A unified approach to finite and boundary element discretization in linear time-harmonic acoustics

This chapter introduces the reader too important physical and mathematical concepts in acoustics. It presents an approach to finite and boundary element techniques for linear time-harmonic acoustics starting from the fundamental axioms of continuum mechanics. Based on these axioms, the wave equation is derived. Using a time-harmonic approximation, the boundary value problem of linear time-harmonic acoustics is formulated in the classic and in the weak form. Subsequently, two types of the weak form are used as the basis for discretization resulting in a Galerkin finite element formulation, in a collocation boundary element formulation and in a Galerkin boundary element formulation. Then, different representations of sources and incident wave-fields in finite and boundary element methods are discussed. In the final part of this chapter, the authors categorize the subsequent twenty chapters of this book. The chapter will be completed by an outlook and some open problems in the development of finite and boundary element techniques from the authors' points of view.