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

This paper introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects, based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calder\'on preconditioner constructed from a modified static electric field integral operator 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 scheme in conjunction with iterative solvers. Numerical experiments for simply- and multiply-connected dielectric scatterers, including highly non-smooth geometries, corroborate the stability and efficiency of the proposed approach and demonstrate its ability to produce accurate derived quantities in the large-timestep regime.