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arXiv · 2510.07989

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

Van Chien Le·Cedric Münger·Francesco P. Andriulli·Kristof Cools
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Abstract

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.

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Van Chien Le, Cedric Münger, Francesco P. Andriulli, Kristof Cools. 2025-10-09. A Stable, Accurate, and Well-Conditioned Time-Domain PMCHWT Formulation. https://doi.org/10.1109/tap.2026.3703814

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