Advances in Computational Mathematics

, Volume 36, Issue 1, pp 3–20 | Cite as

Numerical analysis for the scattering by obstacles in a homogeneous chiral environment

Article

Abstract

The scattering of time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by obstacles is studied. The problem is simplified to a two-dimensional scattering problem, and the existence and the uniqueness of solutions are discussed by a variational approach. The diffraction problem is solved by a finite element method with perfectly matched absorbing layers. Our computational experiments indicate that the method is efficient.

Keywords

Chiral media Chirality admittance Maxwell equations Perfectly matched layer 

Mathematics Subject Classifications (2010)

35Q60 65L60 78A45 

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References

  1. 1.
    Ammari, H., Bao, G.: Coupling of finite element and boundary element methods for the electromagnetic diffraction problem by a periodic chiral structure. J. Comput. Math. 26, 261–283 (2008)MATHMathSciNetGoogle Scholar
  2. 2.
    Ammari, H., Hamdache, K., Nédélec, J.C.: Chirality in the Maxwell equations by the dipole approximation. SIAM J. Appl. Math. 59, 2045–2059 (1999)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Ammari, H., Nédélec, J.C.: Time-harmonic electromagnetic fields in chiral media. In: Meister, E. (ed.) Modern Mathematical Methods in Diffraction Theory and its Applications in Engineering, pp. 174–202 (1997)Google Scholar
  4. 4.
    Ammari, H., Nédélec, J.C.: Small chirality behavior of solutions to electromagnetic scattering problems in chiral media. Math. Methods Appl. Sci. 21, 327–359 (1998)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Ammari, H., Nédélec, J.C.: Time-harmonic electromagnetic fields in thin chiral curved layers. SIAM J. Math. Analy. 29, 395–423 (1998)CrossRefMATHGoogle Scholar
  6. 6.
    Ammari, H., Nédélec, J.C.: Analysis of the diffraction from chiral gratings. In: Mathematical Modelling in Optical Science, pp. 79–106. SIAM Frontiers in Applied Mathematics (2001)Google Scholar
  7. 7.
    Ammari, H., Laouadi, M., Nédélec, J.C.: Low frequency behavior of solutions to electromagnetic scattering problems in chiral media. SIAM J. Appl. Math. 58, 1022–1042 (1998)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Athanasiadis, C., Costakis, G., Stratis, I.G.: Electromagnetic scattering by a homogeneous chiral obstacle in a chiral environment. SIAM J. Appl. Math. 64, 245–258 (2000)MATHMathSciNetGoogle Scholar
  9. 9.
    Babuška, I., Aziz, A.: Survey lectures on mathematical foundations of the finite element method. In: Aziz, A. (ed.) The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations, pp. 5–359. New York (1973)Google Scholar
  10. 10.
    Bao, G., Wu, H.J.: Convergence analysis of the perfectly matched layer problems for time-harmonic Maxwell’s equations. SIAM J. Numer. Anal. 43, 2121–2143 (2005)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Bramble, J., Pasciak, J.: Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems. Math. Comput. 76, 597–614 (2007)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Chen, Z.M., Liu, X.Z.: An adaptive perfectly mathed technique for time-harmonic scattering problems. SIAM J. Numer. Anal. 43, 645–671 (2005)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Chen, Z.M., Wu, H.J.: An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures. SIAM J. Numer. Anal. 41, 799–826 (2003)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Springer-Verlag, New York (1998)MATHGoogle Scholar
  15. 15.
    Kampia, R.D., Lakhtakia, A.: Extended Maxwell Garnett model for chiral-in-chiral composites. J. Phys., D 26, 1746–1758 (1993)CrossRefGoogle Scholar
  16. 16.
    Lakhtakia, A.: Beltrami Fields in Chiral Media. World Scientific Publishing Company, Singapore (1994)CrossRefGoogle Scholar
  17. 17.
    Lakhtakia, A., Varadan, V.K., Varadan, V.V.: Time-harmonic Electromagnetic Fields in Chiral Media. Springer, Berlin, Heidelberg, New York (1989)Google Scholar
  18. 18.
    Lakhtakia, A., Varadan, V.V., Varadan, V.K.: Radiation by a straight thin-wire antenna embedded in an isotropic chiral medium. IEEE Trans. Electromagn. Compat. 30, 84–87 (1988)CrossRefGoogle Scholar
  19. 19.
    Lakhtakia, A., Varadan, V.K., Varadan, V.V.: Radiation by a point electric dipole embedded in a chiral sphere. J. Phys., D 23, 481–485 (1990)CrossRefGoogle Scholar
  20. 20.
    Lakhtakia, A.: Regarding the scattering of electromagnetic waves in a chiral medium by a perfectly conducting sphere. In: Millimeter Wave and Microwave, pp. 223–226. New Delhi, Tata McGraw-Hill (1990)Google Scholar
  21. 21.
    Lindell, I.V., Silverman, M.P.: Plane-waves scattering from a nonchiral object in a chiral environment. J. Opt. Soc. Am. A 14, 79–90 (1997)CrossRefGoogle Scholar
  22. 22.
    Yang, X.Y., Zhang, D.Y., Ma, F.M.: An Optimal Perfectly Matched Layer Technique for Time-harmonic Scattering Problems. Mathematica Numerica Sinica (to appear)Google Scholar
  23. 23.
    Zhang, D.Y., Ma, F.M.: Two-dimensional electromagnetic scattering from periodic chiral structures and its finite element approximation. Northeast. Math. J. 20(2), 236–252 (2004)MATHMathSciNetGoogle Scholar
  24. 24.
    Zhang, D.Y., Ma, F.M.: A finite element method with perfectly matched absorbing layers for the wave scattering by a periodic chiral structure. J. Comput. Math. 25(4), 458–472 (2007)MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Deyue Zhang
    • 1
  • Yukun Guo
    • 1
  • Chengchun Gong
    • 1
  • Guan Wang
    • 1
    • 2
  1. 1.School of MathematicsJilin UniversityChangchunChina
  2. 2.School of MathematicsNortheast Dianli UniversityJilinChina

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