The authors propose a simple but efficient method for design problems. Instead of using directly a heavy numerical code in an optimization process, we successively define some approximated subproblems thanks to an appropriate analytical model. These subproblems can then be solved exactly by a deter-ministic global optimization solver and the procedure is updated until the approximation matches a 3D FEM computation. The method is applied to an axial magnetic coupling, and preliminary results show the effectiveness of this approach.