An analytic computation-driven algorithm for Decentralized Multicore Systems

• Published in: Future generation computer systems Vol. 96; pp. 101 - 110
• Main Authors: Lin, Yezhi, Jin, Xinyuan, Chen, Jiuqiang, Sodhro, Ali Hassan, Pan, Zhifang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2019
• Subjects: Adomian polynomials; Adomian–Rach double decomposition method; Decentralized Multicore Systems; Parallel algorithm; Parallel algorithm; Decentralized Multicore Systems; Adomian polynomials; Adomian–Rach double decomposition method; Adomian-Rach double decomposition method
• ISSN: 0167-739X; 1872-7115; 1872-7115
• DOI: 10.1016/j.future.2019.01.031

In the modern era, increasing numbers of cores per chip are applied for decentralized systems, but there is not any appropriate symbolic computation approach to construct multicore analytic approximation. Thus, it is essential to develop an efficient, simple and unified way for decentralized Adomian decomposition method to increase the potential speed of the multicore systems. In our paper, we present an innovative parallel algorithm of constructing analytic solutions for nonlinear differential system, which based on the Adomian–Rach double decomposition method and Rach’s Adomian polynomials. Based on our algorithm, we further developed a user-friendly Python software package to construct analytic approximations of initial or boundary value problems. Finally, the scope of validity of our Python software package is illustrated by several different types of nonlinear examples. The obtained results demonstrate the effectiveness of our package by compared with exact solution and numeric method, the characteristics of each class of Adomian polynomials and the efficiency of parallel algorithm with multicore processors. We emphasis that the super-linear speedup may happens for the duration of constructing approximate solutions. So, it can be considered as a promising alternative algorithm of decentralized Adomian decomposition method for solving nonlinear problems in science and engineering. •We present an innovative parallel algorithm to calculate approximations for initial or boundary value problems.•A Python package AdomianPy is developed for initial or boundary value problems.•Several examples are given to demonstrate the validity of our software package.•It is a remarkable fact that the speed of executing our python package can be great improved by multi-core, even the super-linear speedup.