Parallel PWTD-Accelerated Explicit Solution of the Time-Domain Electric Field Volume Integral Equation

A parallel plane-wave time-domain (PWTD)accelerated explicit marching-on-in-time (MOT) scheme for solving the time-domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite-difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as O(N
₈
log N
₈
) and O(N
₈
N
_t
), respectively. Here, N
₈
is the number of spatial basis functions and N
_t
is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed-memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.