Low-frequency scaling of the standard and mixed magnetic field and Müller integral equations

Abstract
The standard and mixed discretizations for the magnetic field integral equation (MFIE) and the Müller integral equation (MUIE) are investigated in the context of low-frequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization. © 1963-2012 IEEE.

Citation
Bogaert, I., Cools, K., Andriulli, F. P., & Bagci, H. (2014). Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations. IEEE Transactions on Antennas and Propagation, 62(2), 822–831. doi:10.1109/tap.2013.2293783

Acknowledgements
The work of I. Bogaert was supported by a postdoctoral grant from the Fund for Scientific Research Flanders (FWO-Vlaanderen).

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Antennas and Propagation

DOI
10.1109/TAP.2013.2293783

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