Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme

Details Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme Multisymplectic Geometry Method for Maxwell's Equations and Multisymplectic Scheme

2003-02-24

arxiv.org/abs/math-ph/0302058v1

Physics

Mathematical Physics

13 pages, 4 figures

Scientific paper

In this paper we discussed the self-adjointness of the Maxwell's equations with variable coefficients $\epsilon$ and $\mu$. 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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