[petsc-users] Convergence and improvement of ill conditioned like problem

[Danyang Su]

Hi All,

I have come across an ill conditioned like problem. The matrix in this 
problem is block matrix, in each block, there are some zero entries. The 
preconditioned residual norm drops slowly but the true residual norm 
drops quickly in the first few iterations. So as to improve the 
performance, I would like to stop iteration when the true residual norm 
meet the requirement.

Q1: Do I need to use KSPSetConvergenceTest for this case?

I can use direct solver for this problem and the outer newton iteration 
works fine, usually converged in 10 or less newton iterations. But when 
use PETSc KSP solver, the newton iterations usually need more than 20 
iterations and the timestep cannot increase much due to the large newton 
iteration number.

Q2: Is it possible to increase the precision for KSP solver for this 
problem?

I have read the comments by Jed in the website 
http://scicomp.stackexchange.com/questions/513/why-is-my-iterative-linear-solver-not-converging. 
I don't know what can KSPSetNullSpace or MatNullSpaceRemove do and 
haven't tried to use it.

Thanks and regards,

Danyang