Accuracy Analysis of Div-Conforming Hierarchical Higher-Order Discretization Schemes for the Magnetic Field Integral Equation

The magnetic field surface integral equation for perfect electrically conducting scatterers suffers from accuracy problems when discretized with lowest-order Rao-Wilton-Glisson (RWG) functions. For high-frequency scattering scenarios, one of the various reported countermeasures are hierarchical higher-order (HO) functions. We demonstrate that the accuracy of these HO methods of up to 1.5th order may be further improved by employing a weak-form discretization scheme for the identity operator inside the magnetic field integral equation (MFIE), in particular for scatterers with sharp edges. As expected, the presented numerical results indicate that this approach becomes less effective for increasing order. Moreover, since the weak-form discretization overcomes only the anisotropy problems of the standard discretizations, parts of the accuracy problems of the MFIE persist for HO discretizations if the testing is performed with non dual-space conforming functions.