A Practical Guide to Boundary Element Methods with the Software Library BEMLIB
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.
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arbitrary arc length BEMLIB boundary condition boundary distribution boundary elements boundary-element method boundary-integral representation Call statement circular circular segment component contour control area control volume Coordinates corresponding defined delta function denoted Dirac's delta function discretization divergence theorem double-layer potential dS(x evaluation point expression field point Files flow past fluid free-space Green's function function is given function of Laplace's Gauss elimination gradient harmonic function illustrated in Figure Input integral equation integral identity integral representation Laplace's equation left-hand side linear system matrix Neumann function Newtonian potential nodes normal derivative normal vector Numerical method obtain Output particle particular solution periodic array periodic Green's function point forces point x0 Poisson's equation reciprocal base vector right-hand side scalar semi-infinite domain bounded singular point solution domain solving specified Stokes flow streamline pattern Stress Green's function Subdirectory subroutine surface three dimensions three-dimensional triangle two-dimensional unit normal vector Velocity Green's function wave number