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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
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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,


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 this thread <>

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,


  Yves Renard (       tel : (33)
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE


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