The Formation of Galaxies: A Challenge for Supercomputers -- a Simple Task for GRAPE ?

We present numerical simulations of galaxy formation, one of the most challenging problems in computational astrophysics. The key point in such simulations is the efficient solution of the N--body problem. If the gas of a galaxy is treated by means of smoothed particle hydrodynamics (SPH), the hydrodynamic equations can be reduced to a form similar to that of the N--body problem. A straightforward implementation requires a computational effort $\propto N^2$, making it prohibitively expensive to simulate systems larger than $10^5$ particles even on the largest available supercomputers. After a description of the physical and numerical problems, we shortly review the standard numerical methods to tackle these problems and discuss their advantages and drawbacks. We also present a completely different approach to perform such simulations using a workstation in combination with the special purpose hardware {\sc Grape}. After a discussion of the main features of {\sc Grape}, we present a simple implementation of a {\sc SPH}--N--body code on such a configuration. Comparing results and performance of these two approaches, we show, that with an investment of US \$ 50000, the problem can be solved up to 5 times faster than on a {\sc Cray} YMP.