[petsc-users] Richardson with direct solver does not converge in preconditioned residual norm

[Thomas Witkowski]

Yes, you are right, it's an issue with the null space due to boundary 
conditions.

Thomas

Am 03.02.2012 10:57, schrieb Jed Brown:
> On Fri, Feb 3, 2012 at 10:48, Thomas Witkowski 
> <thomas.witkowski at tu-dresden.de 
> <mailto:thomas.witkowski at tu-dresden.de>> wrote:
>
>     Shouldn't be, but it seems that is is close to singular in
>     computer arithmetic. I would like to understand we it's so. The
>     matrix is a 2x2 block matrix with no coupling between the main
>     blocks. I know that this does not make much sense but its for
>     tests only and I would like to add some couplings later. Both
>     blocks are nonsingular and easy solvable with direct solvers. But
>     when adding both together, the condition number rise to something
>     around 10^23. Is it only a question of scaling both matrices to
>     the same order?
>
>
> If it's *very* poorly scaled, then yes, it could be. You can try to 
> correct it with -ksp_diagonal_scale -ksp_diagonal_scale_fix.
>
> It seems more likely to me that it's a null space issue. How many 
> near-zero eigenvalues are there? Perhaps you effectively have an 
> all-Neumann boundary condition (e.g. incompressible flow with all 
> Dirichlet velocity boundary conditions leaves the pressure 
> undetermined up to a constant).

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