Time domain surface impedance boundary conditions of high order of approximation

The problem of diffusion of transient electromagnetic field into a lossy dielectric homogeneous body is solved by using the perturbations method in the small parameter p, equal to the ratio of the electromagnetic penetration depth and characteristic dimension of the body. 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-SIBCs) are obtained with accuracy up to O(p⁴) It is shown that the proposed SIBCs in the frequency domain generalize well-known Leontovich´s and Mitzner´s boundary conditions that provide approximation errors O(p²) and O(p³), respectively. A numerical example of using the high order SIBCs with the surface integral equations in time domain is considered to illustrate the method