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The computational complexity/efficiency of the method of auxiliary sources (MAS) is significantly reduced at high frequency (high induction number >40) for electromagnetic induction problems. At the same time the small penetration-depth approximation (SPA) is very accurate at high frequency/induction numbers. A hybrid algorithm, combining the MAS with SPA, is efficiently implemented. Numerical experiments are performed for a highly conducting and permeable sphere and a prolate spheroid under a time varying primary magnetic field. Numerical experiments demonstrate that the proposed method is able to produce very accurate results with low computational requirements.