Dispersive properties of multisymplectic integrators
Abbreviated Journal Title
J. Comput. Phys.
Keywords
multisymplectic methods; box schemes; leapfrog method; dispersion; relation; sine-gordon equation; double-pole soliton; WAVE ACTION; CONSERVATION; SCHEMES; PDES; EQUATION; Computer Science, Interdisciplinary Applications; Physics, Mathematical
Abstract
Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space-time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge-Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the NIS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of NIS integrators in the nonlinear regime. (C) 2008 Elsevier Inc. All rights reserved.
Journal Title
Journal of Computational Physics
Volume
227
Issue/Number
10
Publication Date
1-1-2008
Document Type
Article
Language
English
First Page
5090
Last Page
5104
WOS Identifier
ISSN
0021-9991
Recommended Citation
"Dispersive properties of multisymplectic integrators" (2008). Faculty Bibliography 2000s. 944.
https://stars.library.ucf.edu/facultybib2000/944
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