[petsc-users] Possible DIVERGED_BREAKDOWN reasons and ways to avoid it

[Ali Berk Kahraman]

Dear All,

I am trying to solve a Poisson-Neumann Problem which does not have a 
solution by itself on an irregular domain with finite differences. This 
problem arises in the correction step of a veloicty 
prediction-correction scheme of Navier-Stokes equation. It requires a 
least squares solution, or a modified solution.

I have asked here before, and with substantial help of Dr. Smith I have 
learned about KSPLSQR. It helped for some small-sized problems, but when 
the problem size gets larger, for some reason it cannot converge to a 
good spot.

I have been trying another method in the literature, with little success 
again. The literature suggests that an augmented linear system which has 
a solution should be solved. If the poisson neumann problem is Ax=b, the 
augmented system is as follows,

|A   1|    |b|
|       | = |  |
|1   0|     |a|

where a is an arbitrary number.  This system has a solution since vector 
1 is the right null space of A (or so I have read). However, when I try 
to solve thiss system for larger system sizes than appr. 8000, it causes 
a diverged breakdown error for BiCGS with jacobi preconditioning. Is 
there any way to avoid a breakdown in BiCGS? Why might it happen?

Best Regards,

Ali Berk Kahraman
Bogazici Uni., Istanbul,Turkey