一维Burgers方程的一类交替分段并行算法

A Class of Parallel Alternating Group Method for One Dimensional Burgers' Equation

研究并行算法解决应用并行计算机完成规模尽可能大的偏微分方程的数值求解问题。利用Hopf-Cole变换,将一维非线性Burgers方程转化为线性扩散方程,基于第二类Saul’yev型非对称格式和Crank-Nicolson格式对扩散方程进行差分离散,建立解Burgers方程的交替分段并行差分格式,并讨论该方法的稳定性,给出了数值算例。此算法把剖分节点分成若干组,在每组上构造能够独立求解的差分方程,因此具有并行本性,适合在高性能多处理器的并行计算机上使用。数值试验的结果表明此方法是有效的,且有较高的精度。

Parallel algorithm is devised for obtaining numerical solutions of large scale partial differential equations by parallel computer. A kind of alternating group four points method for solving Burgers＇ equation which is changed into a diffusion equation first by Hopf-Cole transformation is constructed here. This method, which is based on Saul＇ yev type asymmetric difference schemes and Crank-Nicolson scheme is unconditionally stable by analysis. The basic idea of the method is that the grid points on the same time level are divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The numerical experiments show that the method has good stability and accuracy.