Why does the StaticSolver not reach the equilibrium configuration at 1st time step?

[adkoessler]

Hello everyone,

I use SOFA to plan deformation of flexible parts manipulated by robots. In this process, I need to perform many simulation steps to estimate numerically an inverse model. To speed up the computation, I am interested in the component StaticSolver. I tried the demo of the component: examples/Components/solver/StaticSolver.scn
I toyed around with the script, tried to increase the iteration limit of the solver, tried to replace it with an exact solver (SparseLDLSolver). But it didn't change the fact that the configuration at the end of the first time step is not the configuration at time = +infinity, which is the result I was expecting.

So here are my questions:

1. What is the reason for this behavior?
2. How can the convergence be detected, in order to avoid continuing the simulation when the system is not going to move anymore?

Best,
Adrien

[hugtalbot]

Hey @adkoessler

New post, new interesting question 👍
I guess that when you say "tried to increase the iteration limit of the solver" you rather mean you increased the number of max iterations of the iterative linear solver you used. Is it correct ? not to be confounded with the number of max iterations of the Newton solver.

I am sorry, again to your questions, I reply with other questions (to better understand your use and provide the appropriate reply): what material law are you defining on your object ? what forces are acting on it ?

How can the convergence be detected, in order to avoid continuing the simulation when the system is not going to move anymore?

To get information messaging, you can activate the printLog boolean data available in all SOFA components.

Best,

Hugo

[adkoessler]

Hi @hugtalbot

Yes I'm talking about the number of iterations of the linear solver, CGLinearSolver in the case of the example I linked.
Still from the example, the behavior I describe can be seen with both MeshSpringForceField and TetrahedronFEMForceField. The only force acting is the gravity.

If you run this scene, you can see that MeshSpringForceField reaches the final state quite quickly, while TetrahedronFEMForceField slowly gets to the final shape. However they both need some steps to stabilize, hence my question: what does some equal to, and how can it be determined.

Best,
Adrien

[hugtalbot]

Hi @adkoessler

Actually the number of iterations in the ConjugateGradient (CG) linear solver impacts quite significantly the simulation accuracy.
Set it to x100 you will notice the change: all beams will behave very similarly.

Moreover, in static analysis, external forces are usually applied gradually (incremental loading) which is not done here.

Let me know whether this clarifies things.

[hugtalbot]

further to our discussion, I let you complete/set as answered the topic if you'd like @adkoessler 💂

[adkoessler]

After discussing it with @hugtalbot, it seems that I looked for a solution around the linear solver, but it was the integration scheme that needed to be set up correctly.
One can see the parameters of the StaticSolver here: https://www.sofa-framework.org/community/doc/components/integrationschemes/staticsolver/
The trap I fell into is that the default value for newton_iterations is equal to 1. However, it's unlikely that a nonlinear problem converges to equilibrium in just one Newton step. Therefore, it is needed to set this parameter to a greater value when instantiating this component in a scene.

Moreover, as suggested above, the printLog data of the StaticSolver shows which termination condition was met. This is useful to set the newton_iterations parameter correctly, depending on the "nonlinearity" of the problem to solve.