The Boundary Element Method - W. S. Hall

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Résumé :
emThe Boundary Element Method/em sets out a simple, efficient and cost effective computational technique which provides numerical solutions -- for objects of any shape -- for a wide range of scientific and engineering problems. br/ emThe Boundary Element Method/em provides a complete approach to formulating boundary integral equations for scientific and engineering problems and solving them numerically using an element approximation. Only a knowledge of elementary calculus is required, since the text begins by relating familiar differential equations to integral equations and then moves on to the simple solution of integral equations. From this starting point, the mathematics of formulation and numerical approximation are developed progressively with every mathematical step being provided. Particular attention is paid to the problem of accurate evaluation of singular integrands and to the use of increasing levels of accuracy provided by constant, linear and quadratic approximations. This enables a full solution to be given for both two dimensional and three dimensional potential problems and finally, for the two dimensional elastostatics problem. br/ emThe Boundary Element Method/em develops the mathematics of the text progressively both within chapters and from chapter to chapter. It is a self-contained, step by step, exposition of the boundary element method, leading to its application to the key problem of elastostatics. br/ emThe Boundary Element Method/em may be used as a standard introductory reference text for the mathematics of this method and is ideal for final year undergraduate study as well as for postgraduates, scientists and engineers new to the subject. Worked examples and exercises are provided throughout the text. br/

Sommaire:
1 Ordinary Integral Equations.- 1.1 Introduction.- 1.2 Ordinary Integral Equations and their Applications.- 1.3 Equivalence between Ordinary Integral and Ordinary Differential Equations.- 1.4 Analytical Methods of Solution.- 1.5 Numerical Methods of Solution.- 1.6 Concluding Remarks.- Exercises.- 2 Two Dimensional Potential Problems.- 2.1 Introduction.- 2.2 Applications of Potential Formulations.- 2.3 Boundary Integral Equation Derivation for Interior Problems.- 2.4 Boundary Integral Equation Derivation for Exterior Problems.- 2.5 Treatment of Boundary Conditions.- 2.6 Concluding Remarks.- Exercises.- 3 Boundary Element Method.- 3.1 Introduction.- 3.2 Numerical Foundation.- 3.3 Linear Approximation.- 3.4 Integration on a Curve.- 3.5 Constant Function Solution for Exterior Heat Conduction.- 3.6 Evaluation of Logarithmic Integral Coefficients.- 3.7 Concluding Remarks.- Exercises.- 4 Linear Isoparametric Solution.- 4.1 Introduction.- 4.2 Linear Function Approximation for Exterior Heat Conduction.- 4.3 Assembly of Left Hand Side Coefficients.- 4.4 Singular and Nonsingular Elements.- 4.5 Evaluation of Right Hand Side Terms.- 4.6 Exterior Neumann Problem for Velocity Potential.- 4.7 Singularity Elimination for the Derivative Kernel.- 4.8 Interior Mixed Boundary Value Problem.- 4.9 Concluding Remarks.- Exercises.- 5 Quadratic Isoparametric Solution.- 5.1 Introduction.- 5.2 Interior Mixed Boundary Value Problems.- 5.3 Treatment of Singular Integrals.- 5.4 Subtraction and Series Expansion Method for Singular Integration.- 5.5 Concluding Remarks.- Exercises.- 6 Three Dimensional Potential Problems.- 6.1 Introduction.- 6.2 Boundary Integral Equation Formulation.- 6.3 Electrostatics Application.- 6.4 Shape functions and boundary elements.- 6.5 The Boundary Element Method.- 6.6 Surface Jacobian.- 6.7 Assembly of Coefficients.- 6.8 Generation of a System of Equations.- 6.9 Summary of the Three Dimensional Boundary Element Method.- 6.10 Concluding Remarks.- Exercises.- 7 Numerical Integration for Three Dimensional Problems.- 7.1 Introduction.- 7.2 Integration in the Local Coordinate Plane.- 7.3 Singular Integration.- 7.4 Concluding Remarks.- Exercises.- 8 Two-Dimensional Elastostatics.- 8.1 Introduction.- 8.2 Review of Linear Elasticity.- 8.3 Derivation of the Boundary Integral Equation.- 8.4 Boundary Element Solution.- 8.5 Concluding remarks.- Exercises.- Appendix A Integration and Differentiation Formulae.- Appendix B Matrix Partitioning for the Mixed Boundary Value Problem.- Appendix C Answers to Selected Exercises.