A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 6, page 1193-1218
  • ISSN: 0764-583X

Abstract

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In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous three-dimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers. Our analysis extends results originally obtained in [Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Model. Numer. Anal. 37 (2003) 159–173] for steady state voltage potentials to time-harmonic Maxwell's equations.

How to cite

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Griesmaier, Roland. "A general perturbation formula for electromagnetic fields in presence of low volume scatterers." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1193-1218. <http://eudml.org/doc/276349>.

@article{Griesmaier2011,
abstract = { In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous three-dimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers. Our analysis extends results originally obtained in [Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Model. Numer. Anal. 37 (2003) 159–173] for steady state voltage potentials to time-harmonic Maxwell's equations. },
author = {Griesmaier, Roland},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Perturbation formulas; electromagnetic scattering; low volume scatterers; asymptotic expansions; perturbation formulas, electromagnetic scattering, low volume scatterers},
language = {eng},
month = {7},
number = {6},
pages = {1193-1218},
publisher = {EDP Sciences},
title = {A general perturbation formula for electromagnetic fields in presence of low volume scatterers},
url = {http://eudml.org/doc/276349},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Griesmaier, Roland
TI - A general perturbation formula for electromagnetic fields in presence of low volume scatterers
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/7//
PB - EDP Sciences
VL - 45
IS - 6
SP - 1193
EP - 1218
AB - In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous three-dimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers. Our analysis extends results originally obtained in [Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Model. Numer. Anal. 37 (2003) 159–173] for steady state voltage potentials to time-harmonic Maxwell's equations.
LA - eng
KW - Perturbation formulas; electromagnetic scattering; low volume scatterers; asymptotic expansions; perturbation formulas, electromagnetic scattering, low volume scatterers
UR - http://eudml.org/doc/276349
ER -

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