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Volume 36, Issue 1
A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings

Ruming Zhang & Bo Zhang

DOI: 10.4208/jcm.1612-m2016-0501

J. Comp. Math., 36 (2018), pp. 110-127.

Published online: 2018-02

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  • Abstract

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formulation is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the Nyström method for the new integral equation. Numerical examples are also shown to illustrate the applicability of the new integral equation formulation.

  • Keywords

Scattering problem, Transmission condition, Periodic interface, Diffraction gratings, Boundary integral equations, Helmholtz equation.

  • AMS Subject Headings

74J20, 65R20.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

foeysii@mail.bnu.edu.cn (Ruming Zhang)

b.zhang@amt.ac.cn (Bo Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-110, author = {Zhang , Ruming and Zhang , Bo}, title = {A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {1}, pages = {110--127}, abstract = {

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formulation is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the Nyström method for the new integral equation. Numerical examples are also shown to illustrate the applicability of the new integral equation formulation.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1612-m2016-0501}, url = {http://global-sci.org/intro/article_detail/jcm/10585.html} }
TY - JOUR T1 - A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings AU - Zhang , Ruming AU - Zhang , Bo JO - Journal of Computational Mathematics VL - 1 SP - 110 EP - 127 PY - 2018 DA - 2018/02 SN - 36 DO - http://doi.org/10.4208/jcm.1612-m2016-0501 UR - https://global-sci.org/intro/article_detail/jcm/10585.html KW - Scattering problem, Transmission condition, Periodic interface, Diffraction gratings, Boundary integral equations, Helmholtz equation. AB -

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formulation is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the Nyström method for the new integral equation. Numerical examples are also shown to illustrate the applicability of the new integral equation formulation.

Zhang , Ruming and Zhang , Bo. (2018). A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings. Journal of Computational Mathematics. 36 (1). 110-127. doi:10.4208/jcm.1612-m2016-0501
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