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Computation of Resonant Modes for Axisymmetric Cavities using hp-Version Finite Elements

by R. Hiptmair and P. D. Ledger

(Report number 2003-15)

Abstract
The computation of the resonant frequencies for open and closed cavities is not a trivial task: Multi-materials and sharp corners all give rise to highly singular eigenfunctions. However, an approach using hp-finite elements is well suited to such problems and, with the correct combination of h- and p-refinements, it yields the theoretically predicated exponential rates of convergence. In this paper, we present a novel approach to the solution of axisymmetric cavity problems which uses a hierarchic H1 and ${\vec H}(\hbox{curl})$ conforming finite element basis. A selection of numerical examples are included and these demonstrate that the exponential rates of convergence are achieved in practice.

Keywords:

@Techreport{HL03_327,
  author = {R. Hiptmair and P. D. Ledger},
  title = {Computation of Resonant Modes for Axisymmetric Cavities using hp-Version Finite Elements},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-15.pdf },
  year = {2003}
}

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