Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

  • Authors:

  • Hélène Barucq;Chokri Bekkey;Rabia Djellouli

  • Affiliations:

  • Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour, IPRA - Avenue de l'Université, BP 1155, Pau Cedex 64013, France;Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie, EPT, BP 743, La Marsa 2070, Tunisia;Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado at Boulder, Boulder, CO

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

We present a general procedure based on the pseudo-differential calculus for deriving artificial boundary conditions for an eigenvalue problem that characterizes the propagation of guided modes in optical waveguides. This new approach allows the construction of local conditions that (a) are independent of the frequency regime, (b) preserve the sparsity pattern of the finite element discretization, and (c) are applicable to arbitrarily shaped convex artificial boundaries. The last feature has the potential for reducing the size of the computational domain. Numerical results are presented to highlight the potential of conditions of order 1/2 and 1, for improving significantly the computational efficiency of finite element methods for the solution of optical waveguide problems.