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

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

doi:10.1002/nme.2807

Cited by 54 publications

(32 citation statements)

References 56 publications

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“…The basic idea of the TFETI method [5,7,32] is to keep all the subdomains floating and enforce the Dirichlet boundary conditions by means of a constraint matrix and Lagrange multipliers, similarly to the gluing conditions along subdomain interfaces. This simplifies the implementation of the stiffness matrix pseudoinverse.…”

Section: Permonfllopmentioning

confidence: 99%

“…The inequality part B s I (possibly empty) describes linearized non-penetration conditions [7] of the subdomain Ω s on the corresponding part of the contact zone. The global constraint right-hand side vector c and vector of Lagrange multipliers λ possess analogous structure.…”

Section: Permonfllopmentioning

confidence: 99%

“…Compared to the basic augmented Lagrangian method, the introduced adaptivity weakens the effect of the proper selection of the penalty sequence and eliminates necessity of exact solution of the inner problems. Optimality results for SMALBE were presented in [10,9,8,7].…”

Section: Smalbementioning

confidence: 99%

See 2 more Smart Citations

Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

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Abstract. PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems lead to inequality constrained quadratic programming problems that can be solved by our PermonQP package.

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Section: Permonfllopmentioning

confidence: 99%

Section: Permonfllopmentioning

confidence: 99%

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Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

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show abstract

“…To make computations more efficient, the TFETI domain decomposition method ( [12,14]) was used. A typical decomposition of 1 and 2 into subdomains is shown in Fig.…”

Section: Comments On the Implementationmentioning

confidence: 99%

Discretization and numerical realization of contact problems for elastic‐perfectly plastic bodies. PART II – numerical realization, limit analysis

et al. 2015

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The paper deals with numerical realization of discretized, frictionless static contact problems for elastic-perfectly plastic materials and the computational limit analysis. Two numerical methods based on the variational formulation in terms of stresses are analyzed: the semi-smooth Newton method with damping and the alternating direction method of multipliers. These methods are used for tracking the loadings path to determine the discretized limit loading parameter and for solving elastic-perfectly plastic problems.

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“…Dostál et al analysed in [1] problem of frictionless contact problem between solid bodies, while they considered both geometrically and materially linear cases. Therein they suggested a new in a sense optimal version of their own previously developed algorithm based on TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Scalable TFETI domain decomposition based contact algorithm

Dobiáš¹,

Pták²,

Dostál³

et al. 2011

Surface Effects and Contact Mechanics X

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This paper is concerned with a novel algorithm for a solution to contact problems stemming from the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. The TFETI method is based on the idea that the compatibility between non-overlapping sub-domains, into which the original domain is partitioned, is enforced by the Lagrange multipliers. The distinctive feature of the TFETI consists of the fact that the method also enforces the Dirichlet boundary conditions by means of the Lagrange multipliers. The TFETI based technique converts the original contact problem to the quadratic programming one with the equalities and simple bound constraints. Moreover, it also results in more efficient preconditioning by an enriched natural coarse grid defined by a priory known kernels of the stiffness matrices. Our new algorithm exhibits both parallel and numerical scalabilities so that it enables us to effectively solve steady-state problems of deformable bodies undergoing contact, geometric and material nonlinear effects. In this paper we propose an algorithm with nested iteration strategy, where its inner part consists of a new version of our previously developed MPRGP and SMALBE algorithms and the outer loop iterates on the geometric and material non-linearities. Numerical experiments include solutions to steady-state problems with non-linear effects and their results document that the proposed algorithms are robust, highly accurate and exhibit both parallel and numerical scalabilities.

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

Cited by 54 publications

References 56 publications

Solving Contact Mechanics Problems with PERMON

Solving Contact Mechanics Problems with PERMON

Discretization and numerical realization of contact problems for elastic‐perfectly plastic bodies. PART II – numerical realization, limit analysis

Scalable TFETI domain decomposition based contact algorithm

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