Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture

Abstract

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's (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. Comparison with widely-used alternate minimization is also performed and we show a reduction in the execution time up to a factor of 50. Moreover, we also demonstrate that this reduction grows even further with increasing problem size and larger loading increments.

References in corpus (12)

• High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
• On penalization in variational phase-field models of brittle fracture
• An accelerated staggered scheme for phase-field modeling of brittle fracture
• Interior-point methods for the phase-field approach to brittle and ductile fracture
• An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
• An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method
• Recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture
• Matrix-free multigrid solvers for phase-field fracture problems
• Second-order phase-field formulations for anisotropic brittle fracture
• Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator
• On the Globalization of ASPIN Employing Trust-Region Control Strategies -- Convergence Analysis and Numerical Examples
• A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods

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• Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
• Nonlinear Schwarz preconditioning for Quasi-Newton methods
• Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
• Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints