Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 8 min ago
PreprintCC BY 4.0arXiv

A Hybridizable Discontinuous Galerkin Method for Time-Modulated Drude--Lorentz Media

  • Jeonghun J. Lee
Open at sourcePDFDOICite

Abstract

We formulate and analyze a hybridizable discontinuous Galerkin (HDG) method for Maxwell's equations coupled to four time-modulated Drude--Lorentz models: modulated in-coupling, modulated polarization density, modulated current density, and modulated effective mass. The use of electric displacement and model-dependent continuous material states gives a common treatment of temporal interfaces while preserving the distinct physical transmission rules. We derive energy and stability estimates, establish spatial and event-aligned time-error bounds, and separate time-integration error from error caused by misplaced switching times. Numerical experiments in three dimensions and in reduced modal systems confirm the predicted spatial, temporal, and switch-timing behavior, including the field-jump effect specific to the polarization-density model.

Related

  1. A Neural-network-based multiscale Hybridizable Discontinuous Galerkin method for solving PDEs in porous media
    Tony Haines, Ke Shi
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. Hybridizable Discontinuous Galerkin methods for the Keller-Segel model
    Silvia Bertoluzza, Gabriella Bretti, Micol Pennacchio +1
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs
    Andrew Welter, Thea Collin, Ngoc Cuong Nguyen +1
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingFluid dynamicsarXiv
  4. The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes
    Leilei Wei, Yanping Chen, Fangfang Qin +2
    Applied Numerical MathematicsPeer-reviewedLicence not stated8 citedGeneral mathematicsOpenAlex
  5. A Local Discontinuous Galerkin method for the modified Camassa--Holm equation
    Xiang-Ke Chang, Yong Liu, Qi Tao
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{lee2026hybridizable,
  title = {{A Hybridizable Discontinuous Galerkin Method for Time-Modulated Drude--Lorentz Media}},
  author = {Jeonghun J. Lee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21991},
  eprint = {2610.21991},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21991},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Hybridizable Discontinuous Galerkin Method for Time-Modulated Drude--Lorentz Media
AU  - Jeonghun J. Lee
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21991
UR  - https://arxiv.org/abs/2610.21991
AB  - We formulate and analyze a hybridizable discontinuous Galerkin (HDG) method for Maxwell's equations coupled to four time-modulated Drude--Lorentz models: modulated in-coupling, modulated polarization density, modulated current density, and modulated effective mass. The use of electric displacement and model-dependent continuous material states gives a common treatment of temporal interfaces while preserving the distinct physical transmission rules. We derive energy and stability estimates, establish spatial and event-aligned time-error bounds, and separate time-integration error from error caused by misplaced switching times. Numerical experiments in three dimensions and in reduced modal systems confirm the predicted spatial, temporal, and switch-timing behavior, including the field-jump effect specific to the polarization-density model.
ER  -