Error control in the perfectly matched layer based multilevel fast multipole algorithm

  • Authors:

  • Dries Vande Ginste;Luc Knockaert;Daniël De Zutter

  • Affiliations:

  • Department of Information Technology, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium;Department of Information Technology, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium;Department of Information Technology, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

The development of efficient algorithms to analyze complex electromagnetic structures is of topical interest. Application of these algorithms in commercial solvers requires rigorous error controllability. In this paper we focus on the perfectly matched layer based multilevel fast multipole algorithm (PML-MLFMA), a dedicated technique constructed to efficiently analyze large planar structures. More specifically the crux of the algorithm, viz. the pertinent layered medium Green functions, is under investigation. Therefore, particular attention is paid to the plane wave decomposition for 2-D homogeneous space Green functions in very lossy media, as needed in the PML-MLFMA. The result of the investigations is twofold. First, upper bounds expressing the required number of samples in the plane wave decomposition as a function of a preset accuracy are rigorously derived. These formulas can be used in 2-D homogeneous (lossy) media MLFMAs. Second, a more heuristic approach to control the error of the PML-MLFMA's Green functions is presented. The theory is verified by means of several numerical experiments.