Numerical and Symbolic Scientific Computing Annual Report 2005 Johannes Kepler

This Annual Report gives a summary of SFB results achieved in 2005. Also in its eighth year of funding, the overall scientific goal of the SFB is the design, verification, implementation , and analysis of numerical, symbolic, and geometrical methods for solving • large-scale direct and inverse problems with constraints and their synergetical use in scientific computing for real life problems of high complexity. This includes so-called field problems, usually described by partial differential equations (PDEs), and algebraic problems , e.g., involving constraints in algebraic formulation. As pointed out in the Annual Report 2004, concerning the fine structure of the Scientific Concept and of the Long Term Goals of the SFB, we permanently have made adaptations in order to focus more properly on our overall objective. These adjustments have been driven by the advice and the suggestions of the referees, by our experience made during the SFB work, but also by the changing requirements in the international research community. To achieve the goal of a proper combination of numerical and symbolic scientific computing, again strong emphasis has been put on supplementary measures, like joint internal seminars between numerical and symbolic groups or a new target-oriented structure of the SFB status seminars. This way the coherence between the numerical and symbolic groups has been further improved. A whole network of concrete links between numerics, symbolics, and geometry has been established and expanded. The scientific results obtained within the SFB by the participating institutes gave rise to various activities concerning knowledge and technology transfer to the industry, especially, in Upper Austria. The highlights are the foundation of the Software Competence Center Hagenberg and the Industrial Mathematics Competence Center in 1999. For more details see the sections describing the scientific progress achieved within the subprojects of the SFB. On the academic level, the efforts of the institutes participating in the SFB to combine numerical-symbolic scientific computing with applied mathematics led to the foundation of the Johann Radon Institute for Computational and Applied Mathematics (RICAM) by the Austrian Academy of Sciences as a Center of Excellence in Applied Mathematics. Outstanding internationally recognized activities under the lead of RICAM have been organized: The following institutes of the University of Linz are currently involved in the subprojects of the SFB: Acknowledgements: We express our thanks to the Austrian Research Fund (FWF), the University of Linz, the Government of Upper Austria, and the City of Linz for …