Locating radiating sources for Maxwell's equations using the approximate inverse
Identifieur interne : 000721 ( Main/Curation ); précédent : 000720; suivant : 000722Locating radiating sources for Maxwell's equations using the approximate inverse
Auteurs : A. Lakhal [Allemagne] ; A K Louis [Allemagne]Source :
- Inverse Problems [ 0266-5611 ] ; 2008.
English descriptors
- Teeft :
- Adjoint problems, Ball centred, Bessel functions, Boundary measurements, Centred, Compact support, Computational effort, Contrast function, Convolution theorem, Current distribution, Current distributions, Current source, Current sources, Decoupled system, Divergence operator, Eld, Electric permittivity, Electric sources, Electromagnetic, Electromagnetic imaging, Electromagnetic waves, Full maxwell equations, Full maxwell model, Full maxwell system, Helmholtz equation, Helmholtz model, Homogeneous ball, Invariance properties, Inverse, Inverse medium problem, Inverse problems, Inverse source problem, Inversion, Lakhal, Legendre polynomial, Linear problems, Magnetic permeability, Many application areas, Maxwell equations, Nonlinear problems, Numerical experiment, Numerical simulations, Other hand, Positive constants, Reconstruction kernel, Refractive index, Regularization, Regularization method, Regularizing operator, Scalar, Scalar approximation, Second formula, Single illumination, Singular value decomposition, Singular values, Smooth boundary, Sobolev, Sobolev spaces, Straightforward computation, Target domain, Target region, Tomography.
Abstract
We present a new approach to solve inverse source problems for the three-dimensional time-harmonic Maxwell's equations using boundary measurements of the radiated fields. The modelling is based on the formulation as a system of integro-differential equations for the electric field. We introduce a method to recast the intertwined vector equations of Maxwell into decoupled scalar problems. The method of the approximate inverse is used both for regularization and the development of fast algorithms. We make the analysis of the method when data are collected on a spherical setting around the object. Based on the singular value decomposition, we study the smoothing properties for the underlying operator and derive an error estimate for the regularized solution in a Sobolev-space framework. Numerical simulations illustrate the efficiency and practical usefulness of the developed method.
Url:
DOI: 10.1088/0266-5611/24/4/045020
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :000F26
- to stream Istex, to step Curation: Pour aller vers cette notice dans l'étape Curation :000E50
- to stream Istex, to step Checkpoint: Pour aller vers cette notice dans l'étape Curation :000545
- to stream Main, to step Merge: Pour aller vers cette notice dans l'étape Curation :000721
Links to Exploration step
ISTEX:940898FE4A2CF81C21E40F8A26BCA21950B9C8F0Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Locating radiating sources for Maxwell's equations using the approximate inverse</title>
<author><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name>
</author>
<author><name sortKey="Louis, A K" sort="Louis, A K" uniqKey="Louis A" first="A K" last="Louis">A K Louis</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:940898FE4A2CF81C21E40F8A26BCA21950B9C8F0</idno>
<date when="2008" year="2008">2008</date>
<idno type="doi">10.1088/0266-5611/24/4/045020</idno>
<idno type="url">https://api.istex.fr/document/940898FE4A2CF81C21E40F8A26BCA21950B9C8F0/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000F26</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000F26</idno>
<idno type="wicri:Area/Istex/Curation">000E50</idno>
<idno type="wicri:Area/Istex/Checkpoint">000545</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000545</idno>
<idno type="wicri:doubleKey">0266-5611:2008:Lakhal A:locating:radiating:sources</idno>
<idno type="wicri:Area/Main/Merge">000721</idno>
<idno type="wicri:Area/Main/Curation">000721</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Locating radiating sources for Maxwell's equations using the approximate inverse</title>
<author><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name>
<affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country>
<wicri:regionArea>University of Saarland, Institute of Applied Mathematics, D-66041 Saarbrcken</wicri:regionArea>
<placeName><region type="land" nuts="2">Sarre (Land)</region>
<settlement type="city">Sarrebruck</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country>
</affiliation>
</author>
<author><name sortKey="Louis, A K" sort="Louis, A K" uniqKey="Louis A" first="A K" last="Louis">A K Louis</name>
<affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country>
<wicri:regionArea>University of Saarland, Institute of Applied Mathematics, D-66041 Saarbrcken</wicri:regionArea>
<placeName><region type="land" nuts="2">Sarre (Land)</region>
<settlement type="city">Sarrebruck</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Inverse Problems</title>
<title level="j" type="abbrev">Inverse Problems</title>
<idno type="ISSN">0266-5611</idno>
<idno type="eISSN">1361-6420</idno>
<imprint><publisher>IOP Publishing</publisher>
<date type="published" when="2008">2008</date>
<biblScope unit="volume">24</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="18">18</biblScope>
<biblScope unit="production">Printed in the UK</biblScope>
</imprint>
<idno type="ISSN">0266-5611</idno>
</series>
<idno type="istex">940898FE4A2CF81C21E40F8A26BCA21950B9C8F0</idno>
<idno type="DOI">10.1088/0266-5611/24/4/045020</idno>
<idno type="PII">S0266-5611(08)64272-0</idno>
<idno type="articleID">264272</idno>
<idno type="articleNumber">045020</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0266-5611</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Adjoint problems</term>
<term>Ball centred</term>
<term>Bessel functions</term>
<term>Boundary measurements</term>
<term>Centred</term>
<term>Compact support</term>
<term>Computational effort</term>
<term>Contrast function</term>
<term>Convolution theorem</term>
<term>Current distribution</term>
<term>Current distributions</term>
<term>Current source</term>
<term>Current sources</term>
<term>Decoupled system</term>
<term>Divergence operator</term>
<term>Eld</term>
<term>Electric permittivity</term>
<term>Electric sources</term>
<term>Electromagnetic</term>
<term>Electromagnetic imaging</term>
<term>Electromagnetic waves</term>
<term>Full maxwell equations</term>
<term>Full maxwell model</term>
<term>Full maxwell system</term>
<term>Helmholtz equation</term>
<term>Helmholtz model</term>
<term>Homogeneous ball</term>
<term>Invariance properties</term>
<term>Inverse</term>
<term>Inverse medium problem</term>
<term>Inverse problems</term>
<term>Inverse source problem</term>
<term>Inversion</term>
<term>Lakhal</term>
<term>Legendre polynomial</term>
<term>Linear problems</term>
<term>Magnetic permeability</term>
<term>Many application areas</term>
<term>Maxwell equations</term>
<term>Nonlinear problems</term>
<term>Numerical experiment</term>
<term>Numerical simulations</term>
<term>Other hand</term>
<term>Positive constants</term>
<term>Reconstruction kernel</term>
<term>Refractive index</term>
<term>Regularization</term>
<term>Regularization method</term>
<term>Regularizing operator</term>
<term>Scalar</term>
<term>Scalar approximation</term>
<term>Second formula</term>
<term>Single illumination</term>
<term>Singular value decomposition</term>
<term>Singular values</term>
<term>Smooth boundary</term>
<term>Sobolev</term>
<term>Sobolev spaces</term>
<term>Straightforward computation</term>
<term>Target domain</term>
<term>Target region</term>
<term>Tomography</term>
</keywords>
</textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract">We present a new approach to solve inverse source problems for the three-dimensional time-harmonic Maxwell's equations using boundary measurements of the radiated fields. The modelling is based on the formulation as a system of integro-differential equations for the electric field. We introduce a method to recast the intertwined vector equations of Maxwell into decoupled scalar problems. The method of the approximate inverse is used both for regularization and the development of fast algorithms. We make the analysis of the method when data are collected on a spherical setting around the object. Based on the singular value decomposition, we study the smoothing properties for the underlying operator and derive an error estimate for the regularized solution in a Sobolev-space framework. Numerical simulations illustrate the efficiency and practical usefulness of the developed method.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Sarre/explor/MusicSarreV3/Data/Main/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000721 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Curation/biblio.hfd -nk 000721 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Sarre |area= MusicSarreV3 |flux= Main |étape= Curation |type= RBID |clé= ISTEX:940898FE4A2CF81C21E40F8A26BCA21950B9C8F0 |texte= Locating radiating sources for Maxwell's equations using the approximate inverse }}
This area was generated with Dilib version V0.6.33. |