Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

Larisa Beilina

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 702-733
  • ISSN: 2391-5455

Abstract

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We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.

How to cite

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Larisa Beilina. "Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system." Open Mathematics 11.4 (2013): 702-733. <http://eudml.org/doc/268949>.

@article{LarisaBeilina2013,
abstract = {We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.},
author = {Larisa Beilina},
journal = {Open Mathematics},
keywords = {Maxwell’s equation; Hybrid finite element/finite difference method; Energy estimates; Gauge condition; Stabilized finite element method; Maxwell's equation; hybrid finite element/finite difference method; energy estimates; gauge condition; stabilized finite element method},
language = {eng},
number = {4},
pages = {702-733},
title = {Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system},
url = {http://eudml.org/doc/268949},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Larisa Beilina
TI - Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 702
EP - 733
AB - We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.
LA - eng
KW - Maxwell’s equation; Hybrid finite element/finite difference method; Energy estimates; Gauge condition; Stabilized finite element method; Maxwell's equation; hybrid finite element/finite difference method; energy estimates; gauge condition; stabilized finite element method
UR - http://eudml.org/doc/268949
ER -

References

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