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Kopanicakova_2022_Else_cmame
Journal article

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

  • 2023
Published in:
  • Computer Methods in Applied Mechanics and Engineering. - 2023, vol. 403, no. Part B, p. 115733
Phase-field fracture
Monolithic scheme
Nonlinear preconditioning
Inexact Newton
English 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.
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Language
  • English
Classification
Computer science and technology
License
CC BY
Open access status
hybrid
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Persistent URL
https://n2t.net/ark:/12658/srd1325620
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