We consider solutions to the time-harmonic Maxwell problem in . For such solution we propose a rigorous derivation of the asymptotic expansions in the interesting practical situation when a finite number of inhomogeneities of small diameter are embedded in the entire space. Then, we describe the behavior of the electromagnetic energy caused by the presence of these inhomogeneities.
Nous considérons des solutions des équations de Maxwell dans en présence d'un nombre fini d'inhomogénéités de petits diamètres. Pour de telles solutions, nous obtenons des formules asymptotiques rigoureuses. Puis, nous décrivons le comportement de l'énergie électromagnétique.
Accepted:
Published online:
@article{CRMATH_2008__346_5-6_287_0, author = {Daveau, Christian and Khelifi, Abdessatar}, title = {On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities}, journal = {Comptes Rendus. Math\'ematique}, pages = {287--292}, publisher = {Elsevier}, volume = {346}, number = {5-6}, year = {2008}, doi = {10.1016/j.crma.2008.01.019}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2008.01.019/} }
TY - JOUR AU - Daveau, Christian AU - Khelifi, Abdessatar TI - On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities JO - Comptes Rendus. Mathématique PY - 2008 SP - 287 EP - 292 VL - 346 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.01.019/ DO - 10.1016/j.crma.2008.01.019 LA - en ID - CRMATH_2008__346_5-6_287_0 ER -
%0 Journal Article %A Daveau, Christian %A Khelifi, Abdessatar %T On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities %J Comptes Rendus. Mathématique %D 2008 %P 287-292 %V 346 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.01.019/ %R 10.1016/j.crma.2008.01.019 %G en %F CRMATH_2008__346_5-6_287_0
Daveau, Christian; Khelifi, Abdessatar. On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities. Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 287-292. doi : 10.1016/j.crma.2008.01.019. http://www.numdam.org/articles/10.1016/j.crma.2008.01.019/
[1] Two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency, SIAM J. Sci. Comput., Volume 27 (2005), pp. 130-158
[2] Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, vol. 1846, Springer-Verlag, Berlin, 2004
[3] Electromagnetic scattering by small dielectric inhomogeneities, J. Math. Pures Appl., Volume 82 (2003), pp. 749-842
[4] Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations, J. Math. Pures Appl., Volume 80 (2001), pp. 769-814
[5] Correction of order three for the expansion of two dimensional electromagnetic fields perturbed by the presence of inhomogeneities of small diameter, J. Comput. Phys., Volume 189 (2003), pp. 371-389
[6] Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems, Volume 14 (1998), pp. 553-595
[7] Perturbation Methods in Applied Mathematics, Blaisdell, Walthan, MA, 1968
[8] Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence, Arch. Rat. Mech. Anal., Volume 105 (1989), pp. 299-326
[9] On the solution of time-harmonic scattering problems for Maxwell's equations, SIAM J. Math. Anal., Volume 27 (1996) no. 6, pp. 1597-1630
[10] Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Translations of Mathematical Monographs, vol. 102, American Mathematical Society, Providence, RI, 1992
[11] The Pólya–Szegö matrices in asymptotic models of dilute media, Eur. J. Appl. Math., Volume 8 (1997), pp. 595-621
[12] Acoustic and Electromagnetic Equations. Integral Representation for Harmonic Problem, Springer-Verlag, New York, 2001
[13] Vibration and Coupling of Continuous Systems, Springer-Verlag, 1989
[14] Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities, Math. Model. Numer. Anal., Volume 34 (2000), pp. 723-748
Cited by Sources: