| Issue |
ESAIM: M2AN
Volume 60, Number 4, July-August 2026
|
|
|---|---|---|
| Page(s) | 1769 - 1803 | |
| DOI | https://doi.org/10.1051/m2an/2026042 | |
| Published online | 03 August 2026 | |
Hybrid FEM/IPDG semi-implicit schemes for time domain electromagnetic wave propagation in non-cylindrical coaxial cables
1 POEMS (UMR CNRS-INRIA-ENSTA Paris) Institut Polytechnique de Paris, Paris, France.
2 LAMMDA-ESST Hammam Sousse, Université de Sousse, Sousse, Tunisie.
3 Inria Saclay, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, Paris, France.
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
7
November
2025
Revised:
18
March
2026
Accepted:
28
April
2026
Abstract
In this work, we develop an efficient numerical method for solving 3D Maxwell’s equations in non-cylindrical coaxial cables. The main challenge arises from the elongated geometry of the computational domain, which induces strong anisotropy between the longitudinal direction (along the cable) and the transverse directions (within the cross-sections). This leads to the use of highly anisotropic meshes, where the longitudinal mesh size is much larger than the transverse one. Our objective is to design a numerical scheme that is explicit in the longitudinal direction, with a CFL stability condition depending only on the longitudinal mesh size. In a previous work, we achieved this for cylindrical cables by employing prismatic edge elements, 1D quadrature for longitudinal mass lumping, and a hybrid explicit/implicit time discretization. The present paper extends this approach to non-cylindrical cables, addressing several new difficulties with the following key ingredients: (1) representing the cable as a deformation of a reference cylindrical cable and employing mapping techniques between the physical and reference domains; (2) using an anisotropic space discretization that combines an interior penalty discontinuous Galerkin (IPDG) method in the transverse directions with a conforming finite element method in the longitudinal direction; (3) utilizing prismatic edge elements on a prismatic mesh of the reference cable; and (4) adapting the construction of the hybrid explicit–implicit time discretization to the new structure of the semi-discrete problem. From a theoretical perspective, the main difficulty lies in the stability analysis, which requires extending and adapting standard techniques for discontinuous Galerkin methods in space and energy methods in time.
Mathematics Subject Classification: 35Q61 / 78M10 / 65M60
Key words: Non-cylindrical coaxial cables / Maxwell's equations / hybrid numerical method / edge elements / discontinuous Galerkin method / numerical simulation
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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