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

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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