Mimetic discretizations for Maxwell's equations

We have constructed reliable finite difference methods for approximating th e solution to Maxwell's equations using accurate discrete analogs of differ ential operators that satisfy the identities and theorems of vector and ten sor calculus in discrete form. The numerical approximation does nor have sp urious modes and mimics many fundamental properties of the underlying physi cal problem including conservation laws, symmetries in the solution, and th e nondivergence of particular vector fields. Numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous a nd for nonorthogonal, nonsmooth computational grids.