WIAS Preprint No. 649, (2001)

Finite element solution of conical diffraction problems



Authors

  • Elschner, Johannes
  • Hinder, Rainer
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 78A45 78M10 65N30

Keywords

  • Conical diffraction, system of Helmholtz equations, transmission problem, strongly elliptic variational formulation, finite element solution

DOI

10.20347/WIAS.PREPRINT.649

Abstract

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in ℝ2 coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.

Appeared in

  • Advances in Computational Mathematics 16 (2002), pp. 139-156

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