147
Views
13
CrossRef citations to date
0
Altmetric
Articles

A volume integral method for solving scattering problems from locally perturbed infinite periodic layers

&
Pages 130-158 | Received 15 Feb 2016, Accepted 04 Aug 2016, Published online: 25 Aug 2016

References

  • Vainikko G. Fast solvers of the Lippmann-Schwinger equation. In: Newark D,editor. Direct and inverse problems of mathematical physics. Vol. 5, International society for analysis, applications and computation. Dordrecht: Kluwer; 2000. p. 423–440.
  • Lechleiter A, Nguyen D-L. A trigonometric Galerkin method for volume integral equations arising in TM grating scattering. Adv. Comput. Math. 2014;40:1–25.
  • Coatléven J. Analyse mathématique et numérique de quelques problèmes d’ondes en milieu périodique [Mathematical and numerical analysis of some wave problems in periodic media] [PhD thesis]. Paris; Vol. 10; 2011.
  • Coatléven J. Helmholtz equation in periodic media with a line defect. J. Comput. Phys. 2012;231:1675–1704.
  • Joly P, Li J-R, Fliss S. Exact boundary conditions for periodic waveguides containing a local perturbation. Commun. Comput. Phys. 2006;1:945–973.
  • Fliss S. Analyse mathématique et numérique de problèmes de propagation des ondes dans des milieux périodiques infinis localement perturbés [Mathematical and numerical analysis of wave propagation problems in infinite locally perturbed periodic media] [PhD thesis]. Paris: Ecole Polytechnique X; 2009.
  • Lechleiter A, Nguyen D-L. Volume integral equations for scattering from anisotropic diffraction gratings. Math. Methods Appl. Sci. 2013;36:262–274.
  • Hohage T. On the numerical solution of a three-dimensional inverse medium scattering problem. Inverse Probl. 2001;17:1743–1763.
  • Hohage T. Fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem. J. Comp. Phys. 2006;214:224–238.
  • Lechleiter A, Ritterbusch S. A variational method for wave scattering from penetrable rough layers. IMA J. Appl. Math. 2010;75:366–391.
  • Bonnet-Bendhia A-S, Starling F. Guided waves by electromagnetic gratings and nonuniqueness examples for the diffraction problem. Math. Methods Appl. Sci. 1994;17:305–338.
  • Chandler-Wilde SN, Monk P, Thomas M. The mathematics of scattering by unbounded, rough, inhomogeneous layers. J. Comput. Appl. Math. 2007;204:549–559.
  • Haddar H, Lechleiter A. Electromagnetic wave scattering from rough penetrable layers. SIAM J. Math. Anal. 2011;43:2418–2443.
  • Lechleiter A, Nguyen D-L. On uniqueness in electromagnetic scattering from biperiodic structures. ESAIM Math. Model. Numer. Anal. 2013;47:1167–1184.
  • Arens T, Hohage T. On radiation conditions for rough surface scattering problems. IMA J. Appl. Math. 2005;70:839–847.
  • Kuchment P. Floquet theory for partial differential equations. Vol. 60, Operator theory: advances and applications. Basel: Birkhäuser Verlag; 1993.
  • Kirsch A. Diffraction by periodic structures. In: Pävarinta L, Somersalo E,editors. Proceedings of the Lapland Conference on inverse problems. Saariselkä: Springer; 1993. p. 87–102.
  • Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 3rd ed. Vol. 93, Applied mathematical sciences. New York (NY): Springer; 2013.
  • Saranen J, Vainikko G. Periodic integral and pseudodifferential equations with numerical approximation. New York (NY): Springer; 2002.
  • Sauter S, Schwab C. Boundary element methods. 1st ed. Berlin: Springer; 2007.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.