Advances in Computational Mathematics

, Volume 16, Issue 2–3, pp 139–156

Finite Element Solution of Conical Diffraction Problems

  • Johannes Elschner
  • Rainer Hinder
  • Gunther Schmidt
Article

DOI: 10.1023/A:1014456026778

Cite this article as:
Elschner, J., Hinder, R. & Schmidt, G. Advances in Computational Mathematics (2002) 16: 139. doi:10.1023/A:1014456026778

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.

conical diffraction system of Helmholtz equations transmission problem strongly elliptic variational formulation finite element solution 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Johannes Elschner
    • 1
  • Rainer Hinder
    • 2
  • Gunther Schmidt
    • 1
  1. 1.Weierstrass Institute of Applied Analysis and StochasticsBerlinGermany
  2. 2.Forschungsinstitut für Optronik und MustererkennungEttlingenGermany

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