Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

• Published in: IEEE transactions on antennas and propagation 2014-02, Vol.62 (2), p.822-831
• Main Authors: Bogaert, Ignace, Cools, Kristof, Andriulli, Francesco P., Bagci, Hakan
• Format: Article
• Language: English
• Subjects: Accuracy; Applied classical electromagnetism; Applied sciences; Diffraction, scattering, reflection; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Electronics; Engineering Sciences; Equations; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Integral equations; low-frequency stability; magnetic field integral equation; Mathematical model; mixed discretization; Müller integral equation; Physics; Radiocommunications; Radiowave propagation; Scattering; Telecommunications; Telecommunications and information theory; Testing
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2013.2293783

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.