Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems

Svolos, Lampros; Berger-Vergiat, Luc; Waisman, Haim

doi:10.1016/j.jcp.2020.109746

Cited by 15 publications

(5 citation statements)

References 73 publications

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“…An important subset of the parallelization methods is the domain decomposition methods, which can be further classified into overlapping and nonoverlapping methods. An overlapping domain decomposition method, the updating strategy developed by Svolos et al 41 aims to solve for dynamic fracture problems with a preconditioner following the idea of Berger‐Vergiat and Waisman 42 for shear band problems. In Reference 41, the whole domain is partitioned into (a) a localized subdomain, which is solved with small time steps, and (b) a healthy subdomain, which is updated with larger time steps.…”

Section: Introductionmentioning

confidence: 99%

“…An overlapping domain decomposition method, the updating strategy developed by Svolos et al 41 aims to solve for dynamic fracture problems with a preconditioner following the idea of Berger‐Vergiat and Waisman 42 for shear band problems. In Reference 41, the whole domain is partitioned into (a) a localized subdomain, which is solved with small time steps, and (b) a healthy subdomain, which is updated with larger time steps. These two types of domains are related by an additive Schwarz method based on the Schur complement.…”

Section: Introductionmentioning

confidence: 99%

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An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method

Hao,

Shen

2023

Numerical Meth Engineering

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The phase field approach to fracture becomes popular for complicated fracture problems in recent years. However, its widespread application is hindered by its high computational cost. In this article, we propose an efficient parallel explicit‐implicit solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method, specifically, the dual‐primal finite element tearing and interconnecting (FETI‐DP) method. In this scheme, the displacement field is updated by an explicit algorithm in parallel, and the phase field is implicitly solved by the FETI‐DP method. In particular, Lagrange multipliers are introduced to ensure the interface continuity of the phase field. In the computational process, the information exchange among subdomains merely exists in a few substeps, which renders the cost for communication very small. Moreover, the size of equations to be solved is proportional to the total area of subdomain interfaces, which is significantly reduced compared with a typical single‐domain solution procedure. The solution scheme is able to perform phase field simulations with a million of degrees of freedom using only 0.034 core hours per load step, and has flexible extensibility for existing phase field codes. Several numerical examples demonstrate the accuracy and efficiency of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method

Hao,

Shen

2023

Numerical Meth Engineering

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“…The other class of strategies is to preserve the discretization scheme but seek efficient preconditioning techniques to reduce the condition number of the discretized system. There are several methods, including the additive Schwarz preconditioner 24,25 and the multigrid preconditioner. 26,27 These methods treat the entire crack area as a special domain and do not distinguish the crack line and crack tip area where the singularities mainly come from.…”

Section: Introductionmentioning

confidence: 99%

A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM

Tian

Huang

Chen

et al. 2022

Numerical Meth Engineering

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In this article, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the computational mesh into two types of subdomains: the regular subdomains and the crack tip subdomains based on the observation that the crack tips have a significant impact on the convergence of the iterative method while the impact of the crack lines is not that different from those of regular mesh points. The tip subdomains consist of mesh points at crack tips and all neighboring points where the branch enrichment functions are applied. The regular subdomains consist of all other mesh points, including those on the crack lines. To overcome the mismatch between the number of subdomains and the number of processor cores, the proposed method is divided into two steps: solve the crack tip problem and then the regular subdomain problem during each iteration. The proposed method was used to develop a parallel XFEM package which is able to test different types of iterative methods. To achieve good parallel efficiency, additional methods were introduced to reduce communication and to maintain the load balance between processors. Numerical experiments indicate that the proposed method significantly reduces the number of iterations and the total computation time compared to the classical methods. In addition, the method scales up to 8192 processor cores with over 70% parallel efficiency to solve problems with more than 2 × 10 8 degrees of freedom.

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“…In the context of domain decomposition methods, standard linear (block) Jacobi and additive Schwarz methods have been investigated in [40,44]. A variant of the linear additive Schwarz method has been also developed in [45], where authors have decomposed the domain into two subdomains, related to localized and healthy parts of the domain. To the best of our knowledge, there have been no attempts to apply nonlinear domain decomposition methods to solve phase-field fracture problems so far.…”

Section: Introductionmentioning

confidence: 99%

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

Kopaničáková¹,

Kothari²,

Krause³

2022

Preprint

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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.

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Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems

Cited by 15 publications

References 73 publications

An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method

An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method

A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM

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

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