  A mimetic spectral element discretization, utilizing a novel Galerkin
projection Hodge star operator, of the macroscopic Maxwell equations in
Hamiltonian form is presented. The idea of splitting purely topological and
metric dependent quantities is natural in the Hamiltonian modeling framework as
the Poisson bracket is metric free with the Hamiltonian containing all metric
information. This idea may be incorporated into the mimetic spectral element
method by directly discretizing the Poincar\'e duality structure. This "split
exterior calculus mimetic spectral element method" yields spatially discretized
Maxwell's equations which are Hamiltonian and exactly and strongly conserve
Gauss's laws. Moreover, the new discrete Hodge star operator is itself of
interest as a partition of the purely topological and metric dependent portions
of the Hodge star operator. As a simple test case, the numerical results of
applying this method to a one-dimensional version of Maxwell's equations are
given.
