Boundary element methods are very important for solving boundary value problems in PDEs.Many boundary value problems of partial dififerential 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 popular boundary element methods and has many distinctive advantages. The variational principle is conserved after the natural boundary reduction，and some useful properties are also preserved faithfully.Moreover，it can be applied directly and 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 (Science Press，Beijing，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 researchers of computational and applied mathematics，scientific computing，computational 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.
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目录
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 Numerical Computation of Hypersingular Integrals §1.5 Convergence and Error Estimates for the Natural Boundary Element Method §1.6 On Computation of Poisson Integral Formulas Chapter II. 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 Chapter III. 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 Operators 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 Equations Chapter IV. Plane Elasticity Problem §4.1 Introduction §4.2 Representation of a Solution by Complex Variable Functions §4.3 Principle of the Natural Boundary Reduction §4.4 Natural Integral Equations and Poisson Integral Formulas for Some Typical Domains §4.5 Natural Integral Operators and Their Inverse Operators §4.6 Direct Study of Natural Integral Equations §4.7 Numerical Solution of Natural Integral Equations Chapter V. Stokes’Problem §5.1 Introduction §5.2 Representation of a Solution by Complex Variable Functions §5.3 Principle of the Natural Boundary Reduction §5.4 Natural Integral Equations and Poisson Integral Formulas for Some Typical Domains §5.5 Natural Integral Operators and Their Inverse Operators §5.6 Direct Study of Natural Integral Equations §5.7 Numerical Solution of Natural Integral Equations Chapter VI. The Coupling of Natural Boundary Elements and Finite Elements and Finite Elements §6.1 Introduction §6.2 The Coupling for the Harmonic Boundary Value Problem §6.3 The Coupling for the Biharmonic Boundary Value Problem §6.4 The Coupling for the Plane Elasticity Problem §6.5 The Coupling for Stokes’Problem §6.6 Approximation of Boundary Conditions at Infinity Chapter VII. Domain Decomposition Methods Based On Natural Boundary Reduction §7.1 Introduction §7.2 Overlapping DDM based on natural boundary reduction §7.3 Non-overlapping DDM based on natural boundary reduction §7.4 Steklov-Poincar6 operators and their inverse operators References Index
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