一类刚性大系统的并行组合方法

PARALLEL COMPOUND METHODS FOR SOWING A CLASS OF STIFF SYSTEMS

本文针对一类分解的刚性大系统提出一种并行组合方法（ＰＣＭ）．该方法将系统分割的并行化方法与方法分割的并行化方法相结合，采用并行显式Ｒｕｎｇｅ－Ｋｕｔｔａ（ＲＫ）方法求解非刚性子系统，采用并行Ｒｏｓｅｎｂｒｏｃｋ方法求解刚性子系统．文中讨论了方法的相容阶，并对方法的收敛性进行了分析．数值结果表明该方法对于分解的刚性大系统的求解是实用和有效的。

Through combination of the parallelism across the system with the parallelism across the method, Parallel Compound Methods (PCM) are constructed for the numerical solution of a class of partitioned stiff systems. Nonstiff equations are integrated by a parallel explicit RK method while an parallel Rosenbrock method is used for the stiff part of the system. Their order conditions and their convergence are discussed, and the numerical tests are conducted on a personal computer and a parallel computer.