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arXiv · 2507.18235

A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain

Leon Herles·Mario Mally·Jörg Ostrowski·Sebastian Schöps·Melina Merkel
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Abstract

Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a Galerkin discretization in space, we apply two different time-discretization schemes that are tailored to the first- and second-order in time partial differential equations of the two-step solution procedure used here. To address the low-frequency instability, we incorporate a generalized tree-cotree gauge that removes the singularity of the curl-curl operator, ensuring robustness even in the static limit. Numerical results on academic and application-oriented 3D problems confirm stability, accuracy, and the method's applicability to nonlinear, temperature-dependent materials.

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Leon Herles, Mario Mally, Jörg Ostrowski, Sebastian Schöps, Melina Merkel. 2025-07-24. A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain. https://doi.org/10.1109/tmag.2025.3619844

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