A Practical Guide to Boundary Element Methods with the Software Library BEMLIB: 1st Edition (Hardback) book cover

A Practical Guide to Boundary Element Methods with the Software Library BEMLIB

1st Edition

By C. Pozrikidis

CRC Press

440 pages | 99 B/W Illus.

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pub: 2002-05-15
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Description

The boundary-element method is a powerful numerical technique for solving partial differential equations encountered in applied mathematics, science, and engineering. The strength of the method derives from its ability to solve with notable efficiency problems in domains with complex and possibly evolving geometry where traditional methods can be demanding, cumbersome, or unreliable. This dual-purpose text provides a concise introduction to the theory and implementation of boundary-element methods, while simultaneously offering hands-on experience based on the software library BEMLIB.

BEMLIB contains four directories comprising a collection of FORTRAN 77 programs and codes on Green's functions and boundary-element methods for Laplace, Helmholtz, and Stokes flow problems. The software is freely available from the Internet site: http://bemlib.ucsd.edu

The first seven chapters of the text discuss the theoretical foundation and practical implementation of the boundary-element method. The material includes both classical topics and recent developments, such as methods for solving inhomogeneous, nonlinear, and time-dependent equations. The last five chapters comprise the BEMLIB user guide, which discusses the mathematical formulation of the problems considered, outlines the numerical methods, and describes the structure of the boundary-element codes.

A Practical Guide to Boundary Element Methods with the Software Library BEMLIB is ideal for self-study and as a text for an introductory course on boundary-element methods, computational mechanics, computational science, and numerical differential equations.

Table of Contents

LAPLACE'S EQUATION IN ONE DIMENSION

Green's First and Second Identities and the Reciprocal Relation

Green's Functions

Boundary-Value Representation

Boundary-Value Equation

LAPLACE'S EQUATION IN TWO DIMENSIONS

Green's First and Second Identities and the Reciprocal Relation

Green's Functions

Integral Representation

Integral Equations

Hypersingular Integrals

Irrotational Flow

Generalized Single- and Double-Layer Representations

BOUNDARY-ELEMENT METHODS FOR LAPLACE'S EQUATION IN TWO DIMENSIONS

Boundary Element Discretization .

Discretization of the Integral Representation

The Boundary-Element Collocation Method

Isoparametric Cubic-Splines Discretization

High-Order Collocation Methods

Galerkin and Global Expansion Methods

LAPLACE'S EQUATION IN THREE DIMENSIONS

Green's First and Second Identities and the Reciprocal Relation

Green's Functions

Integral Representation

Integral Equations

Axisymmetric Fields in Axisymmetric Domains

BOUNDARY-ELEMENT METHODS FOR LAPLACE'S EQUATION IN THREE DIMENSIONS

Discretization

Three-Node Flat Triangles

Six-Node Curved Triangles

High-Order Expansions

INHOMOGENEOUS, NONLINEAR, AND TIME-DEPENDENT PROBLEMS

Distributed Source and Domain Integrals

Particular Solutions and Dual Reciprocity in One Dimension

Particular Solutions and Dual Reciprocity in Two and Three Dimensions

Convection - Diffusion Equation

Time-Dependent Problems

VISCOUS FLOW

Governing Equations

Stokes Flow

Boundary Integral Equations in Two Dimensions

Boundary-Integral Equations in Three Dimensions

Boundary-Element Methods

Interfacial Dynamics

Unsteady, Navier-Stokes, and Non-Newtonian Flow

BEMLIB USER GUIDE

General Information

Terms and Conditions

Directory

DIRECTORY: GRIDS

grid_2d

trgl

DIRECTORY: LAPLACE

lgf_2d

lgf_3d

lgf_ax

flow_1d

flow_1d 1p

flow_2d

body_2d

body_ax

tank_2d

ldr_ 3d

lnm_3d

DIRECTORY: HELMHOLTZ

flow_1d osc

DIRECTORY: STOKES

sgf_2d

sgf_3d

sgf_ax

flow_2d

prtcl_sw

prtcl_2d

prtcl_ax

prtcl_3d

APPENDIX A: MATHEMATICAL SUPPLEMENT

APPENDIX B: GAUSS ELIMINATION AND LINEAR SOLVERS

APPENDIX C: ELASTOSTATICS

REFERENCES

INDEX

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT021000
MATHEMATICS / Number Systems
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical