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A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics

Schneider, Matti 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)

Abstract:

For fast Fourier transform (FFT)-based computational micromechanics, solvers need to be fast, memory-efficient, and independent of tedious parameter calibration. In this work, we investigate the benefits of nonlinear conjugate gradient (CG) methods in the context of FFT-based computational micromechanics. Traditionally, nonlinear CG methods require dedicated line-search procedures to be efficient, rendering them not competitive in the FFT-based context. We contribute to nonlinear CG methods devoid of line searches by exploiting similarities between nonlinear CG methods and accelerated gradient methods. More precisely, by letting the step-size go to zero, we exhibit the Fletcher–Reeves nonlinear CG as a dynamical system with state-dependent nonlinear damping. We show how to implement nonlinear CG methods for FFT-based computational micromechanics, and demonstrate by numerical experiments that the Fletcher–Reeves nonlinear CG represents a competitive, memory-efficient and parameter-choice free solution method for linear and nonlinear homogenization problems, which, in addition, decreases the residual monotonically.

Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0178-7675, 1432-0924
KITopen-ID: 1000119449
Erschienen in Computational mechanics
Verlag Springer
Band 66
Seiten 239-257
Vorab online veröffentlicht am 04.05.2020
Nachgewiesen in Scopus
Dimensions
Web of Science
OpenAlex

Verlagsausgabe §
DOI: 10.5445/IR/1000119449
Veröffentlicht am 16.07.2020
Originalveröffentlichung
DOI: 10.1007/s00466-020-01849-7
Scopus
Zitationen: 37
Web of Science
Zitationen: 34
Dimensions
Zitationen: 42
Seitenaufrufe: 148
seit 26.06.2020
Downloads: 110
seit 17.07.2020
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