A stabilized Two-Step Formulation of Maxwell's Equations in the time-domain
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909849088950272 |
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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 |