Numerical methods and mathematical models of Elmer
Roland
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Joined: 12 Apr 2018, 11:29
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Hi,
Concerning the linear/non linear convergence tolerance of a solver is roughly ok for me about the understanding of how it works.
But I don't understand how the "Steady state convergence tolerance" works when using a solver. How is this convergence tolerance taken into account?
Thanks in advance for any help!
Roland
kevinarden
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### Re: Steady state convergence tolerance

I believe the linear/non linear convergence tolerance of a solver applies to that individual solver.
Each individual solver stops when it converges. Then the next solver starts.

The steady state convergence applies to the equation which is the combination of all the solvers

A common stopping criterion applies a residual level for the equation, below which the equation is deemed to be converged. When the equation satisfy the respective residual control, the simulation then stops.
Roland
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Joined: 12 Apr 2018, 11:29
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### Re: Steady state convergence tolerance

Hi,
But how could this stopping criterion be applied to the equation? What is the error expression defined for this equation which gathers all the concerned solvers? Is there something like a flowchart which could describe this kind of convergence test?
Thanks in advance for any help!
Roland
raback
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### Re: Steady state convergence tolerance

Hi Roland,

The convergence criterion is |u_i - u_j| < c*(|u_i|+|u_j|)/2, where c is the tolerance. For nonlinear system j refers to previous nonlinear iterate. For coupled system j refers to the solution of the previous time the coupled system visited the solver.

Generally it may be a good idea that the tolerances for linear system are the tightest, for nonlinear system a little sloppier, and for steady state system even more so. For example, values 1.0e-8, 1.0e-5 and 1.0e-4 could be used.

-Peter
Roland
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Joined: 12 Apr 2018, 11:29
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### Re: Steady state convergence tolerance

Hi Peter,
But I still don't feel exactly what this convergence criterion (which I understand for non-linear and linear iterations when using a solver) is for " steady state ". What do you mean exactly by "Steady state" ? What confuses me is that you refer to non-linear systems, then to coupled systems. Can you please explain what is exactly the "Steady state" compared with a nonlinear system and a coupled system? And why is it necessary to have a convergence tolerance for "Steady state"?