Title

Conformal Conservation Laws And Geometric Integration For Damped Hamiltonian Pdes

Keywords

Discrete gradient methods; Linear dissipation; Multi-symplectic PDE; Preissman box scheme; Structure-preserving algorithm

Abstract

Conformal conservation laws are defined and derived for a class of multi-symplectic equations with added dissipation. In particular, the conservation laws of energy and momentum are considered, along with those that arise from linear symmetries. Numerical methods that preserve these conformal conservation laws are presented in detail, providing a framework for proving a numerical method exactly preserves the dissipative properties considered. The conformal methods are compared analytically and numerically to standard conservative methods, which includes a thorough inspection of numerical solution behavior for linear equations. Damped Klein-Gordon and sine-Gordon equations, and a damped nonlinear Schrödinger equation, are used as examples to demonstrate the results. © 2012 Elsevier Inc.

Publication Date

1-1-2013

Publication Title

Journal of Computational Physics

Volume

232

Issue

1

Number of Pages

214-233

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jcp.2012.08.010

Socpus ID

84868478081 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84868478081

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