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PreprintCC BY-NC-ND 4.0HAL

Helmholtz problem with a thin layer of variable thickness

  • Jason Tridon
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Abstract

We account for the skin effect in the Helmholtz transmission problem with dissipative permittivities and permeabilities. We derive approximate boundary transmission conditions of Ventcel type via a Taylor expansion in the characteristic size of the thin layer. We show the well-posedness of the resulting problems thanks to the study of saddle-point formulations. The theoretical results are illustrated through numerical simulations with finite elements.

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Cite

BibTeXRIS
BibTeX
@misc{tridon2026helmholtz,
  title = {{Helmholtz problem with a thin layer of variable thickness}},
  author = {Jason Tridon},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://univ-pau.hal.science/hal-05841302v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Helmholtz problem with a thin layer of variable thickness
AU  - Jason Tridon
PY  - 2026
DA  - 2026/10/27
PB  - HAL
UR  - https://univ-pau.hal.science/hal-05841302v1
AB  - We account for the skin effect in the Helmholtz transmission problem with dissipative permittivities and permeabilities. We derive approximate boundary transmission conditions of Ventcel type via a Taylor expansion in the characteristic size of the thin layer. We show the well-posedness of the resulting problems thanks to the study of saddle-point formulations. The theoretical results are illustrated through numerical simulations with finite elements.
ER  -