Abstract

Multigrid algorithms are fast solvers for elliptic partial differential equations. In this thesis, we apply multigrid methods to the model of protein charge-regulation of Hollenbeck, et al. The model of protein charge-regulation requires computing work of charging matrices for two low dielectric spheres in a salt solution, which in turn requires many solutions of the linearized Poisson-Boltzmann equation, or the Debye-Huckel equation. We use multigrid methods to reduce the run time of computing solutions to the Debye-Huckel equation, and compare the results of some simple and more complicated examples. Using the work of Brandt and others, we also construct an interpolation scheme that takes the potentially complicated behavior of the coefficient into account

Library of Congress Subject Headings

Differential equations, Partial--Numerical solutions; Multigrid methods (Numerical analysis)

Publication Date

5-17-2013

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

David S. Ross

Advisor/Committee Member

Chris W. Wahle

Advisor/Committee Member

George M. Thurston

Comments

Physical copy available from RIT's Wallace Library at QA377 .P37 2013

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

Download

Share

COinS