Finite Element Solution of Conical Diffraction Problems

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• 作者：Johannes Elschner ; Rainer Hinder and Gunther Schmidt
• 关键词：conical diffraction ; system of Helmholtz equations ; transmission problem ; strongly elliptic variational formulation ; finite element solution
• 刊名：Advances in Computational Mathematics
• 出版年：2002
• 出版时间：2002
• 年：2002
• 卷：16
• 期：2/3
• 页码：139-156
• 全文大小：162 KB
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Calculus of Variations and Optimal Control
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9044

文摘

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.