Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional

Ali Falsafi; Richard J. Leute; Martin Ladecký; Till Junge

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arXiv · 2207.10657

Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional

Ali Falsafi·Richard J. Leute·Martin Ladecký·Till Junge

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Abstract

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.

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Ali Falsafi, Richard J. Leute, Martin Ladecký, Till Junge. 2022-07-15. Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional. https://arxiv.org/abs/2207.10657

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