Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T08:34:39.846Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical scheme for the electromagnetic response in thin conductors of arbitrary planar shape

Published online by Cambridge University Press:  17 February 2009

P. F. Siew
P. F. Siew
Affiliation:
School of Maths and Stats, Curtin University of Technology, Perth, Western Australia6001.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A calculation of the electromagnetic response of a thin conductor in the presence of an exciting primary magnetic field has been attempted by various authors. Analytic solutions are obtainable when either the conductor is of infinite extent or when the problem possesses some symmetry. The loss of symmetry makes the problem difficult to solve except for the simplest shape – that of a circular conductor. A numerical method has been used for the rectangular conductor by other authors. In this paper we consider the response due to a thin plane conductor of arbitrary shape. The method involves the numerical generation of a set of body-fitted orthogonal curvilinear coordinates which maps the conductor onto a unit square. Good orthogonal grids can be generated for shapes that do not deviate too far from the rectangular. In terms of these curvilinear coordinates the vector potential for the area current density satisfies an integro-differential equation which is solved numerically.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 4 , April 1994 , pp. 479 - 497
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Ashour, A. A., “Electromagnetic induction in thin finite sheets having conductivity decreasing to zero at the edge, with geomagnetic applications I”, Geophys. J. R. Astr. Soc. 22 (1971) 417–443.CrossRefGoogle Scholar
[2]Chikhliwala, E. D. and Yortsos, Y. C., “Application of orthogonal mapping to some two-dimensional domains”, J. Comput. Physics 57 (1985) 391–402.CrossRefGoogle Scholar
[3]Fornberg, B., “A numerical method for conformal mappings”, SIAM J. Sci. Stat. Comput. 1 (1980) 386–400.Google Scholar
[4]Hurley, D. G. and Siew, P. F., “The decay of eddy-currents in thin sheets and related water-wave problems”, IMA J. Appl. Math. 34 (1985) 1–21.Google Scholar
[5]Kang, I. S. and Leal, L. G., “Orthogonal grid generation in a 2D domain via the boundary integral technique”, J. Comp. Phys. 102 (1992) 78–87.CrossRefGoogle Scholar
[6]Lamontagne, Y. and West, G. F., “EM response of a rectangular thin plate”, Geophysics 36 (1971) 1204–1222.CrossRefGoogle Scholar
[7]Price, A. T., “The induction of electric currents in non-uniform thin sheets and shells”, Qtr J. Mech. Appl. Math. 2 (1949) 282–310.Google Scholar
[8]Ryskin, G. and Leal, L. G., “Orthogonal mapping”, J. Comput. Physics 50 (1983) 71–100.Google Scholar
[9]Siew, P. F., “Second order effects in the induction of thin discs”, IMA J. Appl. Math. 48 (1992) 97–106.Google Scholar
[10]Siew, P. F. and Hurley, D. G., “Electromagnetic response of thin discs”, J. Appl Math. Physics (ZAMP) 39 (1988) 619–633.CrossRefGoogle Scholar
[11]Smythe, W. R., Static and dynamic electricity (McGraw-Hill, London, 1968).Google Scholar
[12]Stroud, A. H. and Secrest, D., Gaussian quadrature formulas (Prentice-Hall Inc, 1966).Google Scholar
[13]West, G. F. and Edwards, R. N., “A simple parametric model for the electromagnetic response of an anomalous body in a host medium”, Geophysics 50 (1985) 2542–2557.CrossRefGoogle Scholar