Scalable TFETI with optional preconditioning by conjugate projector for transient frictionless contact problems of elasticity

Dostál, Zdeněk; Kozubek, Tomáš; Brzobohatý, Tomáš; Markopoulos, Alexandros; Vlach, Oldřich

doi:10.1016/j.cma.2012.08.003

Cited by 20 publications

(12 citation statements)

References 29 publications

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“…A special structure of the discretized dual problem was exploited in the development of theoretically supported scalable algorithms for the solution of elliptic variational inequalities such as those describing the equilibrium of a system of elastic bodies in contact [5], including the contact problems with friction [6] and the transient contact problems [7].…”

Section: Introductionmentioning

confidence: 99%

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Dostál

Kozubek

Vlach

et al. 2015

Numerical Linear Algebra App

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SUMMARYA cheap symmetric stiffness-based preconditioning of the Hessian of the dual problem arising from the application of the finite element tearing and interconnecting domain decomposition to the solution of variational inequalities with varying coefficients is proposed. The preconditioning preserves the structure of the inequality constraints and affects both the linear and nonlinear steps, so that it can improve the rate of convergence of the algorithms that exploit the conjugate gradient steps or the gradient projection steps. The bounds on the regular condition number of the Hessian of the preconditioned problem, which are independent of the coefficients, are given. The related stiffness scaling is also considered and analysed. The improvement is demonstrated by numerical experiments including the solution of a contact problem with variationally consistent discretization of the non-penetration conditions. The results are relevant also for linear problems.

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Section: Introductionmentioning

confidence: 99%

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Dostál

Kozubek

Vlach

et al. 2015

Numerical Linear Algebra App

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“…One can read more about the formulation for unilateral contact in [8,9]. Our notation of the multibody case is similar to the prepared article [3] on transient problems.…”

Section: Introductionmentioning

confidence: 99%

“…Since its formulation is given by a variational inequality of the second kind, after discretization we obtain a convex non-smooth constrained minimization problem for a discrete total potential energy function. To increase the efficiency of the quadratic part of the minimized problem we used the TFETI method, a variant (see Dostál et al [2] and [3]) of FETI domain decomposition methods framework et al [4]). Introducing the additional Lagrange multipliers one can release the non-penetration conditions and transform the frictional into a smooth one.…”

Section: Introductionmentioning

confidence: 99%

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

Vlach¹,

́al²,

Kozubek³

et al. 2012

WIT Transactions on the Built Environment

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This paper deals with the solution of the discretized quasistatic 3D Signorini problems with local Coulomb friction. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is decomposed by the TFETI domain decomposition method used in auxiliary contact problems with Tresca friction. The algebraic formulation of these problems in 3D leads to the quadratic programing with equality constraints together with box and separable quadratic constraints. For the solution we used the scalable algorithm SMALSE developed at our department. The efficiency of the method is demonstrated by results of numerical experiments with parallel solution of 3D contact problems of elasticity.

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“…Several domain decomposition approaches have been proposed for contact problems, see [8,3,10,9,4,24,3] amongst others, but a few are concerned with multiple contacts in granular media (for an algebraic-like partition, see [17], and for a geometric partitioning of the discrete granular domain, see [5,2,23,30]). Here, we focus on the comparison of two formulations, one similar to FETI approaches, the other closer to additive Schwarz approaches, and of two implementations of the underlying communication scheme.…”

Section: Domain Decomposition Approachesmentioning

confidence: 99%

High performance computing of discrete nonsmooth contact dynamics with domain decomposition

Visseq

Alart

Dureisseix

2013

Numerical Meth Engineering

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We investigate two algorithms for solving large-scale granular problems using domain decomposition methods. These numerical schemes can be connected to classical domain decompositions, with and without overlapping, developed in continuum mechanics. The two algorithms are compared in terms of implementation and parallel performance. We focus the numerical study on communication procedures between processors, load balancing and scalability, topics particularly crucial in nonlinear evolutive problems. This is the accepted version of the following article: Visseq, V., Alart, P. and Dureisseix, D. (2013), High performance computing of discrete nonsmooth contact dynamics with domain decomposition. Int. J. Numer. Meth. Engng, 96: 584598.

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Scalable TFETI with optional preconditioning by conjugate projector for transient frictionless contact problems of elasticity

Cited by 20 publications

References 29 publications

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

High performance computing of discrete nonsmooth contact dynamics with domain decomposition

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