Wave splitting for time-dependent scattered field separation

Grote, Marcus J.; Kray, Marie; Nataf, Frédéric; Assous, Franck

doi:10.1016/j.crma.2015.03.008

Partial differential equations/Numerical analysis

Wave splitting for time-dependent scattered field separation
[Décomposition d'ondes pour la séparation de champs diffractés dans le domaine temporel]

Présenté par : Haïm Brézis

Grote, Marcus J.¹ ; Kray, Marie ¹ ; Nataf, Frédéric ^2,^3,⁴ ; Assous, Franck ⁵

¹ Department of Mathematics and Computer Sciences, University of Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland
² CNRS, UMR 7598, Laboratoire Jacques-Louis-Lions, 75005 Paris, France
³ UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis-Lions, 75005 Paris, France
⁴ INRIA Rocquencourt, Alpines, BP 105, 78153 Le Chesnay cedex, France
⁵ Department of Computer Sciences and Mathematics, Ariel University, 40700 Ariel, Israel

Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 523-527.

Résumé
Abstract

À partir des conditions aux limites absorbantes classiques, nous proposons une méthode dans le domaine temporel pour la séparation des champs d'onde diffractés dus à des sources ou des obstacles multiples. Contrairement aux techniques antérieures, notre procédé est local en temps et en espace, déterministe, et ne dépend pas de connaissances a priori du spectre de fréquence du signal.

Starting from classical absorbing boundary conditions, we propose a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. In contrast to previous techniques, our method is local in space and time, deterministic, and also avoids a priori assumptions on the frequency spectrum of the signal.

Reçu le : 2014-12-19
Accepté le : 2015-03-06
Publié le : 2015-04-04

DOI : 10.1016/j.crma.2015.03.008

Affiliations des auteurs :

Grote, Marcus J. ¹ ; Kray, Marie ¹ ; Nataf, Frédéric ^{2, 3, 4} ; Assous, Franck ⁵

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     title = {Wave splitting for time-dependent scattered field separation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {523--527},
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Grote, Marcus J.; Kray, Marie; Nataf, Frédéric; Assous, Franck. Wave splitting for time-dependent scattered field separation. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 523-527. doi : 10.1016/j.crma.2015.03.008. http://archive.numdam.org/articles/10.1016/j.crma.2015.03.008/

Bibliographie
Cité par

[1] Acosta, S. On-surface radiation condition for multiple scattering of waves, Comput. Methods Appl. Mech. Eng., Volume 283 (2015), pp. 1296-1309

[2] Ammari, H.; Bretin, E.; Garnier, J.; Jing, W.; Kang, H.; Wahab, A. Localization, stability, and resolution of topological derivative based imaging functionals in elasticity, SIAM J. Imaging Sci., Volume 6 (2013) no. 4, pp. 2174-2212

[3] Bayliss, A.; Turkel, E. Radiation boundary conditions for wave-like equations, Commun. Pure Appl. Math., Volume 33 (1980) no. 6, pp. 707-725

[4] Ben Hassen, F.; Liu, J.; Potthast, R. On source analysis by wave splitting with applications in inverse scattering of multiple obstacles, J. Comput. Math., Volume 25 (2007) no. 3, pp. 266-281

[5] Griesmaier, R.; Hanke, M.; Sylvester, J. Far field splitting for the Helmholtz equation, SIAM J. Numer. Anal., Volume 52 (2014) no. 1, pp. 343-362

[6] Grote, M.J.; Kirsch, C. Dirichlet-to-Neumann boundary conditions for multiple scattering problems, J. Comput. Phys., Volume 201 (2004) no. 2, pp. 630-650

[7] Grote, M.J.; Kirsch, C. Nonreflecting boundary condition for time-dependent multiple scattering, J. Comput. Phys., Volume 221 (2007) no. 1, pp. 41-67

[8] Grote, M.J.; Sim, I. Local nonreflecting boundary condition for time-dependent multiple scattering, J. Comput. Phys., Volume 230 (2011) no. 8, pp. 3135-3154

[9] Hagstrom, T.; Hariharan, S.I. A formulation of asymptotic and exact boundary conditions using local operators, Appl. Numer. Math., Volume 27 (1998), pp. 403-416

[10] Hecht, F. New development in FreeFem++, J. Numer. Math., Volume 20 (2012) no. 3–4, pp. 251-265

[11] Higdon, R.L. Radiation boundary conditions for elastic wave propagation, SIAM J. Numer. Anal., Volume 27 (1990) no. 4, pp. 831-869

[12] Klibanov, A.L.; Rasche, P.T.; Hughes, M.S.; Wojdyla, J.K.; Galen, K.P.; Wible, J.H.J.; Brandenburger, G.H. Detection of individual microbubbles of ultrasound contrast agents: imaging of free-floating and targeted bubbles, Invest. Radiol., Volume 39 (2004) no. 3, pp. 187-195

[13] Pernot, M.; Montaldo, G.; Tanter, M.; Fink, M. ‘Ultrasonic stars’ for time reversal focusing using induced cavitation bubbles, Appl. Phys. Lett., Volume 88 (2006) no. 3, p. 034102

[14] Potthast, R.; Fazi, F.M.; Nelson, P.A. Source splitting via the point source method, Inverse Probl., Volume 26 (2010) no. 4, p. 045002

[15] Twersky, V. On multiple scattering of waves, J. Res. Natl. Bur. Stand., Volume 64D (1960), pp. 715-730

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