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 staentz_b February 13, 2013 19:08

GMRES-solver does not converge correctly

Hi there,

my question is quite specific, but i hope someone can help me out.
I have serious trouble with my GMRES-solver.
This solver has to work on a poisson equation, which arises from a finite-volume discretization. The matrix of the linear system is symmetric and positiv definite.

The solver does minimize the residuum, the solution does fullfill the linear system with a certain error, which is extremely small, the residuum has values to 10⁻15 or so... But it is not the correct solution (i tested it with an alaytical solution, a Jacobi-solver and a BiCGSTAB-solver do work on that problem).
Plus the solution changes when changing the starting vector, the solution is always "near" to the starting vector.
The algorithm definetly works somehow, i calculated the "real" residuum at each iterationstep and it is aquivalent with the residuum, which is calculated by the GMRES-algorithm.

How can that be?
Is there any solution?
Ever heared of such a problem?

Thanks a lot for any kind of help

 andy_ February 14, 2013 06:19

> How can that be?

What is the determinant? Conclusion?

> Is there any solution?

Yes but with a qualification. If you plot your different solutions it should be clear what is happening.

> Ever heared of such a problem?

This is just one example of the many practical insights one gets working with CFD. It is of course much easier performing exercises like this within an experienced CFD group rather than posting to online chat groups.

 FMDenaro February 14, 2013 07:55

Quote:
 Originally Posted by staentz_b (Post 407699) Hi there, my question is quite specific, but i hope someone can help me out. I have serious trouble with my GMRES-solver. This solver has to work on a poisson equation, which arises from a finite-volume discretization. The matrix of the linear system is symmetric and positiv definite. The solver does minimize the residuum, the solution does fullfill the linear system with a certain error, which is extremely small, the residuum has values to 10⁻15 or so... But it is not the correct solution (i tested it with an alaytical solution, a Jacobi-solver and a BiCGSTAB-solver do work on that problem). Plus the solution changes when changing the starting vector, the solution is always "near" to the starting vector. The algorithm definetly works somehow, i calculated the "real" residuum at each iterationstep and it is aquivalent with the residuum, which is calculated by the GMRES-algorithm. How can that be? Is there any solution? Ever heared of such a problem? Thanks a lot for any kind of help

but maybe you are solving for the pressure equation? because your solution will be defined apart a constant... and, if you do not fix the value, such value is fixed somehow by the initial vector ...

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