Natural Borndary Integral Method and Its Applications自然边界元方法的数学理论（英文版）

Boundary element methods are very important for solving boundary value problems in PDEs.Many boundary value problems of partial diffferential equations can be reduced into boundary integral equations by the natural boundary reduction .In this book the natural boundary integral method,suggested and developed by Feng and Yu,is introduced systematically.It is quite different from popuar boundary element methods and has many distinctive advantages The variational principle is conserved after the natural boundary reduction,and some useful properties ar also preserved faithfully.Moreover,it can be applied directlyand naturally in the coupling method and the domain decomposition method of finite and boundary elements Most of the material in this book has only appeared in the author s previous papers.Compared with its Chinese edition (SciencePress,Bejing 1993),many new research results such as the domain decomposition methods based on the natural boundary reduction are added.
This book is intended for graduate students and researcers of compuational and applied mathematics,scientific computing,comutational mechanics and physics,It is also of interest to university lecturers,scientists and engineers who are interested in the application of the boundary element method.

Preface
Chapter I.General Principle of the Natural Boundary Integral Method
1.1 Introduction
1.2 Boundary Reductions and Boundary Element Methods
1.3 Basic Idea of the Natural Boundary Reduction
1.4 Nurnerical Computation of Hypersingular Integrals
1.5 Convergence and Error Estimates for the Natural Boundary
1.6 On Computation of Poisson Integral Formulas
ChapterII.Boundary Value Problem for the Harmonic Equation
2.1 Introduction
2.2 Representation of a Solution by Complex Variable Functions
2.3 Principle of the Natural Boundary Reduction
2.4 Natural Integral Equations and Poisson Integral Formulas for Some Typical Domains
2.5 Natural Boundary Reduction for General Simply Connected Domains
2.6 Natural Integral Operators and Their Inverse Operators
2.7 Direct Study of Natural Integral Equations
2.8 Numerical Solution of Natural Integral Equations
2.9 Numerical Solution of the Natural Integral Equation over a Sector with Crack or Concave Angle
ChapterIII.Boundary Value Problem of the Biharmonic Equation
3.1 Introduction
3.2 Representation of a Solution by Complex Variable Functions
3.3 Principle of the Natural Boundary Reduction
3.4 Natural Integral Equations and Poisson Integral Formulas for Some Typical Domains
3.5 Natural Integral Operatiors and Their Inverse Operators
3.6 Direct Study of Natural Integral Equations
3.7 Numerical Solution of Natural Integral Equations
3.8 Boundary Value Problems of Multi-Harmonic Equatioons
ChapterIV.Plane Elasticity Problem
4.1 Introduction
……
ChapterV.Stokes Problem
ChapterVI.The Coupling of Natural Boundary Elements and Finite Elements
ChapterVII.Domain Decomposition Methods Based On Natural Boundary Reduction
References
Index

In the last twenty years the boundary integral methods, or the boundary element methods, as one kind of important numerical ways for solving partial differential equations, have been rapidly developed and widely applied in numerous fields of scientific and engineering computation. There are already a large number of papers on these methods and their applications. In this book the natural boundary integral method, or the natural boundary element method, is introduced. It has many distinctive advantages and is quite different from the popular ..