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Abstract-For electromagnetic analysis using Method of Moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor 0 equal to the solid angle external to the surface at the testing points, which is 2 everywhere on the surface of the object, except at edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with 0 = 2 leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the 0 factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference.

Galerkin implementations of the method of moments (MoM) of the electric-field integral equation (EFIE) have been traditionally carried out with divergence-conforming sets. The normal-continuity constraint across edges gives rise to cumbersome implementations around junctions for composite objects and to less accurate implementations of the combined field integral equation (CFIE) for closed sharp-edged conductors. We present a new MoM-discretization of the EFIE for closed conductors based on the nonconforming monopolar-RWG set, with no continuity across edges. This new approach, which we call "even-surface odd-volumetric monopolar-RWG discretization of the EFIE", makes use of a hierarchical rearrangement of the monopolar-RWG current space in terms of the divergence-conforming RWG set and the new nonconforming "odd monopolar-RWG" set. In the matrix element generation, we carry out a volumetric testing over a set of tetrahedral elements attached to the surface triangulation inside the object in order to make the hyper-singular Kernel contributions numerically manageable. We show for several closed sharp-edged objects that the proposed EFIE-implementation shows improved accuracy with respect to the RWG-discretization and the recently proposed volumetric monopolar-RWG discretization of the EFIE. Also, the new formulation becomes free from the electric-field low-frequency breakdown after rearranging the monopolar-RWG basis functions in terms of the solenoidal, Loop, and the nonsolenoidal, Star and "odd monopolar-RWG", components.Index Terms-Basis functions, electric field integral equation (EFIE), integral equations, moment method.

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