[petsc-users] external solvers

[Hong Zhang]

Umut:

>>   General purpose iterative methods are likely to be useless for  
>> this type of problem. How large are the problems you wish to solve?  
>> If less then a few million I'd stick to direct methods like MUMPS.
> Say, 5e4 to 1e5.

Sequential mumps can handle 1e4, depends on sparse
structure of matrix factors. Parallel mumps should be able to process  
1e5.

>
> This is also the conclusion, I got from the tests and extensive  
> reading I have done in the last days. The only hope was to be able  
> to espace from the factorizations by using iterative methods.

Factorization is expensive.  But when your matrix is very ill- 
conditioned,
iterative methods simply do not converge, or "useless for this type of  
problem" as Barry mentioned.
>
> Simple MATLAB type tests were giving pretty promising results for a  
> method that I was trying to develop(with the backslash, expensive  
> however).

"\" in Matlab means director solver. It is expensive, but works.

> And it was an idea whether there can be improvement with iterative  
> methods and preconditioning or not(being aware of the facts about  
> the conditioning issues), Thanks again.

Again, for very ill-conditioned problems, only expensive direct  
solvers work.

Hong