This book presents the state-of-the-art in modelling and simulation on supercomputers. Leading German research groups present their results achieved on high-end systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2004. The reports cover all fields of computational science and engineering ranging from computational fluid dynamics via computational physics and chemistry to computer science. Special emphasis is given to industrially relevant applications. Presenting results for both vector-systems and micro-processor based systems the book allows to compare performance levels and usability of a variety of supercomputer architectures. In the light of the success of the Japanese Earth-Simulator this book may serve as a guide book for a US response. The book covers the main methods in high performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for both the scientist and the engineer. The book comes with a wealth of coloured illustrations and tables of results.