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Problem with boundary errors

Posted 20 avr. 2022, 09:52 UTC−4 Modeling Tools & Definitions, Studies & Solvers, Equation-Based Modeling Version 6.0 2 Replies

Aaron Pim
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I am trying to solve Laplace's equation subject to a non-linear boundary condition. T corresponding solution in the bulk of the domain is what I would expect. However on the boundary I have these strange points of discontituity that I cannot seem to get rid of. Advice on how to remove these would be ideal.

The problem

Let . For a given , I seek which satisfies

on

when

when

when

The issue

I use the standard equation solver and when I compute the solution I get these strange points of discontinuity along the boundary (see the attached picture). I am unsure how to get rid of them. I tried to use the inbuilt mesh adjustment, yet that simply did not converge.

2 Replies Last Post 22 avr. 2022, 06:50 UTC−4
Henrik Sönnerlind COMSOL Employee

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Posted: 2 years ago 21 avr. 2022, 09:20 UTC−4

Since the strength of the nonlinearity in your problem is directly proportional to the parameter W, I think it makes sense to solve for a lower value of W and see if the solution converges. If that is the case, you can use such a solution as initial value for a new solution with higher value of W etc.

This procedure can be automatized by using an auxiliary sweep, see the attached screenshot.

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Henrik Sönnerlind
COMSOL
Since the strength of the nonlinearity in your problem is directly proportional to the parameter *W*, I think it makes sense to solve for a lower value of *W* and see if the solution converges. If that is the case, you can use such a solution as initial value for a new solution with higher value of *W* etc. This procedure can be automatized by using an auxiliary sweep, see the attached screenshot.

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Aaron Pim
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Posted: 2 years ago 22 avr. 2022, 06:50 UTC−4

Since the strength of the nonlinearity in your problem is directly proportional to the parameter W, I think it makes sense to solve for a lower value of W and see if the solution converges. If that is the case, you can use such a solution as initial value for a new solution with higher value of W etc.

This procedure can be automatized by using an auxiliary sweep, see the attached screenshot.

That seems to have worked really well, thank you.

>Since the strength of the nonlinearity in your problem is directly proportional to the parameter *W*, I think it makes sense to solve for a lower value of *W* and see if the solution converges. If that is the case, you can use such a solution as initial value for a new solution with higher value of *W* etc. > >This procedure can be automatized by using an auxiliary sweep, see the attached screenshot. That seems to have worked really well, thank you.

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