraints.clear ();
>
> DoFTools::make_hanging_node_constraints (dof_handler, constraints);
>
> const unsigned int   dofs_per_cell   = fe.dofs_per_cell;
> const unsigned int   dofs_per_face   = fe.dofs_per_face;
> std::vector local_dof_indices (dofs_per_cell);
> std::vector local_dof_face_indices 
> (dofs_per_face);
>
> typename DoFHandler::active_cell_iterator
> cell = dof_handler.begin_active(),
> endc = dof_handler.end();
> for (; cell!=endc; ++cell)
> {
> cell->get_dof_indices(local_dof_indices);
>
> for (unsigned int face_n=0;
> face_n::faces_per_cell;
> ++face_n)
> {
> cell->face(face_n)->get_dof_indices(local_dof_face_indices);
> if (cell->at_boundary(face_n))
> {
> if (cell->face(face_n)->boundary_id()==id_bottom_boundary)
> {
> for (unsigned int i = 0; i {
> // see documentation for these functions
> constraints.add_line (local_dof_face_indices.at
> (i));
> constraints.set_inhomogeneity (
> local_dof_face_indices.at(i),
> value_of_dof);
> }
> }
> else // add some constraints on other boundaries. Here: 
> zero-flux
> {
> for (unsigned int i = 0; i {
> constraints.add_line (local_dof_face_indices.at
> (i));
> }
> }
> }
> }
> ++cell_n;
> }
>
> constraints.close();
>
>
> Once you use the DoFTools::make_sparsity_pattern function you need to make 
> sure to keep the inhomogenities:
>
> DoFTools::make_sparsity_pattern(dof_handler,
>   dsp,
>   constraints,
>   /*keep_constrained_dofs = */ 
> true);
>
> The same in the assembly routine:
>
> cell->get_dof_indices(local_dof_indices);
> constraints.distribute_local_to_global(local_matrix,
> 
> local_rhs_local,
> 
> local_dof_indices,
> 
> system_matrix,
> system_rhs,
> /* use 
> inhomogeneities for rhs */ true);
>
> Keep in mind that the dofs for RT elements are edge moments in 2D and 
> face moments in 3D (and not nodal 

Re: [deal.II] MUMPS with PETScWrappers::MPI::BlockSparseMatrix

[Konrad]

Thank you, David, so I will see if I can maybe still use it in the Schur 
complement somehow.

Best,
Konrad

On Friday, September 6, 2019 at 7:46:23 PM UTC+2, David Wells wrote:
>
> Hi Konrad,
>
> I don't think that it is possible to use MUMPS with a block matrix for 
> exactly this reason. I think that if you want to use MUMPS you will need to 
> copy the block matrix into a non-block matrix.
>
> Thanks,
> David
>
> On Fri, Sep 6, 2019 at 12:25 PM Konrad > 
> wrote:
>
>> Dear deal.ii community,
>>
>> is it possible to use MUMPS with a PETScWrappers::MPI::BlockSparseMatrix? 
>> Don't find anything but I see that PETScWrappers::MPI::BlockSparseMatrix 
>> does not inherit from PETScWrappers::MatrixBase.
>>
>> Best,
>> Konrad
>>
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>>
>

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