Free Access
Issue
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
Page(s) 1363 - 1387
DOI https://doi.org/10.1051/m2an/2012006
Published online 11 April 2012
  1. A.-S. Bonnet-Ben Dhia, L. Chesnel and X. Claeys, Radiation condition for a non-smooth interface between a dielectric and a metamaterial [hal-00651008].
  2. A.-S. Bonnet-Ben Dhia, P. Ciarlet Jr. and C.M. Zwölf, A new compactness result for electromagnetic waves. Application to the transmission problem between dielectrics and metamaterials. Math. Models Methods Appl. Sci. 18 (2008) 1605–1631. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  3. A.-S. Bonnet-Ben Dhia, P. Ciarlet Jr. and C.M. Zwölf, Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math. 234 (2010) 1912–1919; Corrigendum J. Comput. Appl. Math. 234 (2010) 2616. [CrossRef] [MathSciNet]
  4. A.-S. Bonnet-Ben Dhia, M. Dauge and K. Ramdani, Analyse spectrale et singularités d’un problème de transmission non coercif. C.R. Acad. Sci. Paris, Ser. I 328 (1999) 717–720. [CrossRef]
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  6. L. Chesnel and P. Ciarlet Jr., Compact imbeddings in electromagnetism with interfaces between classical materials and meta-materials. SIAM J. Math. Anal. 43 (2011) 2150–2169. [CrossRef] [MathSciNet]
  7. X. Claeys, Analyse asymptotique et numérique de la diffraction d’ondes par des fils minces. Ph.D. thesis, Université Versailles – Saint-Quentin (2008) (in French).
  8. M. Costabel and E. Stephan, A direct boundary integral method for transmission problems. J. Math. Anal. Appl. 106 (1985) 367–413. [CrossRef] [MathSciNet]
  9. M. Dauge and B. Texier, Problèmes de transmission non coercifs dans des polygones. Technical Report 97–27, Université de Rennes 1, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France (1997) http://hal.archives-ouvertes.fr/docs/00/56/23/29/PDF/BenjaminT˙arxiv.pdf (in French).
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  11. P. Fernandes and M. Raffetto, Well posedness and finite element approximability of time-harmonic electromagnetic boundary value problems involving bianisotropic materials and metamaterials. Math. Models Methods Appl. Sci. 19 (2009) 2299–2335. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  12. V.A. Kozlov, V.G. Maz’ya and J. Rossmann, Elliptic Boundary Value Problems in Domains with Point Singularities, Mathematical Surveys and Monographs. Americain Mathematical Society 52 (1997).
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  14. W. McLean, Strongly elliptic systems and boundary integral equations. Cambridge University Press, Cambridge (2000).
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  16. S. Nicaise and A.M. Sändig, General interface problems-I. Math. Meth. Appl. Sci. 17 (1994) 395–429. [CrossRef] [MathSciNet]
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  18. S. Nicaise and J. Venel, A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients. J. Comput. Appl. Math. 235 (2011) 4272–4282. [CrossRef] [MathSciNet]
  19. G. Oliveri and M. Raffetto, A warning about metamaterials for users of frequency-domain numerical simulators. IEEE Trans. Antennas Propag. 56 (2008) 792–798. [CrossRef]
  20. J. Peetre, Another approach to elliptic boundary problems. Commun. Pure Appl. Math. 14 (1961) 711–731. [CrossRef] [MathSciNet]
  21. M. Raffetto, Ill-posed waveguide discontinuity problem involving metamaterials with impedance boundary conditions on the two ports. IET Sci. Meas. Technol. 1 (2007) 232–239. [CrossRef]
  22. K. Ramdani, Lignes supraconductrices : analyse mathématique et numérique. Ph.D. thesis, Université Paris 6 (1999) (in French).
  23. A.A. Sukhorukov, I.V. Shadrivov and Y.S. Kivshar, Wave scattering by metamaterial wedges and interfaces. Int. J. Numer. Model. 19 (2006) 105–117. [CrossRef]
  24. H. Wallén, H. Kettunen and A. Sihvola, Surface modes of negative-parameter interfaces and the importance of rounding sharp corners. Metamaterials 2 (2008) 113–121. [CrossRef]
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  26. C.M. Zwölf, Méthodes variationnelles pour la modélisation des problèmes de transmission d’onde électromagnétique entre diélectrique et méta-matériau. Ph.D. thesis, Université Versailles, Saint-Quentin (2008) (in French).

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