ABSTRACT
For an understanding of the boundary element eigenvalue formulations to be developed in the subsequent chapters, a working knowledge of the fundamentals of the boundary element method (BEM) is essential. This chapter is dedicated to introducing the BEM to the reader. Although our objective in the book is to develop numerical techniques for the computation of resonant frequencies in acoustics and elasticity, we shall present the basic principles of the BEM using potential problems as an illustration. This is because potential problems:
(a) Can be represented by a simple scalar unknown variable; (b) Are governed by a relatively simple governing equation, e.g., the Laplace’s
equation; and (c) Represent a broad class of physical phenomena, e.g., heat conduction, potential
flow, seepage, magnetic potential, electrostatics, torsion of shafts, corrosion and many others.
