Electromagnetic optimization procedures require a large number of evaluations in numerical forward models. These computer models simulate complex problems through the use of numerical techniques, e.g. finite elements. Hence, the evaluations need a large computational time. Two-level methods such as space mapping have been developed that include a second model so as to accelerate the inverse procedures. Contrary to existing two-level methods, we propose a scheme that enables acceleration when the second model is based on the initial numerical model with coarse discretizations. This paper validates the proposed refined direct optimization method onto algebraic test functions. Moreover, we applied the methodology onto the geometrical optimization of the magnetic circuit of a switched reluctance motor. The obtained numerical results show the efficiency of the optimization algorithm with respect to the computational time and the accuracy