  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.
