Boundary Integral Equation Methods and Numerical Solutions

Sinopse

This booknbsp;presents and explains a general, efficient, and elegant methodnbsp;fornbsp;solvingnbsp;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 ofnbsp;a boundary elementnbsp;technique.nbsp;nbsp;The text discusses the methodology for constructing a BIEM, derivingnbsp;all the attending mathematical properties with full rigor.nbsp;The modelnbsp;investigatednbsp;in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients.nbsp; The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of anbsp;BIEM, which, in turn, forms the basis for the second part of the book, wherenbsp;approximate solutionsnbsp;are computednbsp;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.nbsp;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 solutionsnbsp;in a wide variety of problems.nbsp;