Minimum-order regular boundary integral equations for three-dimensional eddy-current problem

This paper provides regular boundary integral equations for determining the electromagnetic field for the three-dimensional eddy-current problem. The Mayergoyz approach enables us to split the problem into a magnetic problem and an electric problem, which are solved in succession. The magnetic problem leads to a set of one vector and one scalar regular integral equations (three scalar unknown functions), while the electric problem is reduced to a scalar regular integral equation (a scalar unknown function). In both cases, existence theorems for the solutions are proven.