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.
Checksum
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Recommended Citation
Rigley, Michael, "Physically Based Preconditioning Techniques Applied to the First Order Particle Transport and to Fluid Transport in Porous Media" (2014). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 2160.
https://digitalcommons.usu.edu/etd/2160
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