Title

Conservation Properties Of Multisymplectic Integrators

Keywords

Conservation laws; Hamiltonian PDEs; Long-time dynamics; Multisymplectic integrators

Abstract

Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian PDEs are discussed. We consider multisymplectic (MS) schemes based on Fourier spectral approximations and show that, in addition to a MS conservation law, conservation laws related to linear symmetries of the PDE are preserved exactly. We compare spectral integrators (MS versus non-symplectic) for the nonlinear Schrödinger (NLS) equation, focusing on their ability to preserve local conservation laws and global invariants, over long times. Using Lax-type nonlinear spectral diagnostics we find that the MS spectral method provides an improved resolution of complicated phase space structures. © 2004 Elsevier B.V. All rights reserved.

Publication Date

3-1-2006

Publication Title

Future Generation Computer Systems

Volume

22

Issue

4

Number of Pages

412-422

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.future.2004.11.026

Socpus ID

29644441308 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/29644441308

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