Boundary integral equations of minimum order for the calculation of three-dimensional eddy current problems

Abstract

A three-dimensional eddy current problem is formulated as a boundary value problem for electric and magnetic strengths. Some peculiarities of this boundary value problem are emphasized. The most important of them is the possibility to split this boundary value problem into two boundary value problems which can be solved in succession one after another: 1) the boundary value problem for the magnetic strength in the whole space and 2) the boundary value problem for the electric strength in outer air space. From the practical point of view it is enough to find the solution only of the first boundary value problem. The principle of separate surface imaginary sources is proposed for the solution of this boundary value problem and the boundary integral equations for the densities of these surface sources are derived, These integral equations are of minimum order.