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

Erscheinungsjahr 2010
ISBN: 978-1-4200-3525-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 440 Seiten

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.

Zielgruppe

Professionals, researchers, and students in computational science and engineering disciplines, particularly those in fluid mechanics; applied mathematicians working in partial differential equations and numerical methods; physicists involved in fluid dynamics

Autoren/Hrsg.

Pozrikidis, C.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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