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Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme

Hongling Su·Mengzhao Qin
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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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Hongling Su, Mengzhao Qin. 2003-02-24. Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme. https://arxiv.org/abs/math-ph/0302058

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