Fast-Fourier Methods and Homogenization

Since their inception by Moulinec-Suquet, FFT-based computational methods have become an indispensable tool for computational micromechanics and the materials science of heterogeneous materials due to their impressive computational power. The article at hand gives a compact overview of the critical developments in the field, focusing on alternative discretization methods and fast solution schemes which overcome a few initial limitations of Moulinec-Suquet׳s basic scheme. Moreover, some key extensions and several pressing questions for FFT-based methods are discussed.