Discretization of sources of integral operators

In this paper we examine the background of boundary value problems in order to find the source of some difficulties encountered with numerical approaches exploiting integral operators. Using magnetostatics as an example we introduce a new approach, where the degrees of freedom are sources of the field, not the held or its potential as usually. Furthermore two different discretization schemes, the Galerkin and the de Rham method, for this kind of approach are presented. The numerical effects are demonstrated with a simple example.