A scalable FETI-DP algorithm for a coercive variational inequality

Dostál, Zdeněk; Horák, David; Stefanica, Dan

doi:10.1016/j.apnum.2004.09.009

Cited by 22 publications

(34 citation statements)

References 32 publications

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“…After proving optimality results for the semimonotonic augmented Lagrangians for bound and equality constraints (SMALBE) algorithm [33], they have recently presented a theoretically supported scalable algorithm for scalar variational inequalities [34]. Similar results were obtained by Dostál et al [35,36] for FETI-DP and by Bouchala et al [37] for a boundary element variant of FETI. The aim of this paper is to show optimality results for multibody contact problems of elasticity using our TFETI (Total FETI) variant [38] of the FETI method which enforces the prescribed displacements by Lagrange multipliers.…”

Section: Introductionsupporting

confidence: 58%

Scalable TFETI algorithm for the solution of multibody contact problems of elasticity

Dostál

Kozubek

Vondrák

et al. 2009

Numerical Meth Engineering

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SUMMARYA Total FETI (TFETI)-based domain decomposition algorithm with preconditioning by a natural coarse grid of the rigid body motions is adapted to the solution of multibody contact problems of elasticity in 2D and 3D and proved to be scalable. The algorithm finds an approximate solution at the cost asymptotically proportional to the number of variables provided the ratio of the decomposition parameter and the discretization parameter is bounded. The analysis is based on the classical results by Farhat, Mandel, and Roux on scalability of FETI with a natural coarse grid for linear problems and on our development of optimal quadratic programming algorithms for bound and equality constrained problems. The algorithm preserves parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate a high efficiency of our algorithm. In addition, its performance is illustrated on a real-world problem of analysis of the ball bearing.

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Section: Introductionsupporting

confidence: 58%

Scalable TFETI algorithm for the solution of multibody contact problems of elasticity

Dostál

Kozubek

Vondrák

et al. 2009

Numerical Meth Engineering

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“…. , n}, and let I denote the set of indexes of the constrained variables from problem (1). Then the KKT conditions read x i = i and i ∈ I implies g i 0 and…”

Section: Proofmentioning

confidence: 99%

“…We are interested in large, sparse problems, such as those arising from the discretization of elliptic boundary variational inequalities [1,2]. experiments with the multigrid methods for the solution of (1) presented by Kornhuber [20], Krause and Wohlmuth [21], and Iontcheva and Vassilevski [2].…”

Section: Introductionmentioning

confidence: 99%

Projector preconditioning for partially bound‐constrained quadratic optimization

Domoradova

Dostal

2007

Numerical Linear Algebra App

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SUMMARYPreconditioning by a conjugate projector is combined with the recently proposed modified proportioning with reduced gradient projection (MPRGP) algorithm for the solution of bound-constrained quadratic programming problems. If applied to the partially bound-constrained problems, such as those arising from the application of FETI-based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is shown to have better bound on the rate of convergence than the original MPRGP algorithm. The performance of the algorithm is illustrated on the solution of a model boundary variational inequality.

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“…For an efficient implementation of F it is important to exploit the structure of K; see [8,10] for more details.…”

Section: Feti-dp Discretization Of the Problemmentioning

confidence: 99%

“…To solve the discretized variational inequality, we use our recently proposed algorithms [8,10]. To solve the bound constrained quadratic programming problem (4), we use active set based algorithms with proportioning and gradient projections [4,11].…”

Section: Optimalitymentioning

confidence: 99%

An Overview of Scalable FETI—DP Algorithms for Variational Inequalities

Dostál

Horák

Stefanica

Lecture Notes in Computational Science and Engineering

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Summary. We review our recent results concerning optimal algorithms for numerical solution of both coercive and semi-coercive variational inequalities by combining dual-primal FETI algorithms with recent results for bound and equality constrained quadratic programming problems. The convergence bounds that guarantee the scalability of the algorithms are presented. These results are confirmed by numerical experiments.

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A scalable FETI-DP algorithm for a coercive variational inequality

Cited by 22 publications

References 32 publications

Scalable TFETI algorithm for the solution of multibody contact problems of elasticity

Scalable TFETI algorithm for the solution of multibody contact problems of elasticity

Projector preconditioning for partially bound‐constrained quadratic optimization

An Overview of Scalable FETI—DP Algorithms for Variational Inequalities

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