文章基本信息

标题：A new Approach to the Solution of Large Thermonuclear Burning Networks
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作者：M.W. Guidry
期刊名称：PoS - Proceedings of Science
印刷版ISSN：1824-8039
出版年度：2006
出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：A new algorithm is proposed for solving large networks of stiff coupled differential equations in various scientific applications. The algorithm replaces differencing of abundance variables with evolution of discrete populations. It reproduces quantitatively the results of standard methods, but with important advantages. (1) The algorithm is explicit, yet it decouples accuracy from stability for stiff systems, permitting explicit integration with a timestep set by the former rather than the latter, thereby avoiding implicit solves. (2) It exploits sparseness perfectly, computing only those reaction links that the physical system traverses. (3) It scales linearly with the number of couplings for large sparse networks, in contrast to the quadratic to cubic scaling of standard methods. (4) Unlike Monte Carlo, for large physical particle number, execution time is independent of the number of test particles, allowing even weaker populations to be tracked efficiently. (5) The decoupling of stability from accuracy allows stable tuning of large networks to optimize accuracy versus computational time. We propose that this new approach can be used to solve large, stiff networks for many complex systems, such as the coupling of realistic networks to multidimensional hydrodynamics, that tax the capability of standard methods.