In this work the solution of the eddy current problem for slowly moving conductors is investigated with the volume integral formulation of the EFIE. If in one hand the formulation gives the possibility to mesh only the conductors, if embedded in a uniform insulator, on the other hand the inductance matrix is fully populated limiting thus the size of the problem. Furthermore, the standard solution implies the reassembling of the stiffness matrix for each position assumed by the moving conductors. This results in a limit in the size of the problem to treat and a relevant cost in the computation time. To overcome this limit, in this work, the mutual coupling part of the system with two conductors is computed on the fly giving thus the possibility to solve problems with a higher number of unknowns. Finally, to speed up the solution of the system, the Gauss–Seidel iterative techniques and the Fast Multipole Method (FMM) are applied to take into account the mutual effects between the conductors. A comparison of the proposed method with a reference one shows the effectiveness of this technique.
