[petsc-users] selection of KSP solver

[Umut Tabak]

On 10/22/2013 09:16 PM, Matthew Knepley wrote:
>
> There are no blackbox preconditioners. You must find one that matches 
> your system. The right thing to do
> is to lookup the literature on your problem and see what other people 
> have done. It should be easy to
> replicate in PETSc.
+ The first thing to investigate is the nature of the matrices, is that 
symmetric or not since you use GMRES I assume it is non-symmetric.
+ Second, do you have any ideas on the distribution of the 
eigenvalues(or values of the smallest and largest singular values)
+ If the problem is ill-conditioned(of course this is from personal 
experience), leave iterative methods as soon as possible and stick to 
direct solver unless you can find a well performing preconditioner(which 
is again from experience, very difficult to find).
+ Iterative methods really require one to know what he/she is doing and 
there is a vast literature on that which I find difficult to follow from 
time to time as an engineer.
+ However for well conditioned problems, their performance is amazing, 
although almost all the practical engineering problems are 
ill-conditioned. Moreover the picture gets even worse if two or three 
physics are coupled(the issue of scaling between different field variables).

These are the points from my experience.
Good luck.
Best,
Umut
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