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On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

Wicht, Daniel 1; Schneider, Matti 1; Böhlke, Thomas ORCID iD icon 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)

Abstract:

This work is devoted to investigating the computational power of Quasi‐Newton methods in the context of fast Fourier transform (FFT)‐based computational micromechanics. We revisit FFT‐based Newton‐Krylov solvers as well as modern Quasi‐Newton approaches such as the recently introduced Anderson accelerated basic scheme. In this context, we propose two algorithms based on the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method, one of the most powerful Quasi‐Newton schemes. To be specific, we use the BFGS update formula to approximate the global Hessian or, alternatively, the local material tangent stiffness. Both for Newton and Quasi‐Newton methods, a globalization technique is necessary to ensure global convergence. Specific to the FFT‐based context, we promote a Dong‐type line search, avoiding function evaluations altogether. Furthermore, we investigate the influence of the forcing term, that is, the accuracy for solving the linear system, on the overall performance of inexact (Quasi‐)Newton methods. This work concludes with numerical experiments, comparing the convergence characteristics and runtime of the proposed techniques for complex microstructures with nonlinear material behavior and finite as well as infinite material contrast.


Verlagsausgabe §
DOI: 10.5445/IR/1000104874
Veröffentlicht am 16.02.2021
Originalveröffentlichung
DOI: 10.1002/nme.6283
Scopus
Zitationen: 37
Web of Science
Zitationen: 34
Dimensions
Zitationen: 38
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 04.2020
Sprache Englisch
Identifikator ISSN: 0029-5981, 1097-0207
KITopen-ID: 1000104874
Erschienen in International journal for numerical methods in engineering
Verlag John Wiley and Sons
Band 121
Heft 8
Seiten 1665-1694
Vorab online veröffentlicht am 23.12.2019
Nachgewiesen in Scopus
Web of Science
Dimensions
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