Error Estimation and Performance Control for the (2,4) FDTD Method in Lossy Spaces

A new theoretical approach for the construction of extended-stencil finite-difference time-domain (FDTD) algorithms, particularly suited for 2-D domains comprising lossy materials, is presented in this paper. Rather than implementing the standard type of spatial operators, we apply dispersion-relation-preserving (DRP) concepts and extract modified difference approximations, based on specific accuracy requirements. A key element in this process is the prediction of the combined space/time discretization artifacts with the aid of a suitable error expression, whose proper manipulation facilitates the improvement of the discrete models irrespective of propagation angles. With this tool at hand, three novel schemes are derived, theoretical limits regarding their performance are presented, and illustrative comparisons with the standard (2,4) technique are provided.