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

 From: Yves Renard Subject: Re: [Getfem-users] Computation of reaction forces associated to a dirichlet condition Date: Fri, 30 Jul 2021 13:07:59 +0200 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Thunderbird/78.11.0

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Dear David,

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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.
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Best regards,

Yves

On 30/07/2021 12:41, David Danan wrote:
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```Dear GetFem community,

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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 this thread https://www.mail-archive.com/getfem-users@gna.org/msg01136.html <https://www.mail-archive.com/getfem-users@gna.org/msg01136.html>
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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
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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).
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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.
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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.

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--

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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