nonlinear magnetostatic problem 2D /3D

[Che Gl]

Dear all,

i'm solving magnetostatic problem and have implemented the 2D-magnetostatic problem as following equation:

So the general formulation curl(curl A) can be derived for 2D problem similar Poisson equation (see above). Using the weak formulation i can solve the 2D-problem like step 3 : A(i,j) = integral ( grad(u)*grad(v) ). Until now i have tested some small problem with FE_Q<> (2) element, the result look good and similar to the result computed by Ansys-Maxwell. So i just want to make sure: if i'm missing something here?

+Now i'm trying to implement 2D-nonlinear Problem since (mue) ist dependent on B-H-Curve and nonlinear. I would implement this in 3 steps:
       - step 1: assumption any value of mue, and solved the equation, hence B can be calculated
       - step 2: compare calculated B with B from B-H-Curve corresponding to assumed mue in step 1. If the deviation is small enough, the solution is converged and break. This step has to  be carried out for every cell, which has nonlinear property (e.g. ferromagnetic material)
      - step 3:calculate mue corresponding to B calculated in step 1 and set new mue to the equation and go to step 1

Steps 2 and 3 have to  be carried out for every cell, which has nonlinear property (e.g. ferromagnetic material), so here the old (mue) and new (mue) of those cells need to be saved somehow. What would you suggest as effective way to do that?

Any suggestion would be appreciated.

Best

To

[Guido Kanschat]

Did you consider a Newton iteration?
Guido

[Wolfgang Bangerth]

On 07/25/2014 12:15 AM, Guido Kanschat wrote:
> Did you consider a Newton iteration?

Like the one in step-15, for example.
W.


--
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Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[Bastian]

Dear Che,

I am also trying to solve this problem. Right now I'm not sure how to calculate step-2 and step-3, could you explain me how you get the necessary B-H pair out of your solution to compare it with the magnetic curve? Could you also tell me how you calculate the new mu for the next iteration step?

Thanks a lot
Best regards

Bastian