A wavelet-enhanced adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems

This contribution focuses on the development of an adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems. To this end, the classic Moulinec–Suquet scheme is revisited and enhanced by making use of wavelet analysis. Governing fields are represented in a wavelet basis and higher level stress approximations in a nested set of approximation spaces are successively derived by making use of wavelet transforms. By adaptively refining the computational grid based on the solution profile, localised features can be resolved accurately while the overall number of material model evaluations is significantly reduced. The performance is demonstrated by a detailed study of representative boundary value problems in one- and two-dimensional domains, whereby a reduction in the number of material model evaluations of up to 95% has been achieved. •State of the art wavelet-enhanced FFT-based solution approach.•Adaptive grid refinement.•Significant reduction in number of material model evaluations.•Eshelby–Green operator for wavelet-based discretisations.