Scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions

Dostál, Zdeněk; Vlach, Oldřich; Brzobohatý, Tomáš

doi:10.1016/j.finel.2019.01.002

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…Si l'on prend comme maillage de référence celui qui a été utilisé pour modéliser le contact entre deux aspérités sphériques (Mulvihill et al 2011) avec ≈ 190 000 éléments tétraédriques et hexaédriques pour deux quarts des sphères, on obtient alors que pour simuler une centaine d'aspérités, il nous faudrait résoudre un système avec le nombre de degrés de liberté N dof ≈ 3 × 100 × 190 000 × 2 × 1, 5 = 171 10 6 , où le facteur 3 prend en compte le nombre de degrés de liberté (DDL) par noeud, le facteur 100 est le nombre d'aspérités, le facteur 2 serte à simuler les demi-sphères des aspérités au lieu des quarts, et le facteur 1, 5 sert à prendre en compte le maillage grossier du volume sousjacent et l'espacement entre des aspérités. Une résolution du problème associé avec autant de DDL semble plutôt réaliste pour des puissances modernes des calculateurs et pour le niveau de parallélisme des codes de calcul, par exemple, (Dostál et al 2019). En revanche, des calculs du contact entre des surfaces rugueuses de telle ampleur n'existent pas encore.…”

Section: Application II : Contact Des Surfaces Rugueusesunclassified

Méthodes numériques en contact micromécanique

Yastrebov¹

2023

Modélisation Numérique en Mécanique Fortement Non Linéaire

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Les méthodes numériques pour traiter des problèmes du contact à petites échelles ainsi que des modèles associés sont discutés. Une revue d’applications de la méthode des éléments finis et celle des éléments de frontière aux problèmes du contact rugueux est faite. Les deux applications pertinentes sont présentées en détail : le contact des aspérités et le contact des surfaces rugueuses.

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Section: Application II : Contact Des Surfaces Rugueusesunclassified

Méthodes numériques en contact micromécanique

Yastrebov¹

2023

Modélisation Numérique en Mécanique Fortement Non Linéaire

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“…10 Finite element tearing and interconnecting (FETI) like methods are able to tackle really large-size problems while exhibiting good scalability. 5,11 The range of application of these methods also covers for example, biomechanics, 12 structural dynamics, 13 contact mechanics, 14 digital image correlation, 15 nonlinear problems with specific algorithms 16,17 and isogeometric analysis. 18,19 Continuous effort has been made to be able to deal with real engineering applications that exhibit pathological components that hinder the convergence of the underlying Krylov solver, such as jagged interfaces, bad aspect ratios, strong heterogeneity, incompressibility, and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…Finite element tearing and interconnecting (FETI) like methods are able to tackle really large‐size problems while exhibiting good scalability 5,11 . The range of application of these methods also covers for example, biomechanics, 12 structural dynamics, 13 contact mechanics, 14 digital image correlation, 15 nonlinear problems with specific algorithms 16,17 and isogeometric analysis 18,19 …”

Section: Introductionmentioning

confidence: 99%

On the use of graph centralities to compute generalized inverse of singular finite element operators: Applications to the analysis of floating substructures

Bovet

2023

Numerical Meth Engineering

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This article introduces a robust and affordable method to compute nullspace and generalized inverse of finite element operators involved in dual domain decomposition methods. The methodology relies on the operator partial factorization and on the analysis of a well chosen Schur complement. The sparse linear operator is interpreted as a network and graph centrality measures are used to select the condensation variables. Eigen vector, Katz and Page Rank centralities are evaluated. An extension to deal with symmetric indefinite systems arising from mixed finite elements is also presented. The approach is assessed on highly heterogeneous problems and one industrial application is presented: the numerical homogenization of solid propellant.

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Hybrid TBETI domain decomposition for huge 2D scalar variational inequalities

Dostál,

Sadowská,

Horák

et al. 2024

Numerical Meth Engineering

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The unpreconditioned H‐TFETI‐DP (hybrid total finite element tearing and interconnecting dual‐primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non‐overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three‐level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H‐TBETI‐DP (hybrid total boundary element tearing and interconnecting dual‐primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts.

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Scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions

Cited by 8 publications

References 26 publications

Méthodes numériques en contact micromécanique

Méthodes numériques en contact micromécanique

On the use of graph centralities to compute generalized inverse of singular finite element operators: Applications to the analysis of floating substructures

Hybrid TBETI domain decomposition for huge 2D scalar variational inequalities

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