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