Date of Award:

5-2014

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Joseph V. Koebbe

Committee

Joseph V. Koebbe

Committee

Jim Powell

Committee

Brynja Kohler

Committee

Nghiem Nguyen

Committee

Eric Held

Abstract

Solving linear systems is at the heart of many scientific applications from the PreAlgebra's student solving for x and y for basic geometry problems to the computational scientist solving billions of equations with billions of variables for weather forecasting, modeling fusion reactions, or web search algorithms. In this study we look at improving the efficiency of solving large linear systems that result from two applications. The first includes linear systems that result from solving differential equations for the movement of atomic particles in particle emitting, void, and absorbing regions. The second includes solving linear systems that result from solving differential equations for the flux of fluid in porous media. In both cases we employ methods of improving the linear solvers, called preconditioning, to improve the efficiency of the linear solvers. In both cases the preconditioning significantly improves the efficiency of the linear solver. These methods are also tested in parallel on graphic processing units using CUDA.

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