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Abstract-All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings: (i) they give rise to ill-conditioned systems when the frequency is low (ii) and/or when the discretization density is high, (iii) their applicability is limited to the quasi-static regime, (iv) they require a search for global topological loops,

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Magnetic field integral equation (MFIE) and Calderón preconditioned electric field integral equation (EFIE) operators applied to toroidal surfaces have nontrivial nullspaces in the static limit. The nature of these nullspaces is elucidated and a technique for generating a basis for them presented. In addition, the effects of these nullspaces on the numerical solution of both frequency and time-domain MFIE and Calderón preconditioned EFIEs are investigated. The theoretical analysis is accompanied by corroborating numerical examples that show how these operators' nullspaces affect real-world problems. Index Terms-Boundary integral equations, Calderon preconditioned electric field integral equation (EFIE), magnetic field integral equation (MFIE), nullspace.

Abstract-In this contribution, a novel discretization scheme for the magnetic field integral equation is presented. The new scheme is designated "mixed" because it uses Rao-Wilton-Glisson functions to expand the current density and Buffa-Christiansen functions to test the magnetic field radiated by the candidate solution. The convergent nature of the proposed mixed MFIE is theoretically proven and numerical results showing that the proposed method yields more accurate results than the classical one are presented.