Solid-Angle Error in the Magnetic-Field Integral Equation for Perfectly Electric Conducting Objects

For perfectly electric conducting (PEC) objects, one difference between the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) is related to the solid angle, which only exists in the latter. In this communication, the correct computation of solid-angle contribution in MFIE is first summarized and clarified. Through testing strictly inside triangles (TSIT) and testing on edges (TOE) with or without the correct limit value (CLV) for the solid-angle integral, six versions of MFIE are then implemented by utilizing Rao-Wilton-Glisson (RWG) functions for expansion and utilizing RWG or rotated Buffa-Christiansen (BC) functions for testing. Based on the simulations of typical sharp-edged targets and a sphere by the EFIE and six MFIEs, it is found that using CLVs for the solid-angle integral will improve the simulation accuracy substantially in comparison to that with incorrect limit values (ILVs). Moreover, if the singularities are properly handled, the MFIE implemented by TSIT can achieve the same accuracy with the MFIE implemented by TOE with CLVs.