Locating radiating sources for Maxwell's equations using the approximate inverse
Identifieur interne : 000721 ( Main/Exploration ); 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
Affiliations:
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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><affiliations><list><country><li>Allemagne</li></country><region><li>Sarre (Land)</li></region><settlement><li>Sarrebruck</li></settlement></list><tree><country name="Allemagne"><region name="Sarre (Land)"><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name></region><name sortKey="Lakhal, A" sort="Lakhal, A" uniqKey="Lakhal A" first="A" last="Lakhal">A. Lakhal</name><name sortKey="Louis, A K" sort="Louis, A K" uniqKey="Louis A" first="A K" last="Louis">A K Louis</name><name sortKey="Louis, A K" sort="Louis, A K" uniqKey="Louis A" first="A K" last="Louis">A K Louis</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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