A domain decomposition method for two-body contact problems with Tresca friction

Haslinger, Jaroslav; Kučera, Radek; Riton, Julien; Sassi, Taoufik

doi:10.1007/s10444-013-9299-y

Cited by 8 publications

(2 citation statements)

References 26 publications

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“…As an alternative to the previous methods, there are formulations that allow solving problems for each body separately, with certain boundary conditions at the natural interface. These kinds of methods are named as Dirichlet-Neumann type contact algorithms, and for a complete overview, the reader is referred to [15,16,17,18,19,20]. One of the pioneering works in this area was done by Krause [15], who solved a frictional Signorini contact problem between two elastic bodies based on mortar elements for discretization, and a monotone multigrid method as a subdomain solver.…”

Section: Introductionmentioning

confidence: 99%

A parallel algorithm for unilateral contact problems

Guillamet

Rivero

Zavala-Aké

et al. 2022

Computers & Structures

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Section: Introductionmentioning

confidence: 99%

A parallel algorithm for unilateral contact problems

Guillamet

Rivero

Zavala-Aké

et al. 2022

Computers & Structures

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“…The NSEs obviously becomes larger in scale after the above treatment, effective simulation algorithms for the set of equations must be developed . Numerical method based on domain decomposition is a powerful technique to compute solutions of partial differential equations (Kong et al 2009;Haslinger et al 2014). The method is especially good when a computer's memory is not large enough for the complete problem or when a domain has an irregular shape, which often happens in practical applications.…”

Section: Introductionmentioning

confidence: 99%

A domain decomposition method for the Navier–Stokes equations with stochastic input

2021

Comp. Appl. Math.

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The paper is committed to studying the domain decomposition method for the incompressible Navier–Stokes equations(NSEs) with stochastic input. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space, and the stochastic NSEs system are transformed into deterministic ones via the polynomial chaos expansion. The corresponding deterministic equations are transformed into the constrained optimization problem by minimizing the cost function on the common interface after the whole domain decomposed into two sub-domains. The constrained optimization problems are transformed into unconstrained problems by the Lagrange multiplier rule. A gradient method-based approach to the solutions of domain decomposition problem is proposed to solve the unconstrained optimality system. Finally, one numerical simulation experiment for square cavity flow problem with the stochastic boundary conditions are performed to demonstrate the feasibility and applicability of the gradient method.

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