Applications of Computer Algebra in Scientific Computing

Hans-Joachim Bungartz

FORTWIHR — The Bavarian Consortium for High Performance Scientific Computing c/o Institut für Informatik der Technischen Universität München D-80290 München, Germany

bungartz@informatik.tu-muenchen.de

Abstract

In the field of scientific computing, the methods and tools of classical numerical analysis are traditionally much more common than the use of computer algebra systems. Nevertheless, modern computer algebra systems can support both the development, the theoretical analysis, and the efficient use of algorithms and codes in the different areas of application of scientific computing. Therefore, it turns out to be more and more important to bring together the two worlds of numerical and symbolic computation.

We report a couple of situations where computer algebra tools, recently, have been successfully integrated in scientific computing projects. Here, the areas of application range from support in proving approximation properties of discretization schemes to data compression for purposes of visualization and multi media applications. Finally, results from the implementation of computer algebra modules in programs for computational fluid dynamics are presented.