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Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics

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This paper studies the convergences of several FFT-based discretization schemes that are widely applied in computational micromechanics for deriving effective coefficients, and “convergence” here means the limiting behaviors as spatial resolutions tending to infinity. Those schemes include Moulinec–Suquet’s scheme, Willot’s scheme and the FEM scheme. Under some reasonable assumptions, we prove that the effective coefficients obtained by those schemes all converge to the theoretical ones. Moreover, for the FEM scheme, we can present several convergence rate estimates under additional regularity assumptions.

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  1. Department of Mathematics, The Chinese University of Hong Kong, Sha Tin, Hong Kong Special Administrative Region, China

    Changqing Ye & Eric T. Chung

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The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project Nos. 14304719 and 14302620) and CUHK Faculty of Science Direct Grant 2020-21.

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Ye, C., Chung, E.T. Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics. Bit Numer Math 63, 11 (2023). https://doi.org/10.1007/s10543-023-00950-6

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