A modern view of FFT-based computational methods in micromechanics

Since their inception in the mid-90s by Moulinec and Suquet, computational methods based on the fast Fourier transform (FFT) have demonstrated their extraordinary capabilities for problems in micromechanics. Their success rests on three ingredients. For a start, they operate on a regular grid, rendering complex meshing procedures superfluous. Secondly, the FFT is used to construct computational schemes that are matrix-free and automatically preconditioned. Last but not least, these techniques were designed to handle inelastic constitutive laws from the beginning. The talk is concerned with recent improvements of the original technology, i.e., the development of more powerful solution techniques based upon an optimization perspective and advances in discretization techniques which are critical for applications to high contrast and perforated materials.