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
