Suppressing Low-Frequency Cancellation Errors in Far-Field Computation with the MFIE, M\"uller, and Multitrace M\"uller Integral Equations

Abstract

This paper presents robust numerical formulations for suppressing low-frequency cancellation errors in the magnetic field integral equation (MFIE) for perfect electric conductors and the M\"uller integral equations for homogeneous and composite dielectric objects. The proposed approach combines quasi-Helmholtz projectors, which separate the Helmholtz components of the surface currents, with a tailored rescaling procedure that preserves the components essential for accurate far-field evaluation from finite-precision cancellation. The resulting formulations retain the conditioning properties of the mixed MFIE and M\"uller discretizations in the dense-mesh and low-frequency regimes. Numerical experiments involving simply and multiply connected scatterers, composite dielectric structures, multiscale and high-contrast configurations demonstrate that the proposed methods yield accurate far-field predictions across a broad frequency range, from the full-wave regime to extremely low frequencies.