An accelerated staggered scheme for phase-field modeling of brittle fracture

TL;DR

This paper introduces an accelerated staggered solver for phase-field brittle fracture modeling that combines Anderson acceleration and over-relaxation to improve convergence speed and robustness.

Contribution

It proposes a novel scheme that sequentially applies Anderson acceleration and over-relaxation, enhancing the efficiency of existing staggered solvers with minimal implementation effort.

Findings

The new method accelerates convergence compared to standard schemes.

It maintains robustness across different crack evolution scenarios.

Implementation requires minor modifications to existing software.

Abstract

There is currently an increasing interest in developing efficient solvers for phase-field modeling of brittle fracture. The governing equations for this problem originate from a constrained minimization of a non-convex energy functional, and the most commonly used solver is a staggered solution scheme. This is known to be robust compared to the monolithic Newton method, however, the staggered scheme often requires many iterations to converge when cracks are evolving. The focus of our work is to accelerate the solver through a scheme that sequentially applies Anderson acceleration and over-relaxation, switching back and forth depending on the residual evolution, and thereby ensuring a decreasing tendency. The resulting scheme takes advantage of the complementary strengths of Anderson acceleration and over-relaxation to make a robust and accelerating method for this problem. The new method is applied as a post-processing technique to the increments of the solver, hence, the implementation can be done with minor modifications to already available software. Moreover, the cost of combining the two acceleration schemes is negligible. The robustness and efficiency of the method are demonstrated through numerical examples.