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On the Barzilai‐Borwein basic scheme in FFT‐based computational homogenization
Author(s) -
Schneider Matti
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6023
Subject(s) - mathematics , homogenization (climate) , eigenvalues and eigenvectors , positive definite matrix , fast fourier transform , tangent , equivalence (formal languages) , parametric statistics , mathematical analysis , algorithm , pure mathematics , geometry , biodiversity , ecology , physics , quantum mechanics , biology , statistics
Summary Building upon the equivalence of the basic scheme in the work of Moulinec and Suquet with gradient descent methods, we investigate the effect of using the celebrated Barzilai‐Borwein step size selection technique in this context. We provide an overview of recent convergence theory and present efficient implementations in the context of computational micromechanics, with and without globalization. In contrast to polarization schemes and fast gradient methods, no lower bound on the eigenvalues of the material tangent is necessary for the Barzilai‐Borwein scheme. We demonstrate the power of the proposed method for linear elastic and inelastic large scale problems with finite and infinite material contrast.