Re: [Getfem-users] Dirichlet Boundary Conditions

[Yves Renard]

> Hi
>
> I have been trying to setup a few problems in getfem, but I am havin
> difficulties with dirichlet boundary conditions. I have modified the
> Stokes example from the tests directory to show the problem.
>
> Basically I want to have different  Dirichlet conditions on different
> parts of the boundary (a velocity prescribed on 1 part and noflow on
> others). So I setup 2 different regions and applied the boundary
> conditions. But I end up with a singular matrix in SuperLU.
>
> In the test I attach, I started with the Stokes example and divided the
> Dirichlet boundary into 2 portions. I then set velocities equal to 0 on
> each portion (so the mathematical problem is the same as the Stokes
> example). When I run the example I get the error "SuperLU solve failed:
> info = 2216". My new code is marked with !!!NEW.
>
> Does anyone understand what is going on?
>
> I can resolve the problem by setting one of the  Dirichlet bricks to
>
> "Penalization", but this isn't entirely satisfactory.

For the moment, the Dirichlet bricks do not interact each other. This means 
when you prescribe a Dirichlet on two boundaries having common nodes, a 
problem will occur because the Dirichlet condition will be taken into account 
twice on those nodes.
This is less important of course if the penalization option is chosen, at 
least if the values on the common nodes are compatible. 

Of course a solution is to have only one boundary condition with a RHS 
depending on the boundary.
Otherwise, an interaction mecanism between Dirichlet brick could be added, 
making a priority for instance to the first Dirichlet brick.

Normally, with the multiplier option (augmented constraint), you can also 
solve the problem reducing the mulptiplier space.

I hope it will help you.

Yves.




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  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
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