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\def\gsim{\mathrel{\lower .80ex\hbox{\rlap{$\sim$} \raise .90ex\hbox{$>$} }}} The ``N'' in N-body calculations has doubled every year for the last two decades. To continue this trend, the UW N-body group is working on algorithms for the fast evaluation of gravitational forces on parallel computers and establishing rigorous standards for the computations. In these algorithms, the computational cost per time step is $\sim 10^3$ pairwise forces per particle. A new adaptive time integrator enables us to perform high quality integrations that are fully temporally and spatially adaptive. SPH--smoothed particle hydrodynamics will be added to simulate the effects of dissipating gas and magnetic fields.
The importance of these calculations is two-fold. First, they determine the nonlinear consequences of theories for the structure of the Universe. Second, they are essential for the interpretation of observations. Every galaxy has six coordinates of velocity and position. Observations determine two sky coordinates and a line of sight velocity that bundles universal expansion (distance) together with a random velocity created by the mass distribution. Simulations are needed to determine the underlying structure and masses. The importance of simulations has moved from ex post facto explanation to an integral part of planning large observational programs. I will show why high quality simulations with ``large N'' are essential to accomplish our scientific goals.
This year, our simulations have $N \gsim 10^7$. This is sufficient to tackle some niche problems, but well short of our 5 year goal--simulating {\sl The Sloan Digital Sky Survey} using a few Billion particles (a Teraflop-year simulation). Extrapolating past trends, we would have to ``wait'' 7 years for this hundred-fold improvement. Like past gains, significant changes in the computational methods are required for these advances. I will describe new algorithms, algorithmic hacks and a dedicated computer to perform Billion particle simulations. Finally, I will describe research that can be enabled by Petaflop computers.
This research is supported by the NASA HPCC/ESS program.
