A Non-Uniform Mesh High-Order Finite-Difference Time-Domain Method based on Biorthogonal Interpolating Functions

Abstract

This paper addresses, for the first time, the question of non-uniform meshing within the context of a recently formulated high-order finite-difference technique that employs Deslauriers-Dubuc biorthogonal interpolating basis functions for the expansion of electromagnetic field components in space. To that end, a domain overriding approach is developed and shown to present a very low level of reflections at interfaces between meshes of different densities, enhancing the accuracy and versatility of the Deslauriers-Dubuc scheme (which lends itself to the modeling of complex, inhomogeneous media, unlike earlier similar methods), while providing a generic approach to embedding subgrids within high-order finite-difference meshes.