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I am wondering if anyone knows what is the convergence criterion for a time dependent problem. For a steady state problem, the problem converges when error estimate < relative tolerance (provided damping factor =1). Is there something like this for the time dependent solver?

Thanks,
Sirisha

www.comsol.com/support/knowledgebase/877/


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Comsol 4.1
Ubuntu 10.04.1

That was very helpful Danial!

I have one more question.

What is the variable that is being used for the error estimation/tolerance? I am specifically looking for answers related to fluid structure interaction, solid mechanics and fluid mechanics.

Thanks for the help.

Sincerely,
Sirisha

It looks like that this page has been deleted.

Any one can write a summary about the convergence criterion?

Thanks.

I am wondering if anyone knows what is the convergence criterion for a time dependent problem. For a steady state problem, the problem converges when error estimate < relative tolerance (provided damping factor =1). Is there something like this for the time dependent solver?

Thanks,
Sirisha

www.comsol.com/support/knowledgebase/877/


--
Comsol 4.1
Ubuntu 10.04.1

Below is a copy of knowledgebase 877. I cannot access it anymore but this is an old copy. I am not sure if it applies to versions >4.0 but it should give a basic idea.

sirisha


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Solution Number: 877
Title: Absolute and relative tolerances, a tutorial
Platform: All Platforms
Applies to: All Products
Versions: 3.3, 3.4, 3.5, 3.5a
Created: July 4, 2002
Last Modified: May 22, 2009
Categories: Solver
Keywords:

Problem Description
What is the relative and absolute tolerances for a time dependent problem? How do I know which values to give them? In the manual it says that the absolute tolerance can be a list of degree of freedom names and positive scalars. What does that mean and how do I specify that?

Solution
These two tolerances are used by the time-stepping algorithms employed in the COMSOL Multiphysics time dependent simulation.
The relative tolerance (Rtol) is used in each iteration for all dependent variables. You have to give a value between 0 and 1.
The absolute tolerance (Atol) is used in each iteration. It can be a global value (default is 1e-3) or values specified
separately for each dependent variable, for example u 1e-3 v 1e-3 p 10. Note that while relative tolerance is a
dimensionless quantity, absolute tolerances are assumed to be presented in the same units as the dependent variables to
which they apply.
The time-dependent solver goes to the next step when the estimated local error vector e in the integration step satisfies the
inequality
abs(e(i)) <= Rtol*abs(y(i)) + Atol(y(i))
where y is the vector of dependent variables. Note that this implies that the time-stepping algorithm will effectively use the
tolerance that is the easiest to fulfill.
This means that the absolute tolerance almost always has to be modified since there is no way of giving a good general
default value. As a first approach, it may be a good idea to use a very small absolute tolerance. This makes the relative
tolerance the ruling criterion for the error control. For instance structural mechanics problem often deals with very small
variation of the variable (around 1e-6), thus the default absolute tolerance (1e-3) is too large and the condition for the
estimated error will always be satisfied. It is recommended to set the absolute error one order of magnitude less than the
expected variation.
Since the local error can not always be translated to the global error, one way to check whether you have obtained an
accurate solution to your Differential Algebraic Equations (DAE), is to repeat the solution procedure with half (or double) the
tolerances. If this does not give almost the same solution, the solution should not be trusted.
When manual time-stepping is used (available for the Generalized-alpha method) the time-step is fully user-controlled. No
adjustment of the time-step is made to fulfill an error estimate. However, the absolute and relative tolerances are still
important because they influence the accuracy to which the nonlinear system is solved. Therefore, set the tolerances to the
desired accuracy in the solution. The Generalized-alpha time dependent solver is the default method for fluid mechanics
problems because of its ability to relate the time step to the CFL number. See more info in the Fluid Mechanics section in
the COMSOL Multiphysics Modeling Guide.
For more information about settings for the time-dependent solver, please read the chapter Time-Dependent Solver in the
COMSOL Multiphysics User's Guide. See also knowledge base solution 921.