Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 122, Issue 9, Pages 2287-2311Publisher
WILEY
DOI: 10.1002/nme.6622
Keywords
Anderson acceleration; computational homogenization; directionally solidified eutectics; FFT‐ based method; fiber‐ reinforced composites; metal‐ matrix composites
Funding
- Deutsche Forschungsgemeinschaft [BO 1466/12-2, GRK 2078-2, SCHN 1595/1-1]
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This work investigates the extension of polarization methods by Anderson acceleration and demonstrates that this combination leads to robust and fast general-purpose solvers for computational micromechanics. The study discusses the theoretically optimum parameter choice for polarization methods, describes how Anderson acceleration fits into the picture, and exhibits the characteristics of the newly designed methods for industrial scale and interest problems.
Classical solution methods in fast Fourier transform-based computational micromechanics operate on, either, compatible strain fields or equilibrated stress fields. By contrast, polarization schemes are primal-dual methods whose iterates are neither compatible nor equilibrated. Recently, it was demonstrated that polarization schemes may outperform the classical methods. Unfortunately, their computational power critically depends on a judicious choice of numerical parameters. In this work, we investigate the extension of polarization methods by Anderson acceleration and demonstrate that this combination leads to robust and fast general-purpose solvers for computational micromechanics. We discuss the (theoretically) optimum parameter choice for polarization methods, describe how Anderson acceleration fits into the picture, and exhibit the characteristics of the newly designed methods for problems of industrial scale and interest.
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