An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems

Building upon the previously established equivalence of the basic scheme of Moulinec–Suquet’s FFT-based computational homogenization method with a gradient descent method, this work concerns the impact of the fast gradient method of Nesterov in the context of computational homogenization. Nesterov’s...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2017-03, Vol.315, p.846-866
Main Author: Schneider, Matti
Format: Article
Language:English
Subjects:
Accelerated first order methods
Computation
Computational homogenization
Elastoplasticity
FFT
Homogenization
Plasticity
Rocks
Unit cell
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Summary:Building upon the previously established equivalence of the basic scheme of Moulinec–Suquet’s FFT-based computational homogenization method with a gradient descent method, this work concerns the impact of the fast gradient method of Nesterov in the context of computational homogenization. Nesterov’s method leads to a significant speed up compared to the basic scheme for linear problems with moderate contrast, and compares favorably to the (Newton-)conjugate gradient (CG) method for problems in digital rock physics and (small strain) elastoplasticity. We present an efficient implementation requiring twice the storage of the basic scheme, but only half of the storage of the CG method. •Simple to implement fast gradient method for FFT-based homogenization.•Requires less memory than conjugate gradients.•Can be directly applied to inelastic problems without the need for linearization.•No fine-tuning of algorithmic parameters necessary.•Discussion of convergence criteria included.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2016.11.004