[petsc-users] the convergence of petsc iterative solver

[Hong Zhang]

Debao :
>
> I'm using PETSC iterative solver(PCILU & KSPGMRES) in OOQP, but when the to be solved matrix is ill-posed, say condition number ~ 1e+4, then, KSPGMRES will exceed its maximal iteration number(default as 10000), while when I checked the same data with cholmod direct solver, it can solve the problem and return an answer correctly.
>
> Does it mean the iterative solver(like GMRES) relies more on the well-pose matrix than cholmod direct solver?
Yes. Iterative solvers takes advantage of sparse matrix storage and
are able to solve very large systems.
However, its efficiency depends on the well-pose/conditioning of matrices.
Direct solver is robust, but requires matrix factorization - require
large memory storage and operations.
It is used for the cases that iterative solver fails.

> How can I improve the case to avoid KSPGMRES fail case?
Yes, you need use preconditioner. Run your code with '-help' to check
available pc.
Experimenting various preconditoners. Your condition number 1.e+4 is
not bad. Preconditioning should work.

Hong
>
> Your answer is appreciated.
>
> Thanks,
> Debao
>
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