Integration of Nuclear Reaction Networks for Stellar Hydrodynamics 论文

摘要

Methods for solving the sti system of ordinary dierential equations that constitute nuclear reaction networks are surveyed. Three semi-implicit time integration algorithms are examined; a traditional Ðrst-orderÈaccurate Euler method, a fourth-orderÈaccurate Kaps-Rentrop method, and a variable-order Bader-DeuÑhard method. These three integration methods are coupled to eight dierent 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 behav-ior of the 24 combinations (3 time integration methods times 8 linear algebra packages) are analyzed by running each combination on seven dierent nuclear reaction networks. These reaction networks range from a hardwired 13 isotope a-chain and heavy-ion reaction network, which is suitable for most multidi-mensional 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 methodsÈevaluated across several dierent machine