<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Hi,</div><div><br></div><div>Often for high-order finite elements the subdomains in an additive Schwarz method (using PCASM) are defined according to the elements</div><div>since they can contain a large number of degrees of freedom. This is an approach used extensively by Paul Fischer of Argonne National</div><div>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. </div><div><br></div><div>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</div><div>and each subdomain will fully be on the processor. However, processor P1 with 4 ASM subdomains will have one subdomain that is partly on</div><div>processor P0. </div><div><br></div><div>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 </div><div>that the ASM preconditioning part for this element is performed on processor P1?</div><div><br></div><div>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</div><div>that? </div><div><br></div><div> P0</div><div> </div><div> / ---------------------------------------\ </div><div><br></div><div> | | | | | | | |</div><div> |---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---X---x---x---|</div><div> | | | | | | | |</div><div><br></div><div> \--------------------------------------------------/</div><div> </div><div> P1</div><div><br></div><div>Thanks,</div><div>Travis Austin</div><div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^</div><div>Travis Austin, Ph.D.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Tech-X Corporation</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">5621 Arapahoe Ave, Suite A</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Boulder, CO 80303</div><div><a href="mailto:austin@txcorp.com">austin@txcorp.com</a></div><div>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^</div><br class="Apple-interchange-newline"></span></span>
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<br><div><div>On Oct 6, 2010, at 11:36 AM, Jed Brown wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><a href="http://59A2.org/na/Brown-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf">http://59A2.org/na/Brown-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf</a><br></div></blockquote></div><br></div></body></html>