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

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

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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.show more

Product details

  • Hardback | 440 pages
  • 160.5 x 246.4 x 27.9mm | 743.9g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 99 black & white illustrations, 10 black & white halftones
  • 1584883235
  • 9781584883234

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 INDEXshow more