Overcoming Low-Frequency Breakdown of the Magnetic Field Integral Equation

• Published in: IEEE transactions on antennas and propagation Vol. 61; no. 3; pp. 1285 - 1290
• Main Authors: Vico, F., Gimbutas, Z., Greengard, L., Ferrando-Bataller, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Antennas; Applied classical electromagnetism; Breakdown; Charge; Charge-current formulations; Electric breakdown; Electric charge; Electric fields; Electrical engineering; electromagnetic (EM) scattering; electromagnetic theory; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Integral equations; Low frequencies; low-frequency breakdown; magnetic field integral equation (MFIE); Magnetic fields; Magnetic resonance; Maxwell equations; Physics; Scalars; Studies; Near field; Performance evaluation; Electric breakdown; Electromagnetism; electromagnetic (EM) scattering; electromagnetic theory; Far field; magnetic field integral equation (MFIE); Low frequency; Maxwell equations; low-frequency breakdown; Polynomial function; Time domain method; Integral equations; Charge-current formulations; Electromagnetic waves; Cancellation; Breakdown; Modelling; Electric fields; Preconditioning
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2012.2230232

In the electromagnetics literature, significant attention has been paid to the problem of low-frequency breakdown in the electric field integral equation. By contrast, the magnetic field integral equation is well-conditioned (in simply connected domains) and can be used in the low frequency limit without modification or preconditioning. Reconstruction of the electric field, however, is subject to catastrophic cancellation unless appropriate measure are taken. In this paper, we show that solving an auxiliary (scalar) integral equation for the charge overcomes this form of low frequency breakdown, both in the near and far fields. Moreover, both the current and charge can be discretized using simple piecewise polynomial basis functions on triangulated surfaces. We also analyze an alternative formulation involving magnetic current and charge and illustrate the performance of the methods with several numerical examples.