TABLE OF CONTENTS The problem of modelling short waves is dealt with in this chapter. Short waves are taken to be waves in which the wavelength is much smaller than any other parameters in the problem. The literature on this topic has mushroomed in recent years, and this chapter can only give a brief outline of ongoing research activity.
As was seen in the previous chapter, classical finite element methods can deal relatively easily with linear waves in two and three dimensions, when there are few wavelengths in the problem domain. But many problems of practical importance contain many wavelengths. The computational demands of conventional numerical methods for an accurate solution cannot be met. So in recent years, attention has turned to new types of finite elements for such problems. Similar special variations have also been developed for other numerical methods, such as boundary elements. Surveys of these methods are available. [1], [2] A variety of new finite elements have been developed, and they will be surveyed briefly in this chapter. A common feature is that most incorporate more of our knowledge of waves and wave behaviour into the algorithm. The problem of short waves in a large domain is part of the general class of multi-scale problems. [3], [4] That is the problem of large scale, but the overall behaviour is significantly influenced by small-scale behaviour. Other important examples are the behaviour of structures composed of materials with microstructure, for example composites or concrete, and turbulent...
