Mimetic Discretizations for Maxwell s Equations 1999 16 citations ? 4 self

Abstract:  . We have constructed reliable finite difference methods for approximating the solution to Maxwell's equations using accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form. The numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws, symmetries in the solution, and the nondivergence of particular vector fields. Numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal, nonsmooth computational grids. 1. Introduction. We will construct conservative finite difference methods (FDMs) for two dimensional Maxwell's curl equations for multimaterial medium on nonorthogonal, nonsmooth, logically-rectangula r computational grid. These FDMs are based on the discrete analogs of first-order differential operators, div, grad and curl, that satisfy dis...