[petsc-users] ASM Interface (Additive Schwarz Method)

[Jed Brown]

Mark Adams via petsc-users <petsc-users at mcs.anl.gov> writes:

>> This works perfectly as long as I use PC_ASM_BASIC for the PCASMType. If I
>> switch to PC_ASM_RESTRICT, my GMRES algorithm, does not converge anymore.
>> Why is this?
>>
>
> PC_ASM_RESTRICT specifies the use of a different algorithm. It is a cheaper
> algorithm in terms of work (communication) but is weaker mathematically, in
> parallel.

Notwithstanding whatever Mark means by "weaker mathematically", RESTRICT
often/usually is observed to perform as well or better than BASIC when
using a Krylov method that can tolerate a nonsymmetric preconditioner.
Notably, BASIC does not require identifying the "local" part, just the
full (overlapping) subdomains.  So I think you might have a problem in
the definition of is_local.

If you're using one subdomain per process, the local part is typically
just the owned dofs, e.g., as returned by VecGetOwnershipRange or
MatGetOwnershipIS.  I'm having some trouble understanding your diagram
-- ownership of any rank is contiguous, but it looks like you're doing
something else.  Is that intentional?