MOT Solution of the PMCHWT Equation for Analyzing Transient Scattering from Conductive Dielectrics

Abstract

Transient electromagnetic interactions on conductive dielectric scatterers are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation with a marching on-in-time (MOT) scheme. The proposed scheme, unlike the previously developed ones, permits the analysis on scatterers with multiple volumes of different conductivity. This is achieved by maintaining an extra temporal convolution that only depends on permittivity and conductivity of these volumes. Its discretization and computation come at almost no additional cost and do not change the computational complexity of the resulting MOT solver. Accuracy and applicability of the MOT-PMCHWT solver are demonstrated by numerical examples.

On the initial condition problem of the time domain PMCHWT surface integral equation

“…The MOT scheme developed in [5], [6] can be used to solve (1) for unknowns J(r, t) and M(r, t). TD-PMCHWT-SIE in (1)- (2) involves the second-order time derivative of equivalent surface current densities due to L m {·} operator, which results in non-physical linearly increasing and constant components in the MOT solution as explained above.…”

“…Then, coefficients of J(r, t) and M(r, t) are computed from P jn and Q jn using numerical differentiation. It should be noted here that (i) Z i−j are same as the matrices obtained from the MOT discretization of (1) and computed using the numerical scheme described in [5], [6], and (ii) P(r, t) and Q(r, t) obtained by solving (6) are contaminated by spurious components. However these are eliminated from J(r, t) and M(r, t) by the numerical differentiation applied to P(r, t) and Q(r, t) [see (3)].…”

“…In [5], [6], an MOT scheme, which solves the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation (TD-PMCHWT-SIE), is developed for computing fields scattered from dispersive objects. Like the TD-EFIE, the linearly increasing and constant current components contaminates the MOT solution of this equation.…”

Quantum-corrected plasmonic field analysis using a time domain PMCHWT integral equation

“…These samples are obtained by inverse Fourier transforming the rational functions fitted to the frequency domain samples using the fast relaxed vector fitting (FRVF) algorithm [3]. Computation of the double temporal convolutions involving these time samples, which are called for by the MOT scheme, is carried out using the technique described in [4]. …”

“…I i is solved using the well-known MOT scheme [2]. The elements of Z i−j call for the computation of a double temporal convolution [see the terms Q m {ε m (t) * J l (r, t)} and L m {ε m (t) * M l (r, t)} in (3)], which is carried out efficiently using the method proposed in [4]. It is assumed that all V m are non-magnetic, i.e., µ m = µ 0 .…”