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## [Getfem-users] Imposing Dirichlet boundary conditions with lagrangian mu

 From: GUILMIN Anne-Lise Subject: [Getfem-users] Imposing Dirichlet boundary conditions with lagrangian multipliers Date: Mon, 12 Apr 2010 19:07:52 +0200

Dear all,

First, thank you for developping this library. It is such a pleasure to write a finite element code without bothering (too much) about indices !

I want to impose normal Dirichlet conditions so I define multipliers and use a hand-made brick to fill the matrix and the right hand side.
My problem is that I don't get the right number of lagragian multipliers. It seems to be linked with the add_multiplier function.

I send you a modified version of the getfem test elastostatic.cc to underline this problem. In this one, normal Dirichlet conditions are imposed on the bottom and lateral faces of the mesh.
The following results are given for a linear quadrilateral two-dimensionnal single element : a square with 4 nodes.

When defining the multipliers with add_fem_variable (line 589), we get the right number of lagragian multipliers : 2 on each imposed face = 6.

When defining the multipliers with add_multiplier instead (line 591), we get less multipliers than expected : only 1 on two faces and 2 on the last >
It acts as if no boundary condition was imposed on the bottom left node.

If I understood well, when using the add_multiplier definition, we start creating multipliers on the whole mesh, then we fill the matrix part dedicated to Dirichlet boundary conditions and finally we simplify it to eliminate useless lines and columns (step which is necessary for Gaussian elimination). Could there be a problem in the way that the matrix is simplified which would explain the disappearance of some useful multipliers?
If not, what should I do to get the right number of multipliers using add_multiplier?

I would be thankful for any help or explanation.
Best regards,

Anne-Lise Guilmin
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elastostatic.tar.gz
Description: elastostatic.tar.gz