Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem
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| Title: | Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem |
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| Authors: | Quintana, Ambrose |
| Committee Members: | Lau, Stephen; Stephen Lau; Daniel Appelö; Evangelos A. Coutsias |
| Summary: | When trying to solve elliptical problems such as the Poisson problem on complicated domains, one procedure is to split the domain into a union of simpler subdomains. When solving these problems iteratively, it becomes important to be able to precondition the coupling between the subdomains. Using the Poisson problem as a test case, this thesis explores one idea for preconditioning this coupling, an idea based on interpolative decomposition and random matrices. We find that this procedure does create an efficient preconditioner to get at the coupling between subdomains. |
| URL: | https://digitalrepository.unm.edu/math_etds/43 |
| Database: | OpenDissertations |
| Abstract: | When trying to solve elliptical problems such as the Poisson problem on complicated domains, one procedure is to split the domain into a union of simpler subdomains. When solving these problems iteratively, it becomes important to be able to precondition the coupling between the subdomains. Using the Poisson problem as a test case, this thesis explores one idea for preconditioning this coupling, an idea based on interpolative decomposition and random matrices. We find that this procedure does create an efficient preconditioner to get at the coupling between subdomains. |
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