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

[Jed Brown]

On Fri, Feb 3, 2012 at 10:48, Thomas Witkowski <
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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