A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction

Dostál, Zdeněk; Kozubek, Tomáš; Markopoulos, Alexandros; Brzobohatý, Tomáš; Vondrák, Vít; Horyl, Petr

doi:10.1016/j.cma.2011.02.015

Cited by 32 publications

(20 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The value (k) cgm is proportional to the current outer precision err (k−1) defined in (11) or, if the progress is not sufficient, to the improved inner tolerance (k−1) cgm from the previous step:…”

Section: Adaptive Inner Precision Controlmentioning

confidence: 99%

“…It extends the algorithm of Dostál [7] and Dostál and Schöberl [9] originally developed for simple bound problems. The common feature of these algorithms is the theory comprising the same convergence rate that enables us to prove the scalability of methods for solving 3D contact problems without [7,10] and with [8,11] friction. However, the practical behaviour may be different due to the difference in the finite termination property.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

An interior-point algorithm for the minimization arising from 3D contact problems with friction

Kučera

Machalová

Netuka

et al. 2012

Optimization Methods and Software

View full text Add to dashboard Cite

The paper deals with a variant of the interior-point method for the minimization of strictly quadratic objective function subject to simple bounds and separable quadratic inequality constraints. Such minimizations arise from the finite element approximation of contact problems of linear elasticity with friction in three space dimensions. The main goal of the paper is the convergence analysis of the algorithm and its implementation. The optimal preconditioners for solving ill-conditioned inner linear systems are proposed. Numerical experiments illustrate the computational efficiency for large-scale problems.

show abstract

Section: Adaptive Inner Precision Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

An interior-point algorithm for the minimization arising from 3D contact problems with friction

Kučera

Machalová

Netuka

et al. 2012

Optimization Methods and Software

View full text Add to dashboard Cite

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…All the blocks in the stiffness matrix are positive semidefinite with the kernel of the dimension 6 in the case of 3D problems. Using the standard procedure to modify the non-differentiable term (see Dostál et al [10]), we get…”

Section: Domain Decomposition and Dual Formulation Of The Auxiliary Tmentioning

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction

Cited by 32 publications

References 24 publications

An interior-point algorithm for the minimization arising from 3D contact problems with friction

An interior-point algorithm for the minimization arising from 3D contact problems with friction

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

Contact Info

Product

Resources

About