ABSTRACT
In this chapter, the authors examine mathematical aspects of wave scattering and aims to formulate the appropriate wave equations and discuss the conditions under which existence and uniqueness of solutions can be assured. The method of separation of variables is surveyed as are Green’s functions, integral equation formulations of scattering and dual series equation formulations of scattering that are shown to be equivalent. They describe the equations governing the propagation of acoustic and electromagnetic waves, namely Maxwell’s equations and the Helmholtz equation. The authors utilize the method of separation of variables to construct a general solution of the Helmholtz equation in the basic coordinate systems that they intend to exploit in solving wave-scattering problems for structures with edges. They provide basic descriptions of the acoustic and electromagnetic fields in free space. The authors conclude with a brief survey of various numerical methods for scattering.
