Jie Liu

Graduation Semester and Year

2006

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Guojun Liao

Abstract

New developments of deformation method for grid generation are presented in this work. Theorems for three different cases and different methods for implementing deformation method are presented. One of the new developments is a 3D multi-block moving grid method. In this version, a Poisson equation is solved by finite difference method to get the vector field for moving grid. Special treatment applies to the common boundary of different blocks. Another new development is a numerical method for reconstructing a given differentiable transformations by solving a system of div-curl equation directly formed from each point of the graph. The determinacy and ellipticity of the system of the 3D div-curl equation are analyzed in detail. And the least-square finite element method is used to solve the div-curl equation in order to reconstruct a differentiable mapping. Both 2D and 3D implementations are presented in this work.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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