One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc.

Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.

When the DFG (Deutsche Forschungsgemeinschaft) launched its collabora tive research centre or SFB (Sonderforschungsbereich) 438 "Mathematical Modelling, Simulation, and Verification in Material-Oriented Processes and Intelligent Systems" in July 1997 at the Technische Vniversitat Munchen and at the Vniversitat Augsburg, southern Bavaria got its second nucleus of the still young discipline scientific computing. Whereas the first and older one, FORTWIHR, the Bavarian Consortium for High Performance Scientific Com puting, had put its main emphasis on the supercomputing aspect, this new initiative was now expected to focus on the mathematical part. Consequently, throughout all of the five main research topics (A) adaptive materials and thin layers, (B) adaptive materials in medicine, (C) robotics, aeronautics, and automobile technology, (D) microstructured devices and systems, and (E) transport processes in flows, mathematical aspects play a predominant role. The formation of the SFB 438 and its scientific program are inextricably linked with the name of Karl-Heinz Hoffmann. As full professor for applied mathematics in Augsburg (1981-1991) and in Munchen (since 1992) and as dean of the faculty of mathematics at the TV Munchen, he was the driv ing force of this fascinating, but not always easy-to-realize idea of bringing together scientists from mathematics, physics, engineering, informatics, and medicine for joint efforts in modern applied mathematics. However, scarcely work had begun when the successful captain was called to take command on a bigger boat."

The book is a state-of-the-art overview on high performance computing (HPC) activities to solve scientific and/or engineering problems on supercomputers. This topic has evolved to a key technology playing an important role in determining, or at least shaping, future research and development activities in many branches of industry. The main topics include the development of advanced numerical methods, parallel computing techniques, grid generation, and visualization. Applications of these techniques are directed to fluid dynamics, turbulence, combustion and porous media related flows, computational structural dynamics, material sciences, chemical engineering, dynamic systems, optimal control, and optimization of electronic circuits. The book includes 44 contributions from renowned international experts in the field of HPC and its applications.

Since the creation of the term "Scientific Computing" and of its German counterpart "Wissenschaftliches Rechnen" (whoever has to be blamed for that), scientists from outside the field have been confused about the some what strange distinction between scientific and non-scientific computations. And the insiders, i. e. those who are, at least, convinced of always comput ing in a very scientific way, are far from being happy with this summary of their daily work, even if further characterizations like "High Performance" or "Engineering" try to make things clearer - usually with very modest suc cess, however. Moreover, to increase the unfortunate confusion of terms, who knows the differences between "Computational Science and Engineering" , as indicated in the title of the series these proceedings were given the honour to be published in, and "Scientific and Engineering Computing", as chosen for the title of our book? Actually, though the protagonists of scientific com puting persist in its independence as a scientific discipline (and rightly so, of course), the ideas behind the term diverge wildly. Consequently, the variety of answers one can get to the question "What is scientific computing?" is really impressive and ranges from the (serious) "nothing else but numerical analysis" up to the more mocking "consuming as much CPU-time as possible on the most powerful number crunchers accessible" .

One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.

Founded in April, 1992 and financed by the State of Bavaria and the Bavarian Re search Foundation, the Bavarian Consortium for High Performance Scientific Comput ing (FORTWIHR) consists of more than 40 scientists working in the fields of engineer ing sciences, applied mathematics, and computer science at the Technische Universitat Munchen and at the Friedrich-Alexander-Universitat Erlangen-Nurnberg. Its inter disciplinary concept is based on the recognition that the increasing significance of the yet young discipline High Performance Scientific Computing (HPSC) can only be given due consideration if the technical knowledge of the engineer, the numerical methods of the mathematician, and the computers and up to date methods of computer science are all applied equally. Besides the aim to introduce HPSC into the graduate degree program at the universi ties, there is a strong emphasis on cooperation with industry in all areas of research. Direct cooperation and a transfer of knowledge through training courses and confer ences take place in order to ensure the rapid utilization of all results of research. In this spirit, FORTWIHR annually organizes symposiums on High Performance Scientific Computing and Numerical Simulation in Science and Engineering."