Nonconforming discretization of the Magnetic-Field Integral Equation with volumetric testing

The RWG-discretization in Method of Moments (MoM) of the Magnetic-Field and Electric-Field Integral Equations (MFIE, EFIE) show evident discrepancy in the computed RCS, especially for small objects with edges and corners. The nonconforming monopolar-RWG discretization of the MFIE exhibits a smaller a deviation with respect to the EFIE. The Combined-Field Integral Equation (CFIE), which arises from the combination of the EFIE and the MFIE, is very often implemented with the RWG basis functions, whereby some accuracy with respect to EFIE is lost too. In this paper, we present a new nonconforming monopolar-RWG discretization of the MFIE, based on testing the magnetic field over small tetrahedral elements attached to the surface, inside the body under analysis. This formulation is compatible with a successful nonconforming discretization of the EFIE with the monopolar-RWG expansion of the current and volumetric testing. This allows the development of a nonconforming discretization of the CFIE.