Mimetic Discretizations for Maxwell s Equations 1999 17 citations ? 5 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 highquality of the method when the medium is strongly discontinuous and for nonorthogonal, nonsmooth computational grids. 1. Introduction. We are developing a discrete analog of vector and tensor calculus that can be used to accurately approximate continuum models for a wide range of physical processes on logically rectangular, nonorthogonal, nonsmooth grids. These finite difference methods (FDMs) preserve fundamental properties of the original continuum differe...