Hamed,

On Wednesday, October 19, 2016 at 10:25:37 AM UTC-4, Hamed Babaei wrote:It 
seems that I've been choosing wrong solver for my problem. Since my problem 
has some sort of instability in its nature, 
>
> although my system_matrix is symmetric, it is not necessarily positive 
> definite. So I have two questions: 
> First, Is there any function in Dealii or Petsc to compute the determinant 
> of system_matrix. I have used a determinant function for 3*3 matrices and 
> it doesn't work for higher dimensions.
>
Why do you need this?
 

> Second, which solver and preconditioner can be used for symmetric but 
> non-positive definite system_matrix.
>
For the solver, you can use GMRES, BiCGSTAB, or MinRES. For the 
preconditioner, you can use ILU, SSOR, or algebraic multigrid (AMG). 
Sometimes AMG have difficulties with non-s.p.d. matrices though.

Best,

Bruno 

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