Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme

2003/02/24 by Hongling Su, Su, Hongling, Mengzhao Qin +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0302058

13 pages, 4 figures

arxiv created 2003/02/24 · arxiv updated 2009/11/30

Abstract

In this paper we discussed the self-adjointness of the Maxwell's equations with variable coefficients ε and μ. Three different Lagrangian are attained. By the Legendre transformation, a multisymplectic Bridge's (Hamilton) form is obtained. Based on the multisymplectic structure, the multisymplectic conservation law of the system is derived and a nine-point Preissman multisymplectic scheme which preserve the multisymplectic conservation law is given for the Maxwell's equations in an inhomogeneous, isotropic and lossless medium. At last a numerical example is illustrated.

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