[petsc-users] ASM for High-Order FEM

[Travis Austin]

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?  

                                        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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110314/39f2441c/attachment.htm>