Parallel Subdomain Synthesis of Cell Mapping for Capturing Global Invariant Sets in Higher-Dimensional Dynamical Systems

Author:

Li Zigang1ORCID,Kang Jiaqi1,Jiang Jun2,Hong Ling2

Affiliation:

1. Department of Mechanics, Xi’an University of Science and Technology, Xi’an 710054, P. R. China

2. State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Abstract

Unaffordable computational cost and memory storage induced by the curse of dimensionality has become the bottleneck of numerical methods in different fields. In the global analysis of nonlinear dynamical systems, the capability of numerical methods, like cell mapping methods, are mostly feasible only to a system dimension less than four. Although cell mappings are naturally parallelizable that may be used to greatly enhance the computational efficiency, it is still not enough to release the computational burden on a higher-dimensional system of greater than seven, not to mention the memory in dealing with millions of billion cells. In this paper, the subdomain synthesis method, which partitions the chosen region in state space into subdomains suitable for operating in a computational unit and then synthetizes the so-called virtual invariant sets to get the underlying global invariant sets, is promoted to be parallelizable on the subdomains so as to build a two-layer massively parallel architecture in both cell and subdomain levels. The proposed approach can be implemented by GPU Cluster that can maximize the powerful computation capability of hardwares. Examples with global invariant sets in very fine distances of a Jerk system and in bifurcations of a twelve-dimensional nonsmooth rotor system are presented for the first time to demonstrate then the feasibility of the proposed approach.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3