A sufficient error criterion for the computational solution of the magnetic field boundary integral equation

A major problem in the computational solution of scattering by a perfectly conducting object using boundary integral equations is their non-uniqueness due to the existence of interior field solutions at certain frequencies. Nowadays, the standard technique to overcome this problem is a proper combination of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE). The drawback is the extra computational burden. In addition, there is no error criterion with respect to the errors made in the discretization of the two types of integral equations. In view of the computational simplicity of MFIE, we start with this equation and investigate the analytical and computational consistency in the interior of the scattering object. We show that the L₂-norm over a small closed interior surface leads to a sufficient error criterion for the computational solution at hand. Non-uniqueness problems at certain internal resonances are immediately indicated. Since this interior surface is much smaller than the boundary surface, the extra time for the computation of this norm is no point of discussion. Finally, we show that this internal error criterion can directly be imposed as a sufficient constraint to MFIE to avoid the non-uniqueness.