Cluster computing for the large scale discrete fractional Cable equation

• Main Authors: N.H. Sweilam, Hatem Moharram, N.K. Abdel Moniem
• Format: Article
• Language: English
• Published: Elsevier 2015-03-01
• Series: Egyptian Informatics Journal
• Subjects: Weighted average finite difference method; Fractional Cable equation; Precondition conjugate gradient method (PCG); Parallel computations; Linux PC cluster workstation
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110866514000474

This paper presents a numerical simulation technique for the fractional Cable equation in large scale domain. Special attention is given to the parallel execution of the fractional weighted average finite difference method (FWA-FDM) on distributed system with explicit message passing, where the fractional derivative is defined in Riemann–Liouville sense. The resultant huge system of equations is studied using precondition conjugate gradient method (PCG), with the implementation of cluster computing on it. The proposed approach fulfills the suitability for the implementation on Linux PC cluster through the minimization of inter-process communication. To examine the efficiency and accuracy of the proposed method, numerical test experiments using different number of the Linux PC cluster nodes are studied. The performance metrics clearly show the benefit of using the proposed approach on the Linux PC cluster in terms of execution time reduction and speedup with respect to the sequential running in a single PC.