Spectral-collocation variational integrators

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• 作者：Yiqun Li^a ; ^{liyiqun_hit@163.com} ; Boying Wu^a ; ^{mathwby@hit.edu.cn} ; Melvin Leok^b ; ^{mleok@math.ucsd.edu}
• 关键词：Geometric numerical integration ; Variational integrators ; Spectral-collocation methods ; Lagrangian mechanics
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：332
• 期：Complete
• 页码：83-98
• 全文大小：1369 K
• 卷排序：332

文摘

Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and have a relatively small memory footprint. In this paper, we introduce a general framework to convert a spectral-collocation method into a shooting-based variational integrator for Hamiltonian systems. We also compare the proposed spectral-collocation variational integrators to spectral-collocation methods and Galerkin spectral variational integrators in terms of their ability to reproduce accurate trajectories in configuration and phase space, their ability to conserve momentum and energy, as well as the relative computational efficiency of these methods when applied to some classical Hamiltonian systems. In particular, we note that spectrally-accurate variational integrators, such as the Galerkin spectral variational integrators and the spectral-collocation variational integrators, combine the computational efficiency of spectral methods together with the geometric structure-preserving and long-time structural stability properties of symplectic integrators.