Title

Conformal conservation laws and geometric integration for damped Hamiltonian PDEs

Authors

Authors

B. E. Moore; L. Norena;C. M. Schober

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Comput. Phys.

Keywords

Multi-symplectic PDE; Linear dissipation; Structure-preserving; algorithm; Preissman box scheme; Discrete gradient methods; NONLINEAR SCHRODINGER-EQUATION; PARTIAL-DIFFERENTIAL-EQUATIONS; KLEIN-GORDON EQUATION; DE-VRIES EQUATION; WAVE-EQUATIONS; RUNGE-KUTTA; NUMERICAL-METHODS; VARIATIONAL INTEGRATORS; SPLITTING METHODS; SCHEMES; Computer Science, Interdisciplinary Applications; Physics, Mathematical

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 Schrodinger equation, are used as examples to demonstrate the results. (C) 2012 Elsevier Inc. All rights reserved.

Journal Title

Journal of Computational Physics

Volume

232

Issue/Number

1

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

214

Last Page

233

WOS Identifier

WOS:000310647100015

ISSN

0021-9991

Share

COinS