FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction

Dostál, Zdeněk; Horák, David; Kučera, Radek; Vondrák, Vít; Haslinger, Jaroslav; Dobiáš, Jiří; Pták, Svatopluk

doi:10.1016/j.cma.2004.05.015

Cited by 45 publications

(26 citation statements)

References 19 publications

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“…PermonFLLOP (FETI Light Layer on Top of PETSc) is an extension of the PermonQP package, implementing the algebraic part of DDMs of the FETI type [7], [6], [5], [4]. Let us show how PermonFLLOP is implemented from the user's perspective.…”

Section: Permonfllopmentioning

confidence: 99%

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Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Vašatová¹,

Tomčala²,

Sojka³

et al. 2017

Programs and Algorithms of Numerical Mathematics 18

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Section: Permonfllopmentioning

confidence: 99%

“…The inequality constraint matrix B I describes linearized non-penetration conditions [5] on the contact zones. It is empty for linear (permanent contact only) problems.…”

Section: Permonfllopmentioning

confidence: 99%

Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Vašatová¹,

Tomčala²,

Sojka³

et al. 2017

Programs and Algorithms of Numerical Mathematics 18

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“…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%

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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“…Dostál et al [2]. The newly formulated problem exhibits both numerical and parallel scalabilities [4], which is essential for effective application to high performance computers.…”

Section: Outline Of Theorymentioning

confidence: 99%

Total FETI for contact problems with additional nonlinearities

Dobiáš

Pták

Vondrák

et al. 2008

Proc Appl Math and Mech

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The paper is concerned with application of a new variant of the Finite Element Tearing and Interconnecting (FETI) method, referred to as the Total FETI (TFETI), to the solution to contact problems with additional nonlinearities. While the standard FETI methods assume that the prescribed Dirichlet conditions are inherited by subdomains, TFETI enforces both the compatibility between subdomains and the prescribed displacements by the Lagrange multipliers. If applied to the contact problems, this approach not only transforms the general nonpenetration constraints to the bound constraints, but it also generates an enriched natural coarse grid defined by the a priori known kernels of the stiffness matrices of the subdomains exhibiting rigid body modes. We combine our in a sense optimal algorithms for the solution to bound and equality constrained problems with geometric and material nonlinearities. The section on numerical experiments presents results of solution to bolt and nut contact problem with additional geometric and material nonlinear effects. Outline of theoryThe FETI class of nonoverlapping spatial domain decompositions was introduced by Farhat and Roux in their landmark paper [1]. The basic idea of the FETI methods is that the compatibility between subdomains, into which the original domain is partitioned, is enforced by the Lagrangian multipliers with physical meaning of forces in this mechanical context. Within the framework of the FETI concept, these forces are called the dual variables unlike the displacements which are referred to as the primal variables.After eliminating the primal variables, the original problem is reduced to a small, relatively well conditioned, typically equality constrained quadratic programming problem that is solved iteratively, see e.g. Dostál et al. [2]. The newly formulated problem exhibits both numerical and parallel scalabilities [4], which is essential for effective application to high performance computers.If concept of the FETI method is applied to solution to the contact problems, basically the same methodology can be used to prescribe conditions of nonpenetration between bodies in contact [2]. Total FETIConsider a steady-state contact problem of solid deformable bodies, which constitutes a 2nd order elliptic boundary value problem. The mathematical formulation of the problem is given by the governing equations expressing equilibrium conditions of the system, along with the boundary conditions, see e.g. [3, Chapter 2].The process of partitioning original domain into subdomains in general generates some subdomains, which are well constrained, others which are only partly constrained, and the remaining, which are totally unconstrained. All the subdomains which are not well constrained can move like rigid bodies, or they exhibit rigid body modes, so that their stiffness matrices are singular with dimensions of their kernels, or their defects, ranging from 1 to 6 for 3D problems.The original FETI method assumes that the Dirichlet boundary conditions are inherited from the ...

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FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction

Cited by 45 publications

References 19 publications

Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Solving Contact Mechanics Problems with PERMON

Total FETI for contact problems with additional nonlinearities

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