[petsc-users] ASM for High-Order FEM

[Matthew Knepley]

On Mon, Mar 14, 2011 at 3:17 PM, Travis Austin <austin at txcorp.com> wrote:

> Hi,
>
> Often for high-order finite elements the subdomains in an additive Schwarz
> method (using PCASM) are defined according to the elements
> since they can contain a large number of degrees of freedom.   This is an
> approach used extensively by Paul Fischer of Argonne National
> Lab in his work.  I'm trying to code this up for an example that I have
> using high-order finite elements but I'm running into a few issues.
>
> Below is a trivial partitioning of a 1D problem that illustrates what I am
> trying to overcome.  Processor P0 is going to have 3 ASM subdomains
> and each subdomain will fully be on the processor.  However, processor P1
> with 4 ASM subdomains will have one subdomain that is partly on
> processor P0.
>
> Is there a way that I can define the local subdomain in the ASM
> preconditioning for processor P1 corresponding to the middle most element
> so
> that the ASM preconditioning part for this element is performed on
> processor P1?
>
> Can I define an index set for processor P1 that includes the degree of
> freedom from the P0/P1 interface and expect that PETSc will handle
> that?
>

You can define the block explicitly for ASM,


http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/PC/PCASMSetLocalSubdomains.html

If you want a single block per process, you can use PETSC_NULL for islocal
and only define the overlapping blocks.

   Matt


>                                         P0
>
>               / ---------------------------------------\
>
>               |                 |                 |                 |
>            |                 |                 |                 |
>
>  |---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---|
>               |                 |                 |                 |
>            |                 |                 |                 |
>
>
> \--------------------------------------------------/
>
>
>                             P1
>
> Thanks,
> Travis Austin
>
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Travis Austin, Ph.D.
> Tech-X Corporation
> 5621 Arapahoe Ave, Suite A
> Boulder, CO 80303
> austin at txcorp.com
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>
> On Oct 6, 2010, at 11:36 AM, Jed Brown wrote:
>
> http://59A2.org/na/Brown-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf
>
>
>


-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
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