Parallel computers are meanwhile a generally accepted tool in all parts of applied scientific research. Unfortunately the theoretical speed-up of algorithms is often not as huge as awaited.

This situation is caused by several reasons.

The user of parallel computers would be happy if there would exist reliable program libraries-similar to serial computers- which cover the fundamental problems from numerical algebra, e.g.. These should be independent of a specific hardware architecture. In practice the situation is far away from this state. For most basic problems it is still not known in general how they should most effective be implemented on existing machines.

The intention of the seminar was to bring together scientists from the field of Numerial Analysis, Computer Science, Engineering and Natural Science, respectivley, in order to discuss the state of the art and future developments of parallel processing in the applied sciences. The meeting provided a forum of exchange between these different research fields. The Dagstuhl seminar was attended by 33 participants from four countries.

In 24 talks various parallel algorithms for different computer architectures and parallel software for mathematical modeling of real life applications e.g. in climatology, structural mechanics, tomography and acoustics were presented. This report contains in alphabetic order the abstracts of the given talks and the summary of the plenary session.

Besides of the given talks a plenary session on "Parallelcomputing in the engineering sciences- methods and applications" was organized.

The following points were discussed:

1. Who uses parallel computers?
2. Who delivers the technology (hardware and software)
3. Architecture vs. requirements.
4. Economical and teaching aspects.
5. Transfer of technology.

The contributions to these points can be founded in the Seminar report.

We express our thanks to the administration and to the staff of Schloss Dagstuhl for the pleasant atmosphere and to all people who contributed to the success of the conference.