# An FFT-based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

arXiv: https://arxiv.org/abs/2103.05968 · HTML: https://mlsanity.com/paper/2103.05968/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity](https://mlsanity.com/paper/2507.12233/) (2025)

## Abstract (arXiv)

We introduce an FFT-based solver for the combinatorial continuous maximum flow discretization applied to computing the minimum cut through heterogeneous microstructures. Recently, computational methods were introduced for computing the effective crack energy of periodic and random media. These were based on the continuous minimum cut-maximum flow duality of G. Strang, and made use of discretizations based on trigonometric polynomials and finite elements. For maximum flow problems on graphs, node-based discretization methods avoid metrication artifacts associated to edge-based discretizations. We discretize the minimum cut problem on heterogeneous microstructures by the combinatorial continuous maximum flow discretization introduced by Couprie et al. Furthermore, we introduce an associated FFT-based ADMM solver and provide several adaptive strategies for choosing numerical parameters. We demonstrate the salient features of the proposed approach on problems of industrial scale.