A Stable, Accurate, and Well-Conditioned Time-Domain PMCHWT Formulation

Abstract

This article introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects based on the time-domain Poggio–Miller–Chang–Harrington–Wu–Tsai (TD-PMCHWT) equation. To address dense-mesh breakdown, a multiplicative Calderón preconditioner constructed from a modified static electric field integral operator (EFIO) is employed. Large-timestep breakdown and late-time instability are simultaneously resolved through a rescaling of the Helmholtz components using quasi-Helmholtz projectors, with temporal differentiation and integration serving as the rescaling operators. This rescaling additionally balances the loop and star components in the large-timestep regime, thereby preventing loss of accuracy in the secondary quantities caused by numerical cancellation. The resulting discrete system is solved using a marching-on-in-time (MOT) scheme in conjunction with iterative solvers. Numerical experiments for simply and multiply connected dielectric scatterers, including highly nonsmooth geometries, corroborate the stability and efficiency of the proposed approach and demonstrate its ability to produce accurate derived quantities in the large-timestep regime.