基于MPI的一种有限并行差分格式求解四阶抛物方程.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(2), 114-126 Published Online March 2017 in Hans. /journal/aam /10.12677/aam.2017.62013 A Finite Difference Parallel Scheme Based on MPI Implementation for Fourth Order Parabolic Equations Yuyang Gao, Haiming Gu Qingdao University of Science and Technology, Qingdao Shandong th th st Received: Feb. 27 , 2017; accepted: Mar. 18 , 2017; published: Mar. 21 , 2017 Abstract Parallel computing can save a lot of time in the field of large-scale scientific computing. In this pa- per, the main idea is that a finite difference parallel scheme for fourth order parabolic equations. The scheme is constructed by Saul’yev asymmetric difference schemes which called the four-point scheme. It’s one explicit difference scheme, the computational domain can be divided into a num- ber of large areas; each sub-region computes themselves, and the parallel scheme is uncondition- ally stable. Then, the paper focuses on the numerical calculation of the four-point scheme in MPI parallel environment. Two different MPI parallel algorithms are constructed, one is blocking com- munication (wait communication) mode, and the other is non-blocking communication (non-wait communication) mode. These two parallel algorithms both better than serial algorithm to calcu- late numerical solutions use four-point scheme, and the non-blocking communication mode is higher computational than the other, because the wait time in non-blocking communication mode is less than blocking communication mode. Keywords Fourth Order Parabolic Equations, Finite Difference Parallel Scheme, MPI (Message Passing Interface) 基于MPI的一种有限并行差分格式求解四阶抛 物方程 高玉羊，顾海明 青岛科技大学，山东 青岛 文章引用: 高玉