Abstract
An electromagnetic field can be considered as slowly varying if the wavelength is large compared to the problem region. In the electro-quasistatic case it then may be assumed that the time-derivative of the magnetic flux is negligible, whereas the displacement currents have to be taken into account. Under these assumptions Maxwell’s equations for time harmonic fields reduce to a complex Poisson’s equation and discretization yields a complex symmetric system of equations. Krylov-subspace methods with an algebraic multigrid (AMG) preconditioner are used for fast solution. The electro-quasistatic model is applicable in many different constellations. This paper deals with applications from three different fields: high-voltage engineering, neural sensor-actor systems and the influence of slowly varying fields on human tissue.
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References
H.A. Haus, J.R. Melcher, Electromagnetic Fields and Energy, Prentice-Hall. Inc., 1989.
A. Bunse-Gerstner, R. Stöver, On a Conjugate Gradient-Type Method for Solving Complex Symmetric Linear Systems, Lin.Alg.Appl., Vol. 287 (1999): 105–123.
M. Clemens, R. Schuhmann, U. van Rienen, T. Weiland, Modern Krylov Subspace Methods in Electromagnetic Field Computation Using the Finite Integration Theorie, ACES Journal, Vol. 11 (1996): 70–84.
M. Clemens, T. Weiland, U. van Rienen, Comparison of Krylov-Type Methods for Complex Linear Systems Applied to High-Voltage Problems, IEEE-T.Mag., Vol. 34 (1998): 3335–3338.
J. Dudel, R. Menze, R.F. Schmidt, Neurowissenschaft, Springer, 2001.
R.W. Freund, N.M. Nachtigal, An Implementation of the QMR Method Based on Coupled Two-Term Recurrences, SIAM J.Sci.Comput., Vol. 15 (1994): 297–312.
J. Keener, J. Sneyd, au]Mathematical_Physiology, Springer, 2nd printing, 2001.
S. Keim, D. König, Study of the Behavior of Droplets on Polymeric Surfaces under the Influence of an Applied Electrical Field, Proc. IEEE-CEIDP (1999): 707–710.
M. Kneuer, Diploma Thesis, TU Darmstadt, 2000.
MAFIA 4, CST GmbH, Bad Nauheimer Str. 19, D-64289 Darmstadt, Germany.
S. Reitzinger, U. Schreiber, U. van Rienen, Algebraic Multigrid Methods for Complex Symmetric Matrices and Applications, Journal for Computational and Applied Mathematics, to appear.
S. Reitzinger, PEBBLES — User’s Guide, 1999, www.sfbO13.uni-linz.ac.at.
U. van Rienen, Numerical Methods in Computational Electrodynamics — Linear Systems in Practical Applications, Springer-LNCSE, Vol. 12, 2000.
U. Schreiber, U. van Rienen, S. Keim, Simulation of Electric Field Strength and Force Density on Contaminated H-V Insulators, Springer-LNCSE, Vol. 18 (2001): 79–86.
T. Weiland, A discretization method for the solution of Maxwell’s equation for six-component fields, Electron. Commun. AEÜ, Vol. 31 (1977): 116–120.
E.K. Yeargers, R.W. Shonkwiler, J.V. Herod, An Introduction to the Mathematics of Biology, Birkhäuser, 1996.
F.B. Sachse et al., Comparison of Solutions to the forward Problem in Electrophysiology with homogeneous, heterogeneous and anisotropic Impedance Model, Biomedizinische Technik, Vol. 42 (1997): 277–280.
H. Krüger, Zur numerischen Berechnung transienter elektromagnetischer Felder in gyrotopen Materialien, Der Andere Verlag, 2000.
S. Balay et al., PETSc home page (2001), http://www.mcs.anl.gov/petsc/petsc
S. Balay, W.D. Gropp, L.C. McInnes, B.F. Smith, PETSc Users Manual, Argonne National Laboratory, ANL-95/11 — Revision 2.1.3 (2002).
S. Balay, W.D. Gropp, L.C. Mclnnes, B.F. Smith, Efficient Management of Parallelism in Object Oriented Numerical Software Libraries, in E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.): Modern Software Tools in Scientific Computing, Birkhauser (1997): 163–202.
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Schreiber, U., Flehr, J., Motrescu, V., van Rienen, U. (2004). The Electro—Quasistatic Model in Different Applications. In: Schilders, W.H.A., ter Maten, E.J.W., Houben, S.H.M.J. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55872-6_39
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DOI: https://doi.org/10.1007/978-3-642-55872-6_39
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