The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that differential forms and their discrete counterparts ͑cochains͒ provide a natural bridge between the continuum and the lattice versions of the theory, allowing for a natural factorization of the field equations into topological field equations ͑i.e., invariant under homeomor-phisms͒ and metric field equations. The various potential sources of inconsistency in the discretization process are identified, distinguished, and discussed. A rationale for a consistent extension of the lattice theory to more general situations, such as to irregular lattices, is considered.

No abstract

No abstract

We present an analytical deri¨ation of a 3-D conformal ( ) perfectly matched layer PML for mesh termination in general orthogo-nal cur¨ilinear coordinates. The deri¨ation is based on the analytic continuation to complex space of the normal coordinate to the mesh termination. The resultant fields in the complex space do not obey Maxwell's equations. Howe¨er, it is demonstrated that, through simple field transformations, a new set of fields can be introduced so that they obey Maxwell's equations for an anisotropic medium with properly chosen constituti¨e parameters depending on the local radii of cur¨ature. The formulation presented here reco¨ers, as particular cases, the pre¨iously proposed Cartesian, cylindrical, and spherical PMLs. A pre¨iously ( ) employed anisotropic quasi-PML for conformal terminations is shown to be the large radius of cur¨ature approximation of the anisotropic conformal PML deri¨ed herein.

No abstract