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Not convergent when the mesh is dense, why?

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Dear all,

Convergence problem is kinda mysterious...

This time convergence is nor reached when the mesh is dense. I would say perhaps too dense in some region. Some coarser mesh leads to convergence. What's the possible reason for this?

From my point of view, the sub-domain with more elements has more weight in the quantity used to evaluate convergence. Then importance of sub-domain with too dense mesh may be overemphasized. The convergence becomes sensitive to the behavior there. So too dense mesh only in some part may not be a good idea. What do you think?

Gracias!

Best

5 Replies Last Post 23.10.2012, 17:11 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 22.10.2012, 13:53 GMT-4
Hi

you should have a dense mesh in regions with high gradients on the dependent variables, such to resolve the dependent variables correctly, no reason to have a dense mesh where the gradients is low, but this concerns ALL dependent variables, often we check only 1-2, and forget about the others, not to say the local Langrange variables.

So I agree that the mesh density can influence the error, but I'm not sure that is the main reason

--
Good luck
Ivar
Hi you should have a dense mesh in regions with high gradients on the dependent variables, such to resolve the dependent variables correctly, no reason to have a dense mesh where the gradients is low, but this concerns ALL dependent variables, often we check only 1-2, and forget about the others, not to say the local Langrange variables. So I agree that the mesh density can influence the error, but I'm not sure that is the main reason -- Good luck Ivar

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Posted: 1 decade ago 22.10.2012, 14:17 GMT-4
I agree. But I still don't find where the problem is.
I agree. But I still don't find where the problem is.

Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 23.10.2012, 13:45 GMT-4
Hello Pu,

Some of the most common reasons for non-convergence have nothing to do with the mesh and refining the mesh cannot be expected to help fix the problem.
A couple of such reasons:
- The problem is not well-posed, i.e. there isn't a solution to the problem as posed, or there are multiple solutions
- The initial values provided to the solver are not sufficiently close to the solution of the problem.

If your model is still refusing to converge despite your refining the mesh, I would suggest looking into those two possibilities.
Best,
JF
Hello Pu, Some of the most common reasons for non-convergence have nothing to do with the mesh and refining the mesh cannot be expected to help fix the problem. A couple of such reasons: - The problem is not well-posed, i.e. there isn't a solution to the problem as posed, or there are multiple solutions - The initial values provided to the solver are not sufficiently close to the solution of the problem. If your model is still refusing to converge despite your refining the mesh, I would suggest looking into those two possibilities. Best, JF

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Posted: 1 decade ago 23.10.2012, 15:43 GMT-4
Hi, JF

Thanks for the reply!

As for the two possible reasons you suggested, since the problem does have a unique physical solution, I think only the second is probable. But generally how can one improve the model in this direction? Although putting some approximation as the background field may be one method, it's not really practical to get such an good approximation.

Best!
Hi, JF Thanks for the reply! As for the two possible reasons you suggested, since the problem does have a unique physical solution, I think only the second is probable. But generally how can one improve the model in this direction? Although putting some approximation as the background field may be one method, it's not really practical to get such an good approximation. Best!

Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 23.10.2012, 17:11 GMT-4
- Beware: the fact that the physical problem has a unique solution does not mean that the mathematical model you're using to represent it also does!

- As far as getting better intial conditions, you could try ramping up the nonlinearities or ramping up the loads. There was a minicourse on solvers at the COMSOL Conference earlier this month that covered this topic.
- Beware: the fact that the physical problem has a unique solution does not mean that the mathematical model you're using to represent it also does! - As far as getting better intial conditions, you could try ramping up the nonlinearities or ramping up the loads. There was a minicourse on solvers at the COMSOL Conference earlier this month that covered this topic.

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