  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.
