Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

TL;DR

This paper introduces a finite-element based compatibility projection method for FFT-based homogenization that effectively eliminates ringing artifacts while maintaining computational efficiency.

Contribution

It generalizes the compatibility projection to finite elements, enhancing FFT-based homogenization by removing ringing artifacts without sacrificing convergence.

Findings

Eliminates ringing artifacts in FFT-based homogenization.

Maintains Fourier-acceleration and fast convergence.

Equivalent to finite-element formulations on structured grids.

Abstract

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond\v{r}ejc, Zeman & Marek [Comput. Math. Appl. 68, 156 (2014)] beyond the Fourier basis. In particular, we formulate the compatibility projection for linear finite elements while maintaining Fourier-acceleration and the fast convergence properties of the original method. We demonstrate that this eliminates ringing artifacts and yields an efficient computational homogenization scheme that is equivalent to canonical finite-element formulations on fully structured grids.