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.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
National Science Foundation
Linear systems--Mathematical models, Decomposition (Mathematics), Iterative methods (Mathematics), Random matrices.
Quintana, Ambrose. "Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem." (2013). https://digitalrepository.unm.edu/math_etds/43