Date of Award

Summer 8-2016

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Chair

Dr. James Lambers

Committee Chair Department

Mathematics

Committee Member 2

Dr. Haiyan Tian

Committee Member 2 Department

Mathematics

Committee Member 3

Dr. Huiqing Zhu

Committee Member 3 Department

Mathematics

Abstract

Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.

This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.

ORCID ID

orcid.org/0000-0003-2852-3914

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