Structure-preserving discretization of Maxwell's equations as a port-Hamiltonian system

Authors

Ghislain Haine, Denis Matignon, Florian Monteghetti

Abstract

This work demonstrates the discretization of the boundary-controlled Maxwell equations, recast as a port-Hamiltonian system (pHs). After a reminder on the Stokes-Dirac structure associated with the Maxwell system, we introduce different partitioned weak formulations that preserve the pHs structure, and its associated power balance, at the semi-discrete level. These weak formulations are compared through numerical applications to closed non-perfectly conducting cavities and open waveguides under transverse approximation.

Keywords

Port-Hamiltonian systems; Structure-preserving method; Maxwell’s equations; Charge preservation; Impedance boundary condition

Citation

• Journal: IFAC-PapersOnLine
• Year: 2022
• Volume: 55
• Issue: 30
• Pages: 424–429
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2022.11.090
• Note: 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022- Bayreuth, Germany, September 12-16, 2022

BibTeX

@article{Haine_2022,
  title={{Structure-preserving discretization of Maxwell’s equations as a port-Hamiltonian system}},
  volume={55},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2022.11.090},
  number={30},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Haine, Ghislain and Matignon, Denis and Monteghetti, Florian},
  year={2022},
  pages={424--429}
}

Download the bib file

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