Abstract
The time harmonic eddy current model together with an impedance or [6] boundary condition is used to describe the electromagnetic field exterior to a lossy, highly conducting and possibly magnetic body at low frequencies. The so called penetration depth is assumed to be small. The problem will be reduced to a scalar, hypersingular boundary integral equation (BIE) on the surface Γ of the conductor. Convergence results and numerical examples are given. Some aspects on the computation are discussed in detail.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Ammari, C. Latiri-Grouz and J.C. Nédélec: The Leontovich boundary value problem for the time-harmonic Maxwell equations. Asymp. Anal. 18 (1998), no. 1&2, 33–48.
A. Bossavit: Computational electromagnetism. Academic Press, San Diego (1998).
M. Cessenat: Mathematical methods in electromagnetism. World Scientific, Singapore (1996).
S. Erichsen and S. Sauter: Efficient automatic quadrature in 3-d Galerkin BEM. Computer methods in applied mechanics and engineering, 157 (1998), 215–224.
P.R. Kotiuga: Topological considerations in coupling magnetic scalar potentials to stream functions describing surface currents. IEEE Trans. Mag. 25, no 4, (1989).
L.M. Leontovich: On approximate boundary conditions for electromagnetic fields on the surface of highly conducting bodies (in russian), Research in the propagation of radio waves (Academy of Sciences of the USSR, Moscow 1948).
E. Martensen: Potentialtheorie (Teubner, Stuttgart 1968).
Mayergoyz and G. Bredosian: On finite element implementation of impedance boundary conditions. J. Appl. Phys. 75, 10 (1994), 6027–6029.
K.M. Mitzner: An integral equation approach to scattering from a body of finite conductivity. Radio Science 2 (1967), 1459–1470.
T. v. Petersdorff and C. Schwab: Fully discrete multiscale Galerkin BEM, in Vol. 6 of Wavelet analysis and applications (Dahmen, Kurdila and Oswald, Academic Press 1997), 287 ff.
S.M. Rytov: Calcul du skin-effet par la méthode des perturbations. Journal de Physique USSR, 2 (1940), 233–242.
Y. Saad and M.H. Schultz: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7 (1986), 856–869.
O. Sterz and C. Schwab: A scalar boundary integrodifferential equation for eddy current problems using an impedance boundary condition. Submitted to Computing and Visualization in Science (2000).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sterz, O., Schwab, C. (2001). A Scalar BEM for Time Harmonic Eddy Current Problems with Impedance Boundary Conditions. In: van Rienen, U., Günther, M., Hecht, D. (eds) Scientific Computing in Electrical Engineering. Lecture Notes in Computational Science and Engineering, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56470-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-56470-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42173-3
Online ISBN: 978-3-642-56470-3
eBook Packages: Springer Book Archive