[petsc-users] Problems with the null-space removal

[Matthew Knepley]

On Mon, May 5, 2025 at 3:52 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es> wrote:

> Dear all,
>
> I am working on the resolution of a non-linear problem via SNES with a
> large null-space (at least 70% of the equations are trivial). In a nutshell
> I have a mesh with active and non-active nodes, and the non-active nodes
> introduces the null-space.
>
> So far I've dealing with it using NGMRES but I want to use a scheme based
> on NR. However, despite removing the null-space using PETSc's in-build
> functions the linear solver (KSP+PC) diverges at the first iteration.
> However, If I remove the non-active nodes and use the same solver
> (SNES+KSP+PC), which failed before, now I can solve the non-linear system.
>
> Any clue? I’m missing something?
>

The most likely thing is that the nullspace is slightly wrong, or the
convergence test is not accounting for the nullspace somehow.

However, since so many equations are inactive, I would consider projecting
the problem. I might either

1) Select a subset of the mesh to phrase the problem on. In you use DMPlex,
you could use DMPlexFilter().

2) Use a constraint to get a subsystem for Newton using SNESVI. The
SNESVIRS will project the linear system onto a subspace without the
constraints.

   Thanks,

      Matt


> Thanks,
> Miguel



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