Date of Award
August 2016
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Bruce Wade
Committee Members
Dexuan Xie, Tzu-chu Lin, Lei Wang, Peter Hinow
Keywords
Advection Diffusion Reaction Equations, Dimensional Splitting, Exponential Time Differencing
Abstract
A second order Exponential Time Differencing (ETD) scheme for advection-diffusion reaction systems is developed by using a real distinct poles rational function for approximating the underlying matrix exponential. The scheme is proved to be second order convergent. It is demonstrated to be robust for reaction-diffusion systems with non-smooth initial and boundary conditions, sharp solution gradients, and stiff reaction terms. In order to apply the scheme efficiently to higher dimensional problems, a dimensional splitting technique is also developed. This technique can be applied to all ETD schemes and has been found, in the test problems considered, to reduce computational time by up to 80%.
Recommended Citation
Asante-Asamani, Emmanuel Owusu, "An Exponential Time Differencing Scheme with a Real Distinct Poles Rational Function for Advection-Diffusion Reaction Equations" (2016). Theses and Dissertations. 1252.
https://dc.uwm.edu/etd/1252