Timestepping and Parallel Computing in Highly Dynamic N-body Systems

Joachim Stadel
University of Zurich

As our N-body simulations probe ever finer structures the range in timescales within these simulations grows ever wider. This is particularly true for self-gravitating simulations incorporating extra physical processes; hydrodynamics, star-formation, and feedback. Multi-timescale integration which calculates forces at differing time intervals depending on the dynamical time of each particle provides a way of speeding up the calculations in these cases. However, three different problems arise: 1) that exact conservation of energy/momentum is no longer possible; 2) that the calculation can be dominated by overhead costs which seemed insignificant when forces were computed for all of the particles; 3) that obtaining effective parallel computation becomes much more difficult. In addressing each of these issues I will present the methods used by our parallel gravity treecode (PKDGRAV) and its SPH extension (GASOLINE). I will also present some alternative methods which get around some of these problems. For problems 1 and 2, I will discuss the Leimkuhler integrator's interesting conservation properties. I will present a method of "carving out" highly dynamic protions of the tree and resorting to the O(N^2) algorithm with the benifit of nearly zero overhead for those portions. Finally, I will present some alternative parallel integration techniques where very accurate orbits and conservation properties are essential, these being the Time-Slice Concurrant Method (TSCM) and parallel Lie integration.

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