A finite‐difference time‐domain method using whitney elements

Abstract

A new finite‐difference time‐domain method is proposed. The key feature of this method is the use of Whitney‐element interpolation functions so that field values can be updated explicitly either by the differential or the integral form of Maxwell's equations. Numerical results are given for a 2D parallel‐plate waveguide. © 1994 John Wiley & Sons, Inc.

Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations

“…5 From a finite-difference standpoint, the above provides a strategy to derive stable and consistent-hence convergent [1]-finite-difference stencils in irregular simplicial meshes. This is contrast to some previous explicit time-domain schemes based on Whitney elements [61]- [63] that have (procedural equivalents of) discrete Hodge operators which are not necessarily SPD by construction. The above framework recognizes the need for two distinct finite-difference representations of the curl operators appearing in Maxwell curl equations, viz., and , for a discretization based upon a single mesh (as opposed to obe based upon dual meshes such as Yee's scheme), a property also shared by mimetic finite-difference methods [45].…”