Finite Difference Delay Modeling for Two-Dimensional Transverse Magnetic Time-Domain Integral Equations

Two-dimensional time-domain scattering using the nyström method and finite difference delay modeling

“…Substituting either of these approximations in to Eq. (3) and inverse transforming [2] results in a set of equations…”

“…Over the past decade, much research has been done to improve the efficiency and stability of time domain integral equations (TDIEs) [1,2]. Despite the advances made due to this work, some problems remain extremely difficult to solve accurately.…”

“…In this work, we propose an unconditionally stable TDIE method using the locally corrected Nyström (LCN) method [1,3] for spatial discretization and finite difference delay modeling (FDDM) [2] for temporal discretization. The use of a Nyström method reduces the time required to create the discrete convolution kernel, and simplifies the use of curved geometry models and fast methods.…”

Two‐dimensional transient scattering using the Nyström method and finite difference delay modeling

“…Finite difference delay modeling (FDDM) has the potential to overcome these problems [ Lin and Weile , 2010a]. FDDM was introduced by Wang et al [2008] and Lin and Weile [2010b], and it works by approximating the Laplace domain variable s by a z domain finite difference. While the stability advantages of FDDM were discussed by Wang et al [2008] and Lin and Weile [2010b], this paper goes further by (1) applying the FDDM method to a two‐dimensional problem and (2) using the Nyström method for spatial discretization.…”