An Impedance Boundary Condition EFIE That Is Low-Frequency and Refinement Stable

A discretization of the impedance boundary condition electric field integral equation (IBC-EFIE) is introduced that: 1) yields the correct solution at arbitrarily small frequencies and 2) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilization is based on a projector-based discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behavior of both the EFIE operator and the surface impedance condition. The dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term.