An Introduction to Boundary Element Methods

ISBN-13: 9780849373770 / Angielski / Twarda / 1995 / 384 str.

Prem K. Kythe

Opis

Many engineering and mathematics graduate curricula include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. This textbook provides both theory and applications, necessary for applied courses.

Spis treści

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

O autorze

Kythe\, Prem K.