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

[Smith, Barry F.]

What are the sizes of the entries of A? Instead of a 1 you could try to use a number proportional to the size of the entries in A.

Also what more specifically goes wrong with KSPLSQR for larger problems? Does the convergence slow down too much? What preconditioner did you try?

  Barry


> On Apr 23, 2018, at 2:39 AM, Ali Berk Kahraman <aliberkkahraman at yahoo.com> wrote:
> 
> 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
>