We present a fast direct algorithm for the solution of linear systems
arising from elliptic equations. We extend the work of Xia et al.
(2009) on combining the multifrontal method with hierarchical matrices.
We offer a more geometric interpretation of that approach, extend it in
two dimensions to the unstructured mesh case, and detail an adaptive
decomposition procedure for selectively refined meshes. Linear time
complexity is shown for a quasi-uniform grid and demonstrated via
numerical results for the adaptive algorithm. We also provide an
extension to three dimensions with proven linear complexity but a
more practical variant with slightly worse scaling is also described. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2010-08-1847 |
| Date | 14 December 2010 |
| Creators | Schmitz, Phillip Gordon |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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