On the Late-Time Instability of MOT solution to the Time-Domain PMCHWT Equation

2025/09/18 by Le, Van Chien, Giunzioni, Viviana, Cordel, Pierrick +2 · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2509.14995

Abstract

This paper investigates the late-time instability of marching-on-in-time solution to the time-domain PMCHWT equation. The stability analysis identifies the static solenoidal nullspace of the time-domain electric field integral operator as the primary cause of instability. Furthermore, it reveals that the instability mechanisms of the time-domain PMCHWT equation are fundamentally different from those of the time-domain electric field integral equation. In particular, the PMCHWT's instability is much more sensitive to numerical quadrature errors, and its spectral characteristics are strongly influenced by the topology and smoothness of the scatterer surface.

Citations

• Boundary element methods for the magnetic field integral equation on polyhedra
• A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors

Cited by

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

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