# 基于MPI的一种有限并行差分格式求解四阶抛物方程A Finite Difference Parallel Scheme Based on MPI Implementation for Fourth Order Parabolic Equations

• 全文下载: PDF(718KB)    PP.114-126   DOI: 10.12677/AAM.2017.62013
• 下载量: 221  浏览量: 277

Parallel computing can save a lot of time in the field of large-scale scientific computing. In this paper, 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 number of large areas; each sub-region computes themselves, and the parallel scheme is unconditionally 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 calculate 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.

 [1] Vabishchevich, P.N. (2015) Explicit Schemes for Parabolic and Hyperbolic Equations. Applied Mathematics and Com- putation, 250, 424-431. [2] Evans, D.J. and Abdullah, A.R. (1983) Group Explicit Methods for Parabolic Equations. International Journal Computer Mathematics, 14, 73-105. https://doi.org/10.1080/00207168308803377 [3] Saul’yev, V.K. (1965) Integration of Equations of Parabolic Type by the Method of Nets. Proceedings of the Edinburgh Mathematical Society, 14, 247-248. https://doi.org/10.1017/S0013091500008890 [4] Evans, D.J. and Abdullah, A.R. (1985) A New Explicit Method for the Diffusion-Convection Equation. Computers and Mathematics with Applications, 11, 145-154. [5] Abdullah, A.R. (1991) The Four Point Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver. International Journal of Computer Mathematics, 38, 61-70. https://doi.org/10.1080/00207169108803958 [6] Evans, D.J. (1985) Alternating Group Explicit Method for the Diffusion Equations. Applied Mathematical Modelling, 9, 201-206. [7] Ali, M., Hj, N., Teong, K. and Khoo (2010) Numerical Performance of Parallel Group Explicit Solvers for the Solution of Fourth Order Elliptic Equations. Applied Mathematics and Computation, 217, 2737-2749. [8] Zhang, B.L. and Li, W.Z. (1994) One Alternating Segment Crank-Nicolson Scheme. Parallel Computing, 20, 897-902. [9] 张宝琳. 求解扩散方程的交替分段显–隐式方法[J]. 数值计算与计算机应用, 1991(4): 245-253. [10] Kellogg, R.B. (1964) An Alternating Direction Method for Operator Equations. Journal of the Society of Industrial and Applied Mathematics, 12, 7. https://doi.org/10.1137/0112072