Date of Award

Spring 5-8-2021

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

School

Mathematics and Natural Sciences

Committee Chair

Dr. James Lambers

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

Dr. C.S. Chen

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Dr. Haiyan Tian

Committee Member 3 School

Mathematics and Natural Sciences

Committee Member 4

Dr. Huiqing Zhu

Committee Member 4 School

Mathematics and Natural Sciences

Abstract

Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.

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