Article ID Journal Published Year Pages File Type
522070 Journal of Computational Physics 2008 15 Pages PDF
Abstract

Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space–time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge–Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the MS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of MS integrators in the nonlinear regime.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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