Anderson‐accelerated polarization schemes for fast Fourier transform‐based computational homogenization. (5th February 2021)

• Record Type: Journal Article
• Authors: Wicht, Daniel; Schneider, Matti; Böhlke, Thomas
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 9(2021)
• Page Start: 2287
• Page End: 2311
• Publication Date: 2021-02-05
• Subjects: Anderson acceleration -- computational homogenization -- directionally solidified eutectics -- FFT‐based method -- fiber‐reinforced composites -- metal‐matrix composites; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6622
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: 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.