[petsc-users] floating region help

[Barry Smith]

On Sep 20, 2011, at 4:17 AM, Gong Ding wrote:

>  
> 2011/9/20 Gong Ding <gdiso at ustc.edu>
> Since the conductance of left part and right part is low, the middle region is floating.
> 
> Not really floating, just sensitive to parameters. It has a unique value, of physical interest, but if you change the conductivity or thickness of the thin region on either side, then it's value changes significantly. This is an ill-conditioned problem, but it's ill-conditioned for physically meaningful reasons. It's not singular and the smallest singular value has great significance, so a null space method is not appropriate. You could reformulate for a slightly different problem which would have a constant null space, but not for this problem.
> 
> Thanks. Any recommends for solving this type of problems? 
> It's our bottleneck now.
> Direct solver works, but not efficient for large 3D problem.

   Are you running SuperLU_Dist or MUMPS in parallel? How large a problem do you want to do? I think those direct solvers should be fine in the few million unknown range (slow yes, but likely the best you will find).

    Barry

> Krylov space based solver seems not rubost enough. 
> A more exact ILU preconditioner may help? 
> 
>