Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations

Brian E. Moore

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 1, 20-28

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.

Keywords: Multi-symplectic PDE; Conformal symplectic; Structure-preserving algorithm; Splitting methods; Modified equations (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:1:p:20-28

DOI: 10.1016/j.matcom.2009.06.024

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