Speedup to Virtual Petaflops using Adaptive Potential Solvers and Integrators for Gravitational Systems

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The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect. ---Isaac Newton 1687 Epochal surveys are throwing down the gauntlet for cosmological simulation. We describe three keys to meeting the challenge of N-body simulation: adaptive potential solvers, adaptive integrators and volume renormalization. With these techniques and a dedicated Teraflop facility, simulation can stay even with observation of the Universe. We also describe some problems in the formation and stability of planetary systems. Here, the challenge is to perform accurate integrations that retain Hamiltonian properties for 10 13 timesteps. 1 COSMOLOGICAL N-BODY SIMULATION Simulations are required to calculate the nonlinear final sta...

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