A New Integral Equation Formulation for Scattering by Penetrable Diffraction Gratings

Authors

  • Ruming Zhang Center for Industrial Mathematics, University of Bremen, Bremen 28359, Germany
  • Bo Zhang Institute of Applied Mathematics, Chinese Academy of Sciences Beijing 100080, China

DOI:

https://doi.org/10.4208/jcm.1612-m2016-0501

Keywords:

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

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.

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Published

2018-09-17

Issue

Vol. 36 No. 1 (2018)

Section

Articles