An Introduction to Boundary Element Methods

Series:
Symbolic & Numeric Computation
Published:
April 13, 1995 by CRC Press - 384 Pages
Author(s):
Prem K. Kythe, University of New Orleans, Louisiana, USA
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$115.95
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ISBN 9780849373770
Cat# 7377
 

Features

  • Subject matter is organized with a gradual structure in the development of theory and applications
  • Covers nine different application areas, offering a wide range of interest and appeal to readers with different needs and choices
  • One hundred solved examples provide more practice and help develop problem-solving skills
  • Computer subroutines present skills necessary to either modify existing programs or create new ones

    • Summary

    The finite element and the boundary element methods are the two most important developments in numerical mathematics to occur in this century. Many engineering and mathematics graduate curricula now include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. Both theory and applications, necessary for applied courses, are available in this new textbook.

    An Introduction to Boundary Element Methods is logically organized and easy to read. The topics are carefully selected and meticulously presented. Applications are described for use in identifying potential problems and for heat transfer, diffusion equations, linear elasticity, water waves, ocean acoustics, acoustic scattering, aerodynamics, porous media, and simple laminar flows.

    More than 20 computer subroutines help develop and explain the computational aspect of the subject. Hundreds of figures, exercises, and solved examples supplement text and help clarify important information.

    The computer programs have been tested on some benchmark problems. Even in single precision the results are more accurate and better than those obtained from available Fortran programs.

    Table of Contents

    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

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