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E. McMahon (U. Tennessee; U. Texas), M. Guidry (U. Tennessee; ORNL Physics Division)
We present a new stochastic algorithm for solving the generally stiff system of coupled ordinary differential equations that describes element production in astrophysical environments. Schematically, the algorithm replaces the implicit differencing of isotopic abundances in time with a stochastically-computed classical path integral over time. We demonstrate that the new method is capable of reproducing quantitatively the results of standard methods, but with several important advantages that are associated primarily with scalability: (a) On a single processor the stochastic algorithm exhibits extremely benign scaling with increase in network size, generally scaling more weakly than linear with the number of isotope-isotope couplings included. (b) The algorithm is inherently parallel; thus one obtains speedup approaching 100% on parallel processors with large networks. This extremely attractive scaling behavior is associated with the stochastic nature of the algorithm, which replaces the differencing of floating point numbers with the addition of integers, an inherently stable process, thus decoupling the accuracy issue from the stability issue for the stiff system. In addition, the algorithm exploits perfectly the inherent sparseness of the matrices that appear in the implicit solvers, in essence never computing reaction links that the physical system never follows. We shall discuss whether the favorable scaling behavior of this algorithm could provide an avenue to couple more realistic networks in multidimensional hydrodynamical simulations.
ORNL Physics Division is Managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725.
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Bulletin of the American Astronomical Society, 34, #4
© 2002. The American Astronomical Soceity.