Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T10:48:26.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

Published online by Cambridge University Press:  20 August 2015

J. Coatléven  and
P. Joly
J. Coatléven*
Affiliation:
POems Project Team, UMR ENSTA/CNRS/INRIA, Inria Rocquencourt, 78153 Le Chesnay Cedex, France
P. Joly*
Affiliation:
POems Project Team, UMR ENSTA/CNRS/INRIA, Inria Rocquencourt, 78153 Le Chesnay Cedex, France
*
Corresponding author.Email:[email protected]
Email address:[email protected]
Get access

Abstract

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

Keywords

35C1535J0535Q6074J20Multiple-scatteringharmonic wave equationexact boundary conditionsperiodic media
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 303 - 318
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Balabane, M., Tirel, V., Décomposition de domaine pour un calcul hybride de l’équation de Helmholtz, C. R. Acad. Sci. Paris, t. 324, Série I, p. 281–286, 1997.CrossRefGoogle Scholar
[2]Duruflé, M., Intégration numérique et éléments finis d’ordre élevé appliqués aux équations de Maxwell en régime harmonique, Phd Thesis.Google Scholar
[3]Ehrhardt, M., Discrete Transparent Boundary Conditions for Schroedinger-type equations for non compactly supported initial data, Appl. Numer. Math., Vol. 58, pp. 660–673, 2008.Google Scholar
[4]Fliss, S., Joly, P., Li, J.-R., Exact boundary conditions for periodic waveguides containing a local perturbation, Commun. Comput. Phys., Vol. 1, No. 6, pp. 945–973, 2006.Google Scholar
[5]Fliss, S., Joly, P., Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media, Appl. Numer. Math., Vol. 59, No. 9, pp. 2155–2178, 2009.CrossRefGoogle Scholar
[6]Grote, M. J., Kirsch, C., Dirichlet-to-Neumann boundary conditions for multiple scattering problems, J. Comput. Phys., Vol. 201, 630-650, 2004.CrossRefGoogle Scholar
[7]Johnson, S.G., Joannopoulos, J. D., Photonic Crystal - The Road from Theory to Practice, Kluwer Acad. Publ., 2002.Google Scholar
[8]Martin, P.A., Multiple scattering: Interaction of time harmonic waves with N obstacles, Cambridge University Press, 2006.Google Scholar
[9]Potthast, R., Hassen, F. ben, Liu, J., On source analysis by wave splitting with applications in inverse scattering of multiple obstacles, J. Comput. Math., Vol. 25, No. 3, 266–281, 2007.Google Scholar
[10]Sakoda, K., Optical Properties of Photonic Crystals, Springer Verlag Berlin, 2001.CrossRefGoogle Scholar