ABSTRACT
This chapter provides a very brief account of classical potential theory and shows how it can help reduce a given boundary value problem to an equivalent integral equation at the boundary of the original domain. It also addresses the issue of discretization for the corresponding integral equations, and identifies the difficulties that limit the class of problems solvable by the method of boundary elements. To illustrate the key concepts, it is sufficient to consider the interior and exterior Dirichlet and Neumann boundary value problems for the Laplace equation. The interior and exterior boundary value problems of either Dirichlet or Neumann type are formulated for the Helmholtz equation in the same way as they are set for the Laplace equation.
