Concept Oriented Design of Numerical Software

Abstract

The continuously growing computing power of modern computers admits to tackle numerical problems of extreme complexity. This complexity carries over to the numerical methods applied to solve the problems. Whereas the mathematical formulation of these methods does not raise any difficulties, their implementation turns out to be the bottleneck in the realization of numerical applications. In the last years, in order to afford relief, object oriented methods were applied to promote reusable and extensible numerical software, since this kind of flexibility is the key to manage complexity. It became evident that a carefully chosen modularization of the considered methods is a necessary requirement to provide flexible software components. In this paper we give a brief review of object oriented methods to identify the key issues that support a flexible software design and discuss a modularization technique based on mathematical concepts. Finally, the application of this concept oriented approach to boundary element methods is presented.