Construction of the Local Structure-Preserving Algorithms for the General Multi-Symplectic Hamiltonian System
Year: 2020
Author: Jialing Wang, Yushun Wang, Dong Liang
Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 828–860
Abstract
Many partial differential equations can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, namely multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we systematically give a unified framework to construct the local structure-preserving algorithms for general conservative partial differential equations starting from the multi-symplectic formulation and using the concatenating method. We construct four multi-symplectic algorithms, two local energy-preserving algorithms and two local momentum-preserving algorithms, which are independent of the boundary conditions and can be used to integrate any partial differential equations written in multi-symplectic Hamiltonian form. Among these algorithms, some have been discussed and widely used before while most are novel schemes. These algorithms are illustrated by the nonlinear Schrödinger equation and the Klein-Gordon-Schrödinger equation. Numerical experiments are conducted to show the good performance of the proposed methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0160
Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 828–860
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Multi-symplectic formulation multi-symplectic algorithm energy-preserving algorithm momentum-preserving algorithm concatenating method average vector field method.
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