Thesis (M.S.)--Brigham Young University. Dept. of Physics and Astronomy, 2005. / Includes bibliographical references (p. 93-96).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Thomas F. Edgar. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1964. / Typescript. Abstracted in Dissertation abstracts v. 25 (1964) no. 6, p. 3599. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin, 1966. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaves 75-78). Also available on the Internet.

John L. Wyatt, Jr. / Bibliography: leaf 12. / "September, 1983." / National Science Foundation Grant No. ECS 8006878 Air Force Office of Sponsored Research Contract #F29620-81-C-0054 Defense Advanced Research Projects Agency contract #N00014-80-C-0622

In this thesis, we study problems with heterogeneities using the zeroth order optimized Schwarz preconditioning. There are three main parts in this thesis. In the first part, we propose an Optimized Restricted Additive Schwarz Preconditioned Exact Newton approach (ORASPEN) for nonlinear diffusion problems, where Robin transmission conditions are used to communicate subdomain errors. We find out that for the problems with large heterogeneities, the Robin parameter has a significant impact to the convergence behavior when subdomain boundaries cut through the discontinuities. Therefore, we perform an algebraic analysis for a linear diffusion model problem with piecewise constant diffusion coefficients in the second main part. We carefully discuss two possible choices of Robin parameters on the artificial interfaces and derive asymptotic expressions of both the optimal Robin parameter and the convergence rate for each choice at the discrete level. Finally, in the third main part, we study the time-dependent nonequilibrium Richards equation, which can be used to model preferential flow in physics. We semi-discretize the problem in time, and then apply ORASPEN for the resulting elliptic problems with the Robin parameter studied in the second part.

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