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Magnetic Field Formulation convergence problem
Posted Oct 21, 2017, 10:24 a.m. EDT Electromagnetics, Low-Frequency Electromagnetics, Parameters, Variables, & Functions Version 5.2a 4 Replies
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When using the Magnetic Field Formulation (in 2D, using either Electric or Magnetic Field boundary to induce electric current), having conducting materials together with insulating materials right next to each other, e.g. very high conductivity versus very low conductivity, causes the simulation to fail:
Nonlinear solver did not converge. Maximum number of Newton iterations reached. There was an error message from the linear solver. The relative residual (0.052) is greater than the relative tolerance. Time : 0 Last time step is not converged.
Depending on the scale of the problem, the mesh, etc., the simulation might work but the convergence would be so slow that it is impractical. Alternatively, if I decrease the conductivity of the insulating material from 1e14 to say, 1e4, the simulation works but convergence is very slow; and if I decrease it to 1e-1 the simulation converges fast. I understand that this happens due to a very large difference between the conductivities of two bordering domains, however I do not understand why that is an issue and how I could mitigate this?
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Sounds like ill-conditioning. See my post in this thread, and the blog post I point to there: https://www.comsol.com/forum/thread/141001/current-between-to-dissimilar-contacts?last=2017-04-07T13:54:13Z
Best,
Jeff
-------------------Jeff Hiller
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Sounds like ill-conditioning. See my post in this thread, and the blog post I point to there: https://www.comsol.com/forum/thread/141001/current-between-to-dissimilar-contacts?last=2017-04-07T13:54:13Z
Best,
Jeff
Dear Jeff,
I have visited what you have kindly suggested. Thank you, the information has been helpful.
However, I have been using the Direct solver (left in default settings) for the entire duration of my simulations. In order to illustrate the issue, I would like to bring the attention to COMSOL's superconducting wire example model (https://www.comsol.com/model/superconducting-wire-689). In this model, the resistivity of air is set to 1e2, while the true resistivity of air is more than a dozen of orders of magnitude larger. Setting the value to 1e6 already increases the computational time to impractical lenghts and at 1e13 the simulation produces the error I have quoted in my original post. (NB, the superconductor can be replaced with any material, with the same effect; in fact my investigations suggest that the Magnetic Field Formulation module cannot handle small conductivities, e.g. traditional insulators, regardless of whether there are any domains with large conductivities or not). Hence, my question is, why does that happen?
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What relationship are you using to simulate the SC?
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What relationship are you using to simulate the SC?
It is the E-J power law. However, my point is that the MFH module (as well as it's general form PDE equivalent) just cannot handle very high resistivities; does not have anything to do with superconductivity as I have tested it on several different cases.