Investigation on the asymptotic expansion technique applied to electromagnetic problems

The application of the asymptotic multiple scale expansion to the analysis of laminated cores is discussed. The computations are developed in a one-dimensional structure modeling a periodic layered medium to investigate its electromagnetic behavior. The technique essentially consists of using two variables for describing the overall and small-scale behavior, respectively and of expressing the approximate solution through a truncated series of powers. The approximate solution, analytically computed, is compared with the exact one. An excellent agreement is found in the evaluation of magnetic and electric quantities (magnetic flux density, current density) and in the estimation of Joule losses due to eddy currents. Finally the study evidences some interesting features of the asymptotic expansion technique which, in the considered problem, imply a generalization of the results and a significant reduction of computational efforts