Generalized BIE-BLA formulation of skin and proximity effect problems for an arbitrary regime of the magnetic field generation

The paper presents a new boundary element formulation for skin and proximity effect problems of parallel conductors. The main idea of this formulation is the representation of the functions for which the solution is sought in the form of two sequential approximations, the zero-order approximation giving the solution of the problem in the high frequency limit and the first-order approximation describing the correction of the order boundary layer approximation. Unlike the BIE-IBC formulations used presently, the integral equations for the expansion coefficients allow one to separate the unknown variables into “time-dependent” and “space-dependent” components for electromagnetic pulses of an arbitrary form as well as for a harmonic field. The final form of the integral equations for the “space-dependent” components is independent of the parameters of the magnetic field generation regime and is defined solely by the geometrical parameters of the conductor system under consideration. The formulation is developed for E-H and A-Y formalisms independently, but the resulting integral equations are the same for both formalisms