An introduction to BOUNDARY ELEMENT METHODS

Introduction Historical Background What is BEM ? Boundary Elements Mathematical Preliminaries Results from Calculus Interpolation Functions Distributions Boundary Conditions Dirac Delta Function Fourier Series Problems References and Bibliography Variation and Weighted Residual Methods Weak Variational Formulation Galerkin Method Rayleigh-Ritz Method Choice of Test Functions Problems References and Bibliography One-Dimensional Problems Potential Flow Bending of an Elastic Beam Problems References and Bibliography Fundamental Solutions Eigenpairs and Dirac Delta Function Green's Functions Fundamental Solutions on a Finite Domain Fundamental Solution on an Infinite Domain References and Bibliography Potential Problems Laplace Equation Boundary Elements Constant Elements: Subroutine Be1 Linear Eelements Discontinuous Elements: Subroutine Be2 Quadratic and Higher Elements Poisson Equation Non-Convex Surfaces:Subroutine Be5 Domain Integral Unbounded Regions Mixed Boundary Conditions Indirect Method Problems References and Bibliography Linear Elasticity Basic Relations Virtual Work Somigliana Identity Boundary Integral Equation Derivation of BE Equation:Subroutine Bell Torsion of a Cylindrical Bar Three-Dimensional Medium Axisymmetric Problems Problems References and Bibliography Ocean Acoustics and Helmholtz Equation Water Waves Simple Amplitude Wave Theory Helmholtz Equation BEM:Helmholtz Equation Underwater Acoustic Scattering The CHIEF Algorithm Some Structure Types Problems References and Bibliography Some Fluid Flows and D'Arcy Equation Aerodynamic Flows Navier-Strokes Equation Porous Media Flows Steady-state Groundwater Flows Anisotropic Porous Media Flows with Singularities Problems References and Bibliography Domain Integrals Dual Reciprocity Method Fourier Series Method Multiple Reciprocity Method Problems References and Bibliography Transient Problems Transient Fourier Equation Forward Time Marching Process Laplace Transform BEM Transient DRM Transient MRM Problems References and Bibliography Variational Calculus Line Integrals Variational Notation Multiple Integrals Problems References and Bibliography Potential Theory Electrostatic Potential Dirichlet Problems Neumann Problems References and Bibliography Gauss Quadrature One-Dimensional Gauss Quadrature One-Dimensional Logarithmic Gauss Quadrature Two-Dimensional Gauss Quadrature Formula References and Bibliography Software Development Answers to Selected Problems Index