Sufficient uniqueness conditions for the solution of the time harmonic Maxwell’s equations associated with surface impedance boundary conditions

Implementation of High-Order Impedance Boundary Conditions in Some Integral Equation Formulations

“…Higher order approximations of Z p ( → r , → r ) are usually obtained in the abovementioned literature via second-order tangential derivatives. As an example, the HOIBC termed IBC01 proposed in [14] reads IBC01:…”

“…Second, as explained in Section II-B, coefficients a p 0 and a 1 can be determined that render it more accurate than the IBC0. Third, sufficient uniqueness conditions (SUCs) have been proposed in [14] that guarantee uniqueness of the solutions of Maxwell's equations in the infinite free-space domain surrounding Γ on which the IBC is prescribed. Nonlocality can be achieved by introducing a differential operator in the left-hand side of (3) as, e.g., in the following HOIBC, termed IBC1 and proposed in [14] …”

“…The IBC0 is local (an exact IBC is nonlocal) and constitutes a good approximation for high index materials only. Higher order IBCs (HOIBCs), more or less local, are presented in [4]- [14].…”

“…This drawback is suppressed in [16] by eliminating the magnetic current via the minimization with constraints of the EFIE+MFIE functional, and the resulting system is also symmetric (the corresponding formulation is termed here CFIEB). We present here the implementation in the CFIE and EFIE+MFIE formulations of the IBC0 and of the HOIBCs proposed in [14]. Time dependence exp(jωt) is assumed and suppressed.…”

“…Time dependence exp(jωt) is assumed and suppressed. By invoking the tangent plane approximation, the coefficients involved in these HOIBCs are obtained from the reflection coefficients of a plane wave illuminating the infinite planar coating [10], [11], [14]. This paper is organized as follows.…”