[petsc-users] ASM for High-Order FEM

[Barry Smith]

On Mar 14, 2011, at 3:17 PM, Travis Austin 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?  

   Yes

> 
>                                         P0
>  
>               / ---------------------------------------\    
> 
>               |                 |                 |                 |                  |                 |                 |                 |
>               |---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---|
>               |                 |                 |                 |                  |                 |                 |                 |
> 
>                                                                          \--------------------------------------------------/
>                                
>           
>                                                                                             P1

    The IS used to defined subdomains is done with global indices so on which process  a degree of freedom lives in the matrix doesn't matter in regards to making subdomains for ASM.

    Barry
   
> 
> 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
>