[petsc-users] Tuning the parallel performance of a 3D FEM CFD code

[Henning Sauerland]

On 17.05.2011, at 04:54, Matthew Knepley wrote:

> Anecdotally, I hear that XFEM can produce ill-conditioned matrices, where the conditioning arises from geometric factors. I don't think you can
> a priori rule out differences in conditioning as the process count increases which come from changing geometry of the interface.
> 
>    Matt

Anyway, the ill-conditoning should not be a problem here. Luckily, a diagonal scaling does a great job to improve the condition number. And as you said while the ill-conditioning usually arises from geometric factors I can identify the XFEM degrees of freedom which account for the ill-conditioning. Blocking such DOFs carefully also improves the condition number, which I usually not do as the diagonal scaling already leads to a condition number in the order of the standard FEM matrix.


Henning