Skip to main content
SpringerLink
Log in

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

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ammari, H., Nédélec, J.C.: Time-harmonic electromagnetic fields in thin chiral curved layers. SIAM J. Math. Analy. 29, 395–423 (1998)

    Article  MATH  Google Scholar 

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  14. Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. Springer-Verlag, New York (1998)

    MATH  Google Scholar 

  15. Kampia, R.D., Lakhtakia, A.: Extended Maxwell Garnett model for chiral-in-chiral composites. J. Phys., D 26, 1746–1758 (1993)

    Article  Google Scholar 

  16. Lakhtakia, A.: Beltrami Fields in Chiral Media. World Scientific Publishing Company, Singapore (1994)

    Book  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

  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)

    MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, China

    Deyue Zhang, Yukun Guo, Chengchun Gong & Guan Wang

  2. School of Mathematics, Northeast Dianli University, Jilin, 132012, China

    Guan Wang

Authors
  1. Deyue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yukun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chengchun Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deyue Zhang.

Additional information

Communicated by Martin Stynes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, D., Guo, Y., Gong, C. et al. Numerical analysis for the scattering by obstacles in a homogeneous chiral environment. Adv Comput Math 36, 3–20 (2012). https://doi.org/10.1007/s10444-010-9169-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-010-9169-9

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation