A geometrically adapted reduced set of frequencies for a FFT-based microstructure simulation

TL;DR

This paper introduces a geometrically adapted sampling pattern for a reduced set of frequencies in FFT-based microstructure simulations, improving accuracy and eliminating the need for post-processing reconstruction.

Contribution

It proposes a phase-wise adaptive sampling pattern for MOR in FFT-based microstructure simulations, enhancing accuracy and efficiency over fixed sampling methods.

Findings

Significantly improved microscopic and overall results.

Elimination of post-processing reconstruction step.

Demonstrated robustness in 2D and 3D examples.

Abstract

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the Lippmann-Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique is on the one hand the amount of used frequencies and on the other hand the choice of frequencies used within the simulation. Kochmann et al. [2019] defined the reduced set of frequencies by using a fixed sampling pattern, which is most general but leads to poor microstructural results when considering only a few frequencies. Consequently, a reconstruction algorithm based on the TV1-algorithm [Candes et al., 2006] was used in a post-processing step to generate highly resolved micromechanical fields. The present work deals with a modified sampling pattern generation for this MOR technique. Based on the idea, that the micromechanical material response strongly depends on the phase-wise material behavior, we propose the usage of sampling patterns adapted to the spatial arrangement of the individual phases. This leads to significantly improved microscopic and overall results. Hence, the time-consuming reconstruction in the post-processing step that was necessary in the earlier work is no longer required. To show the adaptability and robustness of this new choice of sampling patterns, several two dimensional examples are investigated. In addition, also the 3D extension of the algorithm is presented.