Discontiuities in material properties

[bjorne]

Hi,

I'm trying to solve an elliptic problem with discontinuous material properties. The values can vary by ~ 10^5, so the system is ill-conditioned. Currently I'm using various other FE solvers that don't deal well with this conditioning.

The first picture in the deal.II website (http://www.dealii.org/) is the included image. It appears also in the gallery (https://github.com/dealii/dealii/wiki/Gallery). My solutions looks similar to this. I was hoping somebody in the community could point me to any examples that solve similar problems, or the code that produced this.

Thanks,

B.

[Jean-Paul Pelteret]

Dear Bjorne,

There are quite a number of examples of Laplace and Poisson problems in deal.II's tutorials. The picture that you've shown could well be produced by a derivative of step-6, but I'm not entirely sure. 

As for solving such an ill-conditioned system, deal.II offers a number of options for direct solvers (e.g. UMFPack, MUMPS and other options through Trilinos's direct solver interface) and high quality preconditioners (for example, Trilinos's AMG and AMGMueLu, and PETSc's BoomerAMG and Parasails) which might be able to work around this problem.

I hope this helps!

Regards,

Jean-Paul

[Wolfgang Bangerth]

If I recall correctly, the code that produced this file used the immersed
boundary method. I don't remember who wrote the code, but remember that it is
not part of either the tutorial or the code gallery -- sorry.

Best
W.

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