A unified approach to boundary element method, numerical conformal mapping and improperly posed BVP

Li, Bao Cheng (1989) A unified approach to boundary element method, numerical conformal mapping and improperly posed BVP. University of Southampton, Doctoral Thesis.

Abstract

The thesis is organized into four parts and each of them consists of two chapters. While the first three parts are largely independent of each other, the fourth part can be viewed as a thread which connects them loosely together. Part I is about the Boundary Element Method (BEM). Chapter 1 presents a brief historical and literatural survey. The author's own judgement and understanding about the technique is also given there. In Chapter 2, the boundary integral equations for the linear elasticity problem are formulated in terms of a general curvilinear coordinate system and the numerical method to solve them is discussed. The advantage and efficiency are demonstrated through a few examples. Part II is about the Numerical Conformal Mapping (NCM). Chapter 3 is a review of the subject. The material in Chapter 4 is a theoretical and numerical study of a new algorithm for NCM. Significant advantage is shown over the most efficient previous algorithms known to the author. It should be considered as a major part of the present work. Part III is about the improperly posed Boundary Value Problem (BVP). Chapter 5 presents the investigation on the problem to construct an analytic function which satisfies the prescribed value on a part of the boundary. In Chapter 6, the classical Cauchy problem for the Palpace equation is studied. Part IV is about the application of the various results obtained in the first three parts. Chapter 7 elaborates on how to combine BEM, NCM and the Fast Fourier Transform (FFT) to solve practical problems. Chapter 8 explores the possibility of solving improperly posed BVP's with BEM.

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