which kind of preconditioner may i use to solve thid kind of matrix A in ifpack

[ztdepztdep]

My matrix A has the following structure. I want to find an efficient preconditioner for it. I am using ifpack ilu , but i found it is too slow.
could you please give me some advices.

[cgcgcg]

The graph of the matrix is not enough information to decide what kind of preconditioner to use. What kind of problem is this? It looks like the discretization of a PDE, so that's good. Symmetric positive definite?

[ztdepztdep]

The graph of the matrix is not enough information to decide what kind of preconditioner to use. What kind of problem is this? It looks like the discretization of a PDE, so that's good. Symmetric positive definite?

It is generated from spectral element method, it is not a sysmmetric.

[cgcgcg]

Alright. How about its nullspace? And what kind of physics?

[ztdepztdep]

Alright. How about its nullspace? And what kind of physics?

it is for incompressible flow solution. and it is a Helmholtz problem.

[cgcgcg]

double-checking: By Helmholtz problem you mean: $$-\Delta u - k^2 u = f$$?

[ztdepztdep]

yes, it is Helmholtz problem .

[cgcgcg]

Ok. These guys are difficult to precondition, as they are indefinite. I would suggest you check the literature for approaches. Both multigrid and domain decomposition can be used (and we have both in Trilinos). I believe we had some multigrid example at some point, but I'll need to find it.

[ztdepztdep]

yes, it is difficult. I use Amesos to precondition, but the speed is a problem.

[cgcgcg]

Have a look at packages/muelu/test/helmholtz. That's mutltigrid with a shifted Laplacian approach.