Title

Conformal Multi-Symplectic Integration Methods For Forced-Damped Semi-Linear Wave Equations

Keywords

Conformal symplectic; Modified equations; Multi-symplectic PDE; Splitting methods; Structure-preserving algorithm

Abstract

Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1 + 1 dimensions. Since a conformal multi-symplectic property has a concise form for these equations, numerical algorithms that preserve this property, from a modified equations point of view, are available. In effect, the modified equations for standard multi-symplectic methods and for space-time splitting methods satisfy a conformal multi-symplectic property, and the splitting schemes exactly preserve global symplecticity in a special case. It is also shown that the splitting schemes yield incorrect rates of energy/momentum dissipation, but this is not the case for standard multi-symplectic schemes. These methods work best for problems where the dissipation coefficients are small, and a forced-damped semi-linear wave equation is considered as an example.

Publication Date

9-1-2009

Publication Title

Mathematics and Computers in Simulation

Volume

80

Issue

1

Number of Pages

20-28

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matcom.2009.06.024

Socpus ID

70349180392 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/70349180392

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