Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture

One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost, caused by the non -convexity of the underlying energy functional and a large number of unknowns required to resolve the damage gradients. In this work, we propose to solve such nonlinear systems in a monolithic manner using the Schwarz preconditioned inexact Newton (SPIN) method. The proposed SPIN method leverages the field split approach and minimizes the energy functional separately with respect to displacement and the phase-field, in an additive and multiplicative manner. In contrast to the standard alternate minimization, the result of this decoupled minimization process is used to construct a preconditioner for a coupled linear system, arising at each Newton's iteration. The overall performance and the convergence properties of the proposed additive and multiplicative SPIN methods are investigated by means of several numerical examples. A comparison with widely-used alternate minimization is also performed showing a significant reduction in terms of execution time. Moreover, we also demonstrate that this reduction grows even further with increasing problem size.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study proposes a nonlinear system solution method, called SPIN, to address the issues of the phase-field approach. The method splits the energy functional into displacement and phase-field parts and solves them separately, using the results to construct a preconditioner for the coupled linear system at each Newton's iteration. Numerical examples demonstrate the significant reduction in execution time, especially with increasing problem size, compared to the widely-used alternate minimization method.