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

Fuente: arXiv
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Main Authors: Herles, Leon, Mally, Mario, Ostrowski, Jörg, Schöps, Sebastian, Merkel, Melina
Format: Preprint
Published: 2025
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author Herles, Leon
Mally, Mario
Ostrowski, Jörg
Schöps, Sebastian
Merkel, Melina
author_facet Herles, Leon
Mally, Mario
Ostrowski, Jörg
Schöps, Sebastian
Merkel, Melina
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_18235
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain
Herles, Leon
Mally, Mario
Ostrowski, Jörg
Schöps, Sebastian
Merkel, Melina
Numerical Analysis
Computational Engineering, Finance, and Science
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.
title A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain
topic Numerical Analysis
Computational Engineering, Finance, and Science
url https://arxiv.org/abs/2507.18235