Boundary Integral Equation Methods and Numerical Solutions

This bookpresents and explains a general, efficient, and elegant methodforsolvingthe 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 ofa boundary elementtechnique.The text discusses the methodology for constructing a BIEM, derivingall the attending mathematical properties with full rigor.The modelinvestigatedin 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 aBIEM, which, in turn, forms the basis for the second part of the book, whereapproximate solutionsare computedwith 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 solutionsin a wide variety of problems.