New integral equation formulation of the measured equation of invariance and the extension to analyze two‐dimensional cylinders with impedance boundary conditions

We have derived a new form of the integral equation formulation of the measured equation of invariance (IE‐MEI). The new formulation clarifies the existence of a relationship between scattered electric and magnetic fields at consecutive nodes in the IE‐MEI and indicates that the relationship in a problem for a perfect electric conductor (PEC) holds for a problem with arbitrary materials. In a scattering problem of a two‐dimensional cylinder with an impedance boundary condition (IBC), every matrix in the IE‐MEI is a band‐like sparse matrix. That is, the solution process in the IE‐MEI with an IBC is the same as that for a PEC. Therefore the IE‐MEI with an IBC has the same merits of the IE‐MEI for a PEC: The more efficient computation can be achieved with the smaller memory than those of the method of moments (MOM). The IE‐MEI with an IBC is validated by numerical examples for a circular cylinder and a square cylinder by comparison with a combined field MOM that satisfies exact boundary conditions. Numerical examples show that the IE‐MEI with an IBC is applicable to the case where the generalized skin depth is less than half the width of a scatterer.