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Multilevel Solution of the Time-Harmonic Maxwell's Equations Based on Edge Elements

Please always quote using this URN: urn:nbn:de:0297-zib-2619
  • A widely used approach for the computation of time-harmonic electromagnetic fields is based on the well-known double-curl equation for either $\vec E$ or $\vec H$. An appealing choice for finite element discretizations are edge elements, the lowest order variant of a $H(curl)$-conforming basis. However, the large nullspace of the curl-operator gives rise to serious drawbacks. It comprises a considerable part of all spectral modes on the finite element grid, polluting the solution with non-physical contributions and causing the deterioration of standard iterative solvers. We tackle these problems by a nested multilevel algorithm. After every V-cycle in the $H(curl)$-conforming basis, the non-physical contributions are removed by a projection scheme. It requires the solution of Poisson's equation in the nullspace, which can be carried out efficiently by another multilevel iteration. The whole procedure yields convergence rates independent of the refinement level of the mesh. Numerical examples demonstrate the efficiency of the method.

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Metadaten
Author:Rudolf Beck, Ralf Hiptmair
Document Type:ZIB-Report
Date of first Publication:1996/12/04
Series (Serial Number):ZIB-Report (SC-96-51)
ZIB-Reportnumber:SC-96-51
Published in:Appeared in: Int. J. Numer. Meth. Engng. 45, 1999, pp. 901-920
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