Introduction

Abstract

This chapter sets the scene for the problems to be studied in this book. Typical problems from which boundary integral equations arise, namely, the scattering of time harmonic waves and cracks in elastic media, are introduced. Single-layer and double-layer potentials with the appropriate fundamental solutions are given together with the first kind integral equations for Dirichlet and Neumann problems with weakly-singular and hypersingular boundary integral equations, respectively. The h-, p-, and hp-versions of the Galerkin scheme on quasi-uniform and graded meshes are briefly described.