ABSTRACT
In the previous chapters, we presented the wave characteristics of 1D and 2D waveguides of different materials and structures. We have seen that the heart of analysis in all these waveguides is spectral analysis, which uses the governing differential equations of the material system in which we are interested in studying the propagation of waves. The governing differential equation that governs the motion of a particular waveguide is normally referred to as the strong form of the governing differential equation. In the last few chapters, we mostly presented the wave characteristics of different wave-guides in terms of its wavenumbers and wave speeds and inferred on the nature of the wave propagation. In order to ascertain the inference made as regards the nature of wave propagation based on the obtained wave parameters in a particular waveguide, it is necessary to obtain the actual time responses. This requires the exact solution of the strong form of the governing differential equation; such exact solutions for most governing equations are non-existent and hence one has to resort to approximate or numerical methods to solve the governing equations. There are several different numerical schemes available and one such method, which is considered very powerful, is the finite element method (FEM). In this chapter, we outline the basics of FEM and discuss this method to solve wave propagation problems.
