**AAS 201st Meeting, January, 2003**

*Session 56. Supernovae Potpourri*

Poster, Tuesday, January 7, 2003, 9:20am-6:30pm, Exhibit Hall AB
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## [56.11] A New Stochastic Algorithm for Element Production Calculations

*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.