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In this paper, an updated equivalence principle algorithm (EPA) is presented. Compared with previous work by the authors, the high-order point sampling scheme is used to reduce the high-frequency noise in field projection. An updated tap basis scheme is introduced to simplify the formulation. With these schemes, the equivalence principle algorithm can be used to solve multiscale problems by substituting the oversampled region with a proper equivalence surface. Moreover, EPA can also be accelerated using attached unknown accelerations and multilevel fast multipole algorithm so that large multiscale problems can be solved efficiently.