Publication Date

9-3-2013

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.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Advisor

Lau, Stephen

First Committee Member (Chair)

Appelo, Daniel

Second Committee Member

Coutsias, Evangelos

Project Sponsors

National Science Foundation

Language

English

Keywords

Linear systems--Mathematical models, Decomposition (Mathematics), Iterative methods (Mathematics), Random matrices.

Document Type

Thesis

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