Efficient numerical methods for the large‐scale, parallel solution of elastoplastic contact problems

Frohne, Jörg; Heister, Timo; Bangerth, Wolfgang

doi:10.1002/nme.4977

Cited by 19 publications

(9 citation statements)

References 44 publications

(78 reference statements)

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“…The programming software is based on deal.II [33,34] and specifically on the adaptation and extension of the template for solving fully-coupled multiphysics problems [35] combined with the implementation of the primal-dual active set strategy from deal.II's step-41 [36].…”

Section: Programming Codementioning

confidence: 99%

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Heister

Wheeler²,

Wick

2015

Computer Methods in Applied Mechanics and Engineering

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352

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In this paper, we consider phase-field-based fracture propagation in elastic media. The main purpose is the development of a robust and efficient numerical scheme. To enforce crack irreversibility as a constraint, we use a primal-dual active set strategy, which can be identified as a semi-smooth Newton's method. The active set iteration is merged with the Newton iteration for solving the fully-coupled nonlinear partial differential equation discretized using finite elements, resulting in a single, rapidly converging nonlinear scheme. It is well known that phase-field models require fine meshes to accurately capture the propagation dynamics of the crack. Because traditional estimators based on adaptive mesh refinement schemes are not appropriate, we develop a predictorcorrector scheme for local mesh adaptivity to reduce the computational cost. This method is both robust and efficient and allows us to treat temporal and spatial refinements and to study the influence of model regularization parameters. Finally, our proposed approach is substantiated with different numerical tests for crack propagation in elastic media and pressurized fracture propagation in homogeneous and heterogeneous media.

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Section: Programming Codementioning

confidence: 99%

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Heister

Wheeler²,

Wick

2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

350

352

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“…The use of better-suited parallel solvers and preconditioners is also under investigation. Based on the results presented in Frohne et al (2013), for similar problems in elastoplasticity, the choice of the AMG preconditioner and BiCGStab solver should provide a good starting point.…”

Section: Discussionmentioning

confidence: 99%

“…It is clear that for problems of a reasonable size, the bottleneck is the solution of the linear system which accounts here for 77.7% of the simulation time. A distributed parallel implementation utilising an AMG preconditioner, in the spirit of the approach used by Frohne et al (2013), would be one way to address this issue.…”

Section: Appendix B Features Of the Implementation In Dealiimentioning

confidence: 99%

A finite element implementation of surface elasticity at finite strains using the deal.II library

McBride¹,

Javili²,

Steinmann³

et al. 2015

Preprint

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The potentially significant role of the surface of an elastic body in the overall response of the continuum can be described using the mature theory of surface elasticity. The objective of this contribution is to detail the finite element approximation of the underlying governing equations (both in the volume and on its surface) and their solution using the open-source finite element library deal.II. The fully-nonlinear (geometric and material) setting is considered. The nonlinear problem is solved using a Newton-Raphson procedure wherein the tangent contributions from the volume and surface are computed exactly. The finite element formulation is implemented within the total Lagrangian framework and a Bubnov-Galerkin spatial discretization of the volume and the surface employed. The surface is assumed material. A map between the degrees of freedom on the surface and on the boundary of the volume is used to allocate the contribution from the surface to the global system matrix and residual vector. The deal.II library greatly facilitates the computation of the various surface operators, allowing the numerical implementation to closely match the theory developed in a companion paper. Key features of the theory and the numerical implementation are elucidated using a series of benchmark example problems. The full, documented source code is provided.

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“…Cho et al 34 expanded the two‐level algorithm into a multilayered grouping parallel algorithm suitable for large‐scale multiple‐level multiscale analyses. Frohne et al 35 proposed an efficient, large‐scale, parallel solution method for elastoplastic contact problems. Neiva et al 36 proposed a parallel fully‐distributed finite element framework for growing geometries and applied to metal additive manufacturing.…”

Section: Introductionmentioning

confidence: 99%

Multiscale analysis for 3D lattice structures based on parallel computing

Yan

Huo

et al. 2021

Numerical Meth Engineering

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In this study, a parallel framework for the multiscale analysis of three‐dimensional lattice structures is developed. The established parallel framework performs the multiscale analysis using the extended multiscale finite element method (EMsFEM) in a parallel environment provided by the portable and extensible toolkit for scientific computation (PETSc), which is a high‐performance parallel scientific computing library. To realize this aim, we developed several modifications of the original EMsFEM method and adopted some routines from PETSc. Through numerical examples, the efficiency and accuracy of the proposed parallel computing framework were verified first. Then, the parallel acceleration ratio and parallel efficiency of the proposed parallel framework were studied. The proposed parallel computing framework shows good efficiency and can be used to deal with the analysis of large‐scale lattice structures.

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Efficient numerical methods for the large‐scale, parallel solution of elastoplastic contact problems

Cited by 19 publications

References 44 publications

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

A finite element implementation of surface elasticity at finite strains using the deal.II library

Multiscale analysis for 3D lattice structures based on parallel computing

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