Time-dependent electromagnetic waves in a cavity

Bo Kjellmert; Thomas Strömberg

Applications of Mathematics (2009)

  • Volume: 54, Issue: 1, page 17-45
  • ISSN: 0862-7940

Abstract

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The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential 𝐀 satisfying a wave equation with initial-boundary conditions. This description through 𝐀 is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed.

How to cite

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Kjellmert, Bo, and Strömberg, Thomas. "Time-dependent electromagnetic waves in a cavity." Applications of Mathematics 54.1 (2009): 17-45. <http://eudml.org/doc/37805>.

@article{Kjellmert2009,
abstract = {The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential $\{\bf A\}$ satisfying a wave equation with initial-boundary conditions. This description through $\{\bf A\}$ is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed.},
author = {Kjellmert, Bo, Strömberg, Thomas},
journal = {Applications of Mathematics},
keywords = {time-dependent electromagnetic field; cavity; vector and scalar potentials; Lorenz gauge; Chebyshev collocation; time-dependent electromagnetic field; cavity; vector and scalar potentials; Lorenz gauge; Chebyshev collocation},
language = {eng},
number = {1},
pages = {17-45},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Time-dependent electromagnetic waves in a cavity},
url = {http://eudml.org/doc/37805},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Kjellmert, Bo
AU - Strömberg, Thomas
TI - Time-dependent electromagnetic waves in a cavity
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 17
EP - 45
AB - The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential ${\bf A}$ satisfying a wave equation with initial-boundary conditions. This description through ${\bf A}$ is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed.
LA - eng
KW - time-dependent electromagnetic field; cavity; vector and scalar potentials; Lorenz gauge; Chebyshev collocation; time-dependent electromagnetic field; cavity; vector and scalar potentials; Lorenz gauge; Chebyshev collocation
UR - http://eudml.org/doc/37805
ER -

References

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