A PARALLEL INTEGRATION METHOD FOR SOLAR-SYSTEM DYNAMICS

We describe how long-term solar system orbit integration could be impl emented on a parallel computer. The interesting feature of our algorit hm is that each processor is assigned not to a planet or a pair of pla nets but to a time-interval. Thus, the 1st week, 2nd week,..., 1000th week of an orbit are computed concurrently. The problem of matching th e input to the (n + 1)-st processor with the output of the n-th proces sor can be solved efficiently by an iterative procedure. Our work is r elated to the so-called waveform relaxation methods in the computation al mathematics literature, but is specialized to the Hamiltonian and n early integrable nature of solar system orbits. Simulations on serial machines suggest that, for the reasonable accuracy requirement of 1 '' per century, our preliminary parallel algorithm running on a 1000-pro cessor machine would be about 50 times faster than the fastest availab le serial algorithm. We also discuss prospects for further improvement s. (C) 1997 American Astronomical Society.