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 eecient solution of the N{body problem. If the gas of a galaxy is treated by means of smoothed particle hydro-dynamics (Sph), the hydrodynamic equations can be reduced to a form similar to that of the N{body problem. A straightforward implementation requires a computational eeort / 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 diierent approach to perform such simulations using a workstation in combination with the special purpose hardware Grape. After a discussion of the main features of Grape, we present a simple implementation of a SPH{N{body code on such a connguration. 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 Cray YMP.