[Getdp] Magnetodynamic 3D - Electromagnetic circuit element

[Christophe Geuzaine]

Florin CIUPRINA wrote:
> Hello Christophe,
> 
> Algorithm=11 and full matrix and this time I obtained
> the solution which seems to be OK, for coarse mesh and low frequency.
> However, for a dense mesh, there are problems with the memory (obviously
> due to the full storage), and I cannot solve the problem at all.

OK, fair enough :-)

> 
> 3) other trials with iterative algorithms
> 
> For a relatively dense mesh (which I cannot solve with LU due to memory
> limitation),
> I have tried all the other available iterative algoritms. The only
> one that converged was algorithm=10, but the convergence was extremely slow.
> I improved its convergence by using scaling=4.
> 
>             Matrix_Format            1
>           Matrix_Printing            0
>            Matrix_Storage            0
>                   Scaling            4
>     Renumbering_Technique            1
>            Preconditioner            2
>   Preconditioner_Position            2
>                   Nb_Fill           20
>     Permutation_Tolerance         0.05
>        Dropping_Tolerance            0
>     Diagonal_Compensation            0
>                Re_Use_ILU            0
>                 Algorithm           10
>               Krylov_Size           40
>           IC_Acceleration            1
>                 Re_Use_LU            0
>     Iterative_Improvement            0
>               Nb_Iter_Max         5000
>             Stopping_Test        1e-10
> 
> In this case, for 100Hz it takes 154 iterations, but, if I want to increase
> the frequency (e.g. 10 KHz) it takes 817 iterations.

You should try to increase Nb_Fill: this will make the incomplete LU
decomposition (used as a preconditioner) be closer and closer to the
complete LU. This should improve convergence a lot.

> 
> So, I wonder if:
> - Can I use a direct solver for sparse matrices?

There is none implemented in getdp at the moment. If you have one you
would like to contribute, that would be great.

> - Is there any possibility to improve the convergence of the iterative
> method that
> worked for this problem (algorithm=10) so that I would be able to work
> with high
> frequencies (up to GHz maybe...)?
> 
> I also noticed that, when using several frequencies in the same
> resolution, the
> number of iterations is greater than the maximum number of iterations of the
> independent resolutions for each frequency. I assume that this is due to
> different
> initializations. So, what do you reccommend? Is it better (faster) to
> solve for
> each frequency separately?

I never did that kind of thing.

Johan, an opinion?

Christophe

-- 
Christophe Geuzaine

Tel: (626) 395-4552    http://www.geuz.org
Fax: (626) 578-0124    mailto:geuzaine at acm.caltech.edu