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• W2918241421 startingPage "112720" @default.
• W2918241421 abstract "The simulation of crack initiation and propagation in an elastic material is difficult, as crack paths with complex topologies have to be resolved. Phase-field approaches allow to simulate crack behavior without the need to explicitly model crack paths. However, the underlying mathematical model gives rise to a non-convex constrained minimization problem. In this work, we propose a recursive multilevel trust region (RMTR) method to efficiently solve such a minimization problem. The RMTR method combines global convergence properties of trust region methods with the optimality of multilevel methods. The solution process is accelerated by employing level dependent objective functions, minimization of which provides correction to the original/fine-level problem. In the context of the phase-field fracture approach, it is challenging to design efficient level dependent objective functions as a certain mesh resolution is required to resolve fracture bands. We introduce level dependent objective functions that combine fine level description of the crack path with the coarse level discretization. The overall performance and the convergence properties of the proposed RMTR method are investigated by means of several numerical examples in three dimensions." @default.
• W2918241421 created "2019-03-11" @default.
• W2918241421 creator A5052850078 @default.
• W2918241421 creator A5080114950 @default.
• W2918241421 date "2020-03-01" @default.
• W2918241421 modified "2023-10-16" @default.
• W2918241421 title "A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture" @default.
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• W2918241421 doi "https://doi.org/10.1016/j.cma.2019.112720" @default.
• W2918241421 hasPublicationYear "2020" @default.
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