Study of Accuracy of Approximate Boundary Conditions for Scattering by Dielectric Objects

Approximate boundary condition is an efficient way to reduce computationally expensive electromagnetic scattering problems involving dielectric objects. A commonly used approximation known as the Leontovich Impedance Boundary Condition, however, can not be conformingly discretized and requires a preconditioner that does not resemble a PEC-EFIE preconditioner. In this work, the Leontovich boundary condition and an alternate boundary condition previously introduced by Dely et al. to overcome the limitation in the Leontovich condition are numerically studied to assess their accuracy with respect to the exact problem. Their equivalence up to the lowest order in the spectral coordinates is established. The errors in the energy norm for the sequence of approximate solutions for the two different approximate boundary conditions with respect to the solution of the exact problem through numerical experiments are reported. The behavior of the field along sharp corners for both approximations is compared.