Date of Award

Summer 8-2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Committee Chair

Dr. James V. Lambers

Committee Chair Department

Mathematics

Committee Member 2

Dr. Ching-Shyang Chen

Committee Member 2 Department

Mathematics

Committee Member 3

Dr. Haiyan Tian

Committee Member 3 Department

Mathematics

Committee Member 4

Dr. Huiqing Zhu

Committee Member 4 Department

Mathematics

Abstract

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits of KSS methods observed in linear PDE to be extended to the nonlinear case. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become dramatically reduced, thus improving efficiency and scalability.

Masters thesis: http://aquila.usm.edu/masters_theses/208/

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