Impedance boundary conditions of high order approximation for electromagnetic transient scattering problems

The problem of the diffusion of a transient electromagnetic field into a lossy dielectric body was solved by using the method of perturbations in the small parameter p that is equal to the ratio of the electromagnetic penetration depth and characteristic dimension of the body. The time- and frequency domain solutions for the tangential component of the electric field and the normal component of the magnetic field on the smooth curved surface of the body (the surface impedance boundary conditions-SIBC) have been obtained accurate to O(p⁴). It is shown that the proposed SIBC in the frequency domain generalizes the well-known Leontovich (1948)and Mitzner (1967) boundary conditions that provide an approximation accuracy within the errors O(p²) and O(p³), respectively