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

Schneider, Matti

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.

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Verlagsausgabe §
DOI: 10.5445/IR/1000119449
Veröffentlicht am 16.07.2020
Originalveröffentlichung
DOI: 10.1007/s00466-020-01849-7
Scopus
Zitationen: 1
Web of Science
Zitationen: 1
Cover der Publikation
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
Web of Science
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