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We present a model order reduction (MOR) method for finite strain FFT solvers to reduce the computational costs of the FFT simulation scheme of a two-scale FE-FFT simulation. The underlying method is based on a reduced set of frequencies which leads to a reduced fixed-point scheme. The reduced set of frequencies is determined offline, based on the Fourier grid and predominantly consists of low frequencies. After performing the entire simulation with this reduced set of frequencies, the compressed sensing technique is used to reconstruct highly resolved micromechanical fields in a post-processing step. Compared to the unreduced solution scheme, a significant speed-up in the CPU time at a negligibly small loss of accuracy in the overall solution is observed. As a numerical example an elastic composite in a finite strain setting is investigated.

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