Log In Sign Up

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

by   Felix Ernesti, et al.

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.


page 3

page 14

page 15

page 17

page 18

page 19

page 20


Generalized max-flows and min-cuts in simplicial complexes

We consider high dimensional variants of the maximum flow and minimum cu...

Faster Minimum k-cut of a Simple Graph

We consider the (exact, minimum) k-cut problem: given a graph and an int...

Combinatorial Continuous Maximal Flows

Maximum flow (and minimum cut) algorithms have had a strong impact on co...

Decomposable Submodular Function Minimization via Maximum Flow

This paper bridges discrete and continuous optimization approaches for d...

Energy Complexity of Distance Computation in Multi-hop Networks

Energy efficiency is a critical issue for wireless devices operated unde...

Competitive Analysis of Minimum-Cut Maximum Flow Algorithms in Vision Problems

Rapid advances in image acquisition and storage technology underline the...