Boundary Integral Equation Methods and Numerical Solutions

Authors: Constanda, Christian, Doty, Dale, Hamill, William
​Presents and explains a general, efficient, and elegant method of a solution for boundary value problems for an elliptic system of partial differential equations
Shows in detail a methodology for constructing a boundary integral equation method (BIEM), and all the attending mathematical properties are derived with full rigor
Develops and employs a numerical scheme directly related to the BIEMs to compute approximate solutions

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy.

The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.

Number of Illustrations and Tables
55 b/w illustrations, 196 illustrations in colour
Topics
Integral Equations
Partial Differential Equations
Functions of a Complex Variable

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