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We present a new technique for reducing computation time of numerical solutions to optimal design problems. We incorporate in the optimization procedure a coarse model. Our technique, the two-level response and parameter mapping (RPM) algorithm, is based on space mapping and manifold mapping. Space mapping (SM) performs a mapping between the parameter spaces of the coarse and fine models, while manifold mapping (MM) makes a mapping between the response spaces of the coarse and fine models through the use of response correction. Here, we use and compare the three two-level optimization procedures, SM, MM, and RPM, for the optimization of passive and active shields in induction heating. The results demonstrate accurate and time-efficient optimization of magnetic shields by the RPM algorithm.