Explicit Solution of the Time Domain Volume Integral Equation Using a Stable Predictor-Corrector Scheme

Abstract

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposed method is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.Index Terms-Electromagnetic transients, explicit scheme, marching-on-in-time, time-domain analysis, time-domain volume integral equation.

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

“…developed explicit MOT-TD-EFVIE solver, which leverages a predictor-corrector (PC) scheme to "stabilize" updates of the flux density during time marching [22]. Moreover, CPU parallelized [23] and GPU accelerated [24] implementations are developed to further advance the capability of the solver.…”

“…Then, a finite difference scheme is applied to the samples of the vector potential to "predict" the electric fields. At the corrector step, the electric fields are updated (i.e., corrected) using a time-dependent averaging factor that improves the accuracy while maintaining the stability (as opposed to stabilization scheme that leverages a constant averaging factor as proposed in [22]). Furthermore, a scalable CPU parallelized implementation of the proposed PWTD-PC-EFVIE solver is also described.…”

“…In (8), [ ] ⋅ G is the first order central difference approximation of the spatial operator ∇∇ ⋅ , which can be found in Appendix of [22].…”

Porting an explicit time-domain volume-integral-equation solver on gpus with openacc [open problems in cem]

“…T ime-domain volume-integral-equation (TDVIE) solvers are becoming attractive alternatives to fi nite-difference and fi nite-element schemes in analyzing transient electromagnetic scattering from inhomogeneous dielectric objects [1][2][3][4][5][6][7][8].…”

“…TDVIEs are oftentimes solved using the marching-on-intime (MOT) technique [1][2][3][4][5][6]. The marching-on-in-time scheme expands fi elds induced on the scatterer using local spatiotem poral basis functions.…”