On the Barzilai‐Borwein basic scheme in FFT‐based computational homogenization

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 presen...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2019-05, Vol.118 (8), p.482-494
Main Author: Schneider, Matti
Format: Article
Language:English
Subjects:
Barzilai‐Borwein method
Eigenvalues
FFT‐based solver
Globalization
inelastic material behavior
Lower bounds
Micromechanics
porous material
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Summary: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.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6023