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A fast algorithm for reiterated homogenization

Abstract. This paper considers the numerical evaluation of effective coefficients for multiscale homogenization problems and proposes a highly efficient algorithm for a certain class of reiterated homogenization problems of practical importance. The main idea of the proposed approach is to introduce a novel object called the homogenization map, approximate it through adaptive interpolation, and replace solutions of the cell problems with fast evaluations of the interpolant. Numerical results are provided for both 2D and 3D problems to demonstrate the efficiency and accuracy of the proposed algorithm.