Fourier-accelerated micromechanical homogenization has been developed and applied to a variety of problems, despite being prone to ringing artifacts. In addition, the majority of Fourier-accelerated solvers applied to FFT-accelerated schemes only apply to convex problems. We here introduce a that allows to employ modern efficient and non-convex iterative solvers, such as trust-region solvers or LBFGS in a FFT-accelerated scheme. These solvers need the explicit energy functional of the system in their standard form. We develop a modified trust region solver, capable of handling non-convex micromechanical homogenization problems such as continuum damage employing the approximate incremental energy functional. We use the developed solver as the solver of a ringing-free FFT-accelerated solution scheme, namely the projection based scheme with finite element discretization.
@article{arxiv.2207.10657,
title = {Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional},
author = {Ali Falsafi and Richard J. Leute and Martin Ladecký and Till Junge},
journal= {arXiv preprint arXiv:2207.10657},
year = {2022}
}