Multigrid for Time-Harmonic Eddy Currents without Gauge

  • O. Sterz
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 4)


The application of multigrid (MG) methods for the solution of electromagnetic problems has attracted attention in recent years (e.g. [8]). These problems are related to bilinear forms (curl·, curl·)L Ω 2 +α (·, ·)L Ω 2 , α ∈ ℝ, which require special smoothers as presented in [1,7]. This paper shows by numerical experiments that these ideas also work for the time-harmonic eddy currents, i.e. for complex bilinear forms (curl·, curl·)L Ω 2 +iα (·, ·)L Ω 2 . Furthermore, an approximate projection procedure is presented that allows the application of multigrid to an un-gauged electric formulation even if there are regions with zero conductivity. Numerical results are shown for the TEAM Workshop problem 7.


Bilinear Form Benchmark Problem Multigrid Method Weak Divergence Projection Step 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • O. Sterz
    • 1
  1. 1.Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)Universität HeidelbergHeidelbergGermany

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