Integration of Nuclear Reaction Networks for Stellar Hydrodynamics
Abstract
Methods for solving the stiff system of ordinary differential equations that constitute nuclear reaction networks are surveyed. Three semiimplicit time integration algorithms are examined; a traditional firstorderaccurate Euler method, a fourthorderaccurate KapsRentrop method, and a variableorder BaderDeuflhard method. These three integration methods are coupled to eight different linear algebra packages. Four of the linear algebra packages operate on dense matrices (LAPACK, LUDCMP, LEQS, GIFT), three of them are designed for the direct solution of sparse matrices (MA28, UMFPACK, Y12M), and one uses an iterative method for sparse matrices (BiCG). The scaling properties and behavior of the 24 combinations (3 time integration methods times 8 linear algebra packages) are analyzed by running each combination on seven different nuclear reaction networks. These reaction networks range from a hardwired 13 isotope αchain and heavyion reaction network, which is suitable for most multidimensional simulations of stellar phenomena, to a 489 isotope reaction network, which is suitable for determining the yields of isotopes lighter than technetium in spherically symmetric models of Type II supernovae. Each of the time integration methods and linear algebra packages are capable of generating accurate results, but the efficiency of the various methodsevaluated across several different machine architectures and compiler optionsdiffer dramatically. If the execution speed of reaction networks that contain less than about 50 isotopes is an overriding concern, then the variableorder BaderDeuflhard time integration method coupled with routines generated from the GIFT matrix package or LAPACK with vendoroptimized BLAS routines is a good choice. If the amount of storage needed for any reaction network is a concern, then any of the sparse matrix packages will reduce the storage costs by 70%90%. When a balance between accuracy, overall efficiency, and ease of use is desirable, then the variableorder BaderDeuflhard time integration method coupled with the MA28 sparse matrix package is a strong choice.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 September 1999
 DOI:
 10.1086/313257
 Bibcode:
 1999ApJS..124..241T
 Keywords:

 HYDRODYNAMICS;
 METHODS: NUMERICAL;
 NUCLEAR REACTIONS;
 NUCLEOSYNTHESIS;
 ABUNDANCES;
 STARS: INTERIORS;
 Hydrodynamics;
 Methods: Numerical;
 Nuclear Reactions;
 Nucleosynthesis;
 Abundances;
 Stars: Interiors