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

[Gong Ding]

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 
2) SNES should know the null vector and do a search in the direction of null vector to find the root.
Do you think I am in the right way?

Gong Ding