Concept oriented design of numerical software

The continuously growing computing power of modern comput ers 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 di culties their implementation turns out to be the bottleneck in the realization of numerical applications In the last years in order to a ord relief object oriented methods were applied to promote reusable and extensible numerical software since this kind of exibility is the key to manage complexity It be came evident that a carefully chosen modularization of the considered methods is a necessary requirement to provide exible software com ponents In this paper we give a brief review of object oriented methods to identify the key issues that support a exible 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 Presented at the th GAMM Seminar on Concepts of Numerical Software Christian Albrechts Universit at Kiel January th to th in press in Notes on Numerical Fluid Mechanics Vieweg