声明
Contents
Abstract
摘要
Introduction
Chapter 1 Preliminaries
1．1 Introduction
1．2 Spheroidal coordinates
1．2．1 Prolate spheroid coordinates
1．2．2 Ellipsoidal coordinates
1．3 Special functions
1．3．1 Legendre functions
1．3．2 Associated Legendre functions
1．3．3 Spherical harmonic functions
1．3．4 Lamé functions
1．3．5 Ellipsoidal harmonic functions
1．4 Sobolev spaces
1．4．1 Some important Sobolev spaces
1．4．2 Some important theorems
Chapter 2 A D-N algorithm for exterior 3-D Poisson problem with prolate spheroid boundary
2．1 Introduction
2．2 A D-N alternating algorithm based on NBR
2．3 Analysis of convergence
2．4 Error estimates
2．5 Numerical experiments
2．6 Conclusions
Chapter 3 A D-N algorithm for exterior 3-D Poisson problem with ellipsoidal boundary
3．1 Introduction
3．2 A D-N alternating algorithm based on NBR
3．3 Analysis of convergence
3．4 Error estimates
3．5 Numerical experiments
3．6 Conclusions
Chapter 4 A Schwarz algorithm for exterior 3-D harmonic problem with prolate spheroid boundary
4．1 Introduction
4．2 A Schwarz alternating algorithm based on NBR
4．3 Analysis of convergence
4．4 Analysis of convergence rate
4．5 Error estimates
4．6 Numerical experiments
4．7 Conclusions
Chapter 5 Summary and prospect
Bibliography
Publications and finished papers
致谢
