Author

Yaguang Gu

Year of Award

8-14-2019

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics.

Principal Supervisor

Kwok, Felix(Writer on scientific computing)

Keywords

Decomposition method ; Differential equations, Partial ; Nonlinear theories

Language

English

Abstract

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.

Comments

Principal supervisor: Doctor Felix Kwok ; Thesis submitted to the Department of Mathematics ; Thesis (Ph.D.)--Hong Kong Baptist University, 2019.

Bibliography

Includes bibliographical references (pages 106-111).

Available for download on Sunday, October 17, 2021



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