Study on the finite element method of Hamiltonian system with chaos

Qiong Tang (), YangFan Liu, Yujun Zheng () and ChengJie Xu ()
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Qiong Tang: College of Science, Hunan University of Technology, ZhuZhou 412007, Hunan, P. R. China
YangFan Liu: School of Materials Science and Engineering, Central South University, ChangSha 410083, Hunan, P. R. China
Yujun Zheng: College of Science, Hunan University of Science and Engineering, YongZhou 425199, Hunan, P. R. China
ChengJie Xu: College of Science, Hunan University of Technology, ZhuZhou 412007, Hunan, P. R. China

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 11, 1-12

Abstract: By comparing with symplectic different methods, the quadratic element is an approximately symplectic method which can keep high accuracy approximate of symplectic structure for Hamiltonian chaos, and it is also energy conservative when there have chaos phenomenon. We use the quadratic finite element method to solve the Hênon–Heiles system, and this method was never used before. Combining with Poincarê section, when we increase the energy of the systems, KAM tori are broken and the motion from regular to chaotic. Without chaos, three kinds of methods to calculate the Poincarê section point numbers are the same, and the numbers are different with chaos. In long-term calculation, the finite element method can better keep dynamic characteristics of conservative system with chaotic motion.

Keywords: Hamiltonian systems; chaos; finite element methods; symplectic algorithm; Poincarê section (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S012918312050165X

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