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Comparison of integral equations for the Maxwell transmission problem with general permittivities

Helsing, Johan LU ; Karlsson, Anders LU and Rosén, Andreas (2021) In Advances in Computational Mathematics 47(5).
Abstract

Two recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for non-magnetic materials. The winning integral equation turns out to be entirely free from false eigenwavenumbers for any passive materials, also for purely negative permittivity ratios and in the static limit, as well as free from false essential spectrum on non-smooth surfaces. It also appears to be numerically competitive to all other available integral equation reformulations of the Maxwell transmission problem, despite using eight scalar surface densities.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Boundary integral equation, Electromagnetic scattering, Maxwell’s equations, Non-smooth object, Surface plasmon wave, Transmission problem
in
Advances in Computational Mathematics
volume
47
issue
5
article number
76
publisher
Springer
external identifiers
  • scopus:85117341855
ISSN
1019-7168
DOI
10.1007/s10444-021-09904-4
language
English
LU publication?
yes
id
5d296630-460a-4a5c-b995-bb25770a0f79
date added to LUP
2021-12-16 16:02:21
date last changed
2022-04-27 06:44:16
@article{5d296630-460a-4a5c-b995-bb25770a0f79,
  abstract     = {{<p>Two recently derived integral equations for the Maxwell transmission problem are compared through numerical tests on simply connected axially symmetric domains for non-magnetic materials. The winning integral equation turns out to be entirely free from false eigenwavenumbers for any passive materials, also for purely negative permittivity ratios and in the static limit, as well as free from false essential spectrum on non-smooth surfaces. It also appears to be numerically competitive to all other available integral equation reformulations of the Maxwell transmission problem, despite using eight scalar surface densities.</p>}},
  author       = {{Helsing, Johan and Karlsson, Anders and Rosén, Andreas}},
  issn         = {{1019-7168}},
  keywords     = {{Boundary integral equation; Electromagnetic scattering; Maxwell’s equations; Non-smooth object; Surface plasmon wave; Transmission problem}},
  language     = {{eng}},
  number       = {{5}},
  publisher    = {{Springer}},
  series       = {{Advances in Computational Mathematics}},
  title        = {{Comparison of integral equations for the Maxwell transmission problem with general permittivities}},
  url          = {{http://dx.doi.org/10.1007/s10444-021-09904-4}},
  doi          = {{10.1007/s10444-021-09904-4}},
  volume       = {{47}},
  year         = {{2021}},
}