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## Re: [Getfem-users] Computation of reaction forces associated to a dirich

 From: David Danan Subject: Re: [Getfem-users] Computation of reaction forces associated to a dirichlet condition Date: Fri, 30 Jul 2021 18:50:04 +0200

Dear Yves,

I gave it a try to check whether i could first retrieve the nodal forces from the force density (i did exactly as you suggested, except i multiplied the mass matrix by the value given by the multipliers) and i got exactly the same nodal forces as i had with the residual method. Therefore, if i want to improve my result i guess i should avoid using the nodal forces as an input for the model.

Instead of using an add explicit rhs, is there a way to enforce the force density directly? In other words, is it possible to initialize the multiplier for the dirichlet condition with a given value (the one found in the first computation for instance) and make it a data instead of a variable of the problem?
I had tried a disable_variable on mult_on_u followed by a set_variable but i am not sure this is the proper way to do that, what do you think?

David.

Le ven. 30 juil. 2021 à 13:08, Yves Renard <Yves.Renard@insa-lyon.fr> a écrit :

Dear David,

I don't know if this explains the difference obtained because it is
really important, but the residual of the linear system and the
multiplier are not  really comparable. The residual is not a force
density, its components represent some equivalent nodal forces whose
intensity depends on the mesh size, whereas the multiplier is taken from
a finite element field and represents a force density. To obtain a force
density from the nodal forces, a mass matrix must be inverted on the
contact boundary.

Best regards,

Yves

On 30/07/2021 12:41, David Danan wrote:
> Dear GetFem community,
>
> i am trying to compute the reaction forces associated to a dirichlet
> condition, in order to do so, i have followed the advices given in
> https://www.mail-archive.com/getfem-users@gna.org/msg01136.html
> <https://www.mail-archive.com/getfem-users@gna.org/msg01136.html>
>
> You can also find enclosed my test case, using the python interface.
> The steps are the following:
> -Solve a simple 2D elasticity problem on a rectangle (dirichlet on the
> left, neumann on the top)
> -Compute the reaction forces arising from the residual without the
> dirichlet condition, by using the solution in displacement, the
> tangent matrix and the right hand side term
> -Retrieve the value of the multiplier associated to the dirichlet
> condition
>
> In fact, i expected both quantity to be the same but they were not (2
> order of magnitude different, i didn't expect such large values for
> the multipliers) and i was wondering which one was correct.
> If it helps, you can find both quantities in Mult.png (Multipliers is
> the true multiplier and MultipliersResidual is the residual without
> the dirichlet condition).
>
> Next, i built a second model similar to the first one but without a
> dirichlet condition. I added an explicit rhs using the
> MultipliersResidual  ( Multipliers gave strange results) and tried to
> solve the problem, you can see the original solution "Displacement"
> and newsolution "Displacement_test" result in Sol.png.
>
> It seems i am missing something there, i expected the solutions to be
> the same, not just close enough.
> Can you enlighten me?
>
> Best regards,
> David.
>

--

Yves Renard (Yves.Renard@insa-lyon.fr)       tel : (33) 04.72.43.87.08
INSA-Lyon
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard

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