Darwin Approximation to Maxwell’s Equations

Abstract

Abstract. Maxwell's equations are the foundation of electromagnetics, its extensive applications make computational electromagnetics a new rapidly growing subject. However, since the electric and the magnetic fields are coupling in the Maxwell system, the numerical solution of the full system of Maxwell's equations is extremely expensive in terms of computer time. Darwin model, which decouple the coupled system, is such a good approximation to Maxwell's equations. In three dimensional space case, it neglects the transverse component of the displacement current; while in two dimensional space case, Darwin model is equivalent to TE, TM models. For these reasons, it is worthwhile to investigate Darwin model, and a lot of works have been done to it. In this paper, we review the advance in the Darwin model and introduce some of our new results about the exterior problems of Darwin model and its numerical solutions with infinite elements methods.