Multigrid for the dual formulation of the frictionless Signorini problem
Informazioni aggiuntive
Autori
Rovi G.,
Kober B.,
Starke G.,
Krause R.
Tipo
Articolo pubblicato in rivista scientifica
Anno
2023
Lingua
Inglese
Sommario
We examine the dual formulation of the frictionless Signorini problem for a deformable body in contact with a rigid obstacle. We discretize the problem by means of the finite element method. Since the dual formulation solves directly for the stress variable and is not affected by locking, it is very attractive for many engineering applications. However, it is hard to solve it efficiently, since many challenges arise. First, the stress belongs to the non-Sobolev space Hdiv. Second, the matrix block related to the stress is only semi-positive definite in the incompressible limit. Third, global equality constraints and box-constraints are enforced. In this paper, we propose a novel and optimal nonlinear multigrid method for the dual formulation of the Signorini problem, that works even in the incompressible limit. We opt for the combination of a truncation of the basis functions strategy and a nonlinear monolithic patch smoother with Robin conditions of parameter α. Numerical experiments show that multigrid performance is recovered if α is chosen properly. We propose an algorithm to dynamically update the parameter α during the multigrid process, in order to provide a near optimal value of α.
Parole chiave
Nonlinear, Multigrid, Dual Signorini problem, Incompressibility, Robin conditions
Periodico
International journal for numerical methods in engineering
Volume
124
Numero ( Mese )
10
Pagine (o numero dell’articolo)
2367-2388
DOI
Diffusione
Licenza
CC BY-NC-ND
Visibilità
Pubblico
Status open access
Hybrid
