[petsc-users] Additive Schwarz sub-domain definition

[Jed Brown]

On Mon, Dec 12, 2011 at 16:51, Sebastian Skatulla <
sebastian.skatulla at googlemail.com> wrote:

> I am struggling to solve an incompressible solid mechanics problem using
> a meshfree code based on Moving Least Square approximations. My
> knowledge of solvers and preconditioners is quite limited. But it seems
> that Additive Schwarz or Gram Schmidt preconditioners together with
> GMRES is a good choice - yet still not good enough in my case. So, I was
> experimenting with exact (LU) solves in each subdomain which does the
> trick but the memory need is significant. Now, my question is what
> purpose serves the function PCASMSetOverlap and could it be used to
> improve this setup in any way? Thanks.
>

Incompressible problems generally lead to indefinite or saddle-point
matrices. These cause two problems for Schwarz preconditioners:

1. Local problems must be stable. A general way to compute stable
subdomains is to take a set of dual variables (e.g. all owned pressure
dofs) and add all primal variables that are connected to those dual
variables (e.g. all displacements that influence those pressures).

2. Local solves are more delicate. Incomplete factorization is unreliable
and very order-dependent. Direct solves work, but are more expensive. You
can use "block preconditioners" as the local solve (this could be as simple
as -sub_pc_type fieldsplit -sub_pc_fieldsplit_type schur
-sub_pc_fieldsplit_detect_saddle_point, but you will likely have to learn a
bit about PCFieldSplit and how to build block preconditioners for your
problem).
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