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 deterministic 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. Comparative results show the effectiveness of this approach, and real design cases are studied thanks to this method.