  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.
