On variational and symplectic time integrators for Hamiltonian systems
On variational and symplectic time integrators for Hamiltonian systems
复制标题
DOI：
10.1016/j.jcp.2015.11.049
复制
发表时间：
2016-02
期刊：
影响因子：
--
通讯作者：
E. Gagarina;V. Ambati;S. Nurijanyan;J. V. D. Vegt;O. Bokhove
中科院分区：
文献类型：
--
作者：
E. Gagarina;V. Ambati;S. Nurijanyan;J. V. D. Vegt;O. Bokhove
自然界中的各种系统都具有哈密顿结构，因此这些系统的精确时间积分器具有很大的实际用途。在本文中，将探索有限元方法，以系统的方式导出（非）自治系统的辛时间步进方案。所使用的技术是时间上的变分间断伽辽金有限元法。这种方法提供了一个统一的框架来导出已知的和新的辛时间积分器。将提供新时间积分器的扩展分析。分析表明，本文提出的一种新型三阶时间积分器具有优异的色散特性。这些新的时间步长方案对于获得（受迫）水波和其他非自主变分系统的准确和稳定的模拟是必要的，我们在数值结果中对此进行了说明。
Various systems in nature have a Hamiltonian structure and therefore accurate time integrators for those systems are of great practical use. In this paper, a finite element method will be explored to derive symplectic time stepping schemes for (non-)autonomous systems in a systematic way. The technique used is a variational discontinuous Galerkin finite element method in time. This approach provides a unified framework to derive known and new symplectic time integrators. An extended analysis for the new time integrators will be provided. The analysis shows that a novel third order time integrator presented in this paper has excellent dispersion properties. These new time stepping schemes are necessary to get accurate and stable simulations of (forced) water waves and other non-autonomous variational systems, which we illustrate in our numerical results.