## Charge relaxation problem

Numerical methods and mathematical models of Elmer
PauloFonte
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### Charge relaxation problem

Dear Elmer experts

I would like to solve a charge relaxation problem. That is

The related Elmer solver seems to be the StatCurrentSolver

Searched the forum and the most relevant discussion I could found was
http://elmerfem.org/forum/viewtopic.php ... =10#p16162
It seems that the time derivative is not included in StatCurrentSolver and there is a suggestion of a modification, but I have no idea how to use it (and don't want to become an expert myself...).

I also dreamed that the rhs term could be calculated in a parallel solver, but couldn't find a way to calculate the time derivative. Also, have no clue about the chances of convergence of such contraption.

Any suggestions welcome. Thanks in advance

raback
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### Re: Charge relaxation problem

Hi

As written before this would be just a few lines of code. We may be soon writing an optimized version of the StatCurrentSolver and could include that term in the process.

-Peter

raback
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### Re: Charge relaxation problem

Hi All,

I'm in the process of writing a new optimized version of StatCurrentSolver. At the same time I could augment it to be more complete. Hence I thought about adding this relaxation term. Here \sigma is electric conductivity and \eps is permittivity and the source term is given.
NewStatCurrent.PNG (5.93 KiB) Viewed 54 times
Would this solve the charge relaxation problem. Any other ideas while we are at it?

-Peter

PauloFonte
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Joined: 24 Aug 2018, 23:47
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### Re: Charge relaxation problem

For me this will be fine.
Don't know how this fits the general philosophy of Elmer, but in some cases the frequency domain version (d/dt -> Iw) may be more useful (and, I guess, simpler to calculate).