Solid-angle factor in the magnetic-field integral equation

Abstract

The magnetic-field integral equation (MFIE) contains a geometry-dependent solid-angle factor due to the limit value of the magnetic field at the source region. Determination of the solid-angle factor becomes bewildering, especially at the points of geometric discontinuities caused by the simultaneous discretization of the MFIE and the geometry. In this paper, we clarify the ambiguity by scrutinizing the magnetic-field radiation integrals of the MFIE formulation. We prove that the solid-angle factor can be implicitly determined if the singular source-region magnetic-field expressions are correctly treated, thus eliminating the need for guessing or explicitly inserting solid-angle values in the formulation.