This volume contains a selection from the papers presented at the Fourth European Multigrid Conference, held in Amsterdam, July 6-9,1993. There were 78 registered participants from 14 different countries, and 56 presentations were given. The preceding conferences in this series were held in Cologne (1981, 1985) and in Bonn (1990). Also at the other side of the Atlantic special multigrid conferences are held regularly, at intervals of two years, always in Copper Mountain, Colorado, US. The Sixth Copper Mountain Conference on Multigrid Methods took place in April, 1993. Circumstances prevented us from putting a larger time interval between the Copper and Amsterdam meetings. The next European meeting is planned in 1996, a year later than the next Copper Meeting. When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists. The past twenty years have shown a rapid growth in theoretical understanding, useful applications and widespread acceptance of multi grid in the applied disciplines. Hence, one might ask whether there is still a need today for conferences specially dedicated to multigrid. The general consensus is that the answer is affirmative. New issues have arisen that are best addressed or need also be addressed from a special multigrid point of view."

This book contains the course notes of the Summerschool on High Performance Computing in Fluid Dynamics, held at the Delft University of Technology, June 24-28, 1996. The lectures presented deal to a large extent with algorithmic, programming and implementation issues, as well as experiences gained so far on parallel platforms. Attention is also given to mathematics aspects, notably domain decomposition and scalable algorithms. Topics considered are: basic concepts of parallel computers, parallelization strategies, programming aspects, parallel algorithms, applications in computational fluid dynamics, the present hardware situation and developments to be expected. The book is addressed to students on a graduate level and researchers in industry engaged in scientific computing, who have little or no experience with high performance computing, but who want to learn more, and/or want to port their code to parallel platforms. It is a good starting point for those who want to enter the field of high performance computing, especially if applications in fluid dynamics are envisaged.

The lectures presented in this text deal to a large extent with algorithmic, programming and implementation issues, as well as experiences gained so far on parallel platforms. Attention is also given to mathematics aspects, notably: domain decomposition and scalable algorithms; parallelization strategies; programming aspects; parallel algorithms; applications in computational fluid dynamics; and the present hardware situation and developments to be expected. The book is addressed to students on a graduate level and researchers in industry engaged in scientific computing, who have little or no experience with high performance computing, but who want to learn more, and/or want to port their code to parallel platforms. It should be a good starting point for those who want to enter the field of high performance computing, especially if applications in fluid dynamics are envisaged.