[petsc-users] Finally, pseudo time method eliminated singular problem

[Matthew Knepley]

2011/4/9 Gong Ding <gdiso at ustc.edu>

> Hi all,
> In the past several weeks, I am dealing with the nearly singular problem.
> The structure has a metal connected two semiconductor devices. when two
> devices are both shutdown with high resistance,
> the metal connector is floating.
> This singular problem finally be shifted to well conditioned by simple
> pseudo time method --
> just introducing pseudo time to the nearly floating domain (as a capacity
> to ground).
> Now iterative method works well.
>
> Here, I must give thanks to Jose Roman, the slepc package gives quick
> evaluation
> of eigen value of the jacobian matrix. I can easliy target where the
> singular arising.
> And it helps to determine the pseudo time step.
>
> And to Matt and Jed, thank you for the idea of null sapce.
> Pseudo time method is not as efficient as null space dropping.
> I guess the algorithm to nonlinear singular problem should
> 1) drop null space within krylov iteration
>

Yes, you can do this using KSPSetNullSpace()


http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/KSP/KSPSetNullSpace.html


> 2) SNES should know the null vector and do a search in the direction of
> null vector to find the root.
>

I am not sure why this is necessary. Since KSP will project out the
nullspace in each Newton solve,
it should not appear in the update. Unless it is a component of the solution
(which would be strange since
the Jacobian gives no information about it), in which case you can add that
as the initial guess.

   Matt


> Do you think I am in the right way?
>
> Gong Ding
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-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
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