Implementation of Boundary Elements in Microcomputers

Abstract

In this chapter we are going to develop some aspects of the implementation of the boundary element method (BEM)in microcomputers. At the moment the BEM is established as a powerful tool for problem-solving and several codes have been developed and maintained on an industrial basis for large computers. It is also well known that one of the more attractive features of the BEM is the reduction of the discretization to the boundary of the domain under study. As drawbacks, we found the non-bandedness of the final matrix, wich is a full asymmetric one, and the computational difficulties related to obtaining the integrals which appear in the influence coefficients. Te reduction in dimensionality is crucial from the point of view of microcomputers, and we believe that it can be used to obtain competitive results against other domain methods. We shall discuss two applications in this chapter. The first one is related to plane linear elastostatic situations, and the second refers to plane potential problems. In the first case we shall present the classical isoparametric BEM approach, using linear elements to represent both the geometry and the variables. The second case shows how to implement a p-adaptive procedure using the BEM. This latter case has not been studied until recently, and we think that the future of the BEM will be related to its development and to the judicious exploitation of the graphics capabilities of modern micros. Some examples will be included to demonstrate the kind of results that can be expected and sections of printouts will show useful details of implementation. In order to broaden their applicability, these printouts have been prepared in Basic, although no doubt other languages may be more appropiate for effective implementation.