Computation of Electromagnetic Fields for a Humidity Sensor

  • Wolfgang Hackbusch
  • Steffen Börm
Chapter

Abstract

We simulate an electromagnetic humidity sensor in order to determine its eigenfrequencies. The underlying model is given by Maxwell’s field equations, they are transformed into two decoupled two-dimensional problems by eliminating the magnetic field and changing to cylinder coordinates.

A time-harmonic approach leads to two generalized eigenproblems that are discretized using appropriate finite elements. The usual multigrid solvers are modified in order to cope with the anisotropic structure of the resulting matrices. These modifications can be used in order to build robust eigenproblem solvers of optimal asymptotic complexity.

Numerical experiments show that the resulting method is able to capture those effects that are relevant for the sensor under investigation.

Keywords

Multigrid Method Subspace Iteration Multigrid Solver Multigrid Technique Approximate Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Börm. Mehrgitterverfahren für die Simulation zylindersymmetrischer elektromagnetischer Felder. PhD thesis, Universität Kiel, 2000.Google Scholar
  2. 2.
    S. Börm. Robust multigrid for maxwell’s equation. Technical report, Universität Kiel, 2000.Google Scholar
  3. 3.
    S. Börm and R. Hiptmair. Analysis of tensor product multigrid. Technical Report 123, SFB 382, Universität Tübingen, Juni 1999. Submitted to Adv. Comp. Math.Google Scholar
  4. 4.
    S. Börm and R. Hiptmair. Multigrid computation of axisymmetric electromagnetic fields. Technical Report 138, SFB 382, Universität Tübingen, Oktober 1999.Google Scholar
  5. 5.
    J. Bramble, A. Knyazev, and J. Pasciak. A subspace preconditioning algorithm for eigenvector/eigenvalue computation. Advances Comp. Math., 6:159–189, 1996.MathSciNetCrossRefGoogle Scholar
  6. 6.
    G.H. Golub and C.F. Van Loan. Matrix computations. John Hopkins University Press, Baltimore, London, 2nd edition, 1989.MATHGoogle Scholar
  7. 7.
    W. Hackbusch. On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method. SIAM J. Numer. Anal., 16:201–223, 1979.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    W. Hackbusch. Multi-grid Methods and Applications. Springer-Verlag, Berlin, 1985.MATHGoogle Scholar
  9. 9.
    R. Hiptmair. Multigrid method for Maxwell’s equations. SIAM J. Numer. Anal. 361 204–225 1999Google Scholar
  10. 10.
    A. Knyazev. Preconditioned eigensolvers: Practical algorithms. Technical Report UCD-CCM 143, Center for Computational Mathematics, University of Colorado at Denver, 1999.Google Scholar
  11. 11.
    J.C. Nédélec. Mixed finite elements in R 3. Numer. Math., 35:315–341, 1980.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    C. Pflaum. A robust multilevel algorithm for anisotropic elliptic equations. Technical Report 224, Mathematisches Institut, Universität Würzburg, Würzbug, Germany, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  • Steffen Börm
    • 2
  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Universität KielGermany

Personalised recommendations