Un algorithme de type Robin pour des problèmes de contact unilatéral

Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity

“…Among the domain decomposition methods for unilateral two-body contact problems obtained on the continuous level, one should mention Dirichlet-Neumann [13,14,15], Neumann-Neumann [16,17] and optimization based [18] iterative algorithms. A generalization of Lions' Robin-Robin domain decomposition algorithm to a two-body contact problem was proposed in works [19,20,21]. All of these methods in each iteration require to solve a nonlinear one-sided contact problem with a rigid body (Signorini problem) for one of the bodies, and a linear elasticity problem with Neumann [13,14,15] or Dirichlet [16,17,18] boundary conditions on the possible contact area for the other body, or require to solve nonlinear Signorini problems for both of the bodies [19,20,21].…”

“…A generalization of Lions' Robin-Robin domain decomposition algorithm to a two-body contact problem was proposed in works [19,20,21]. All of these methods in each iteration require to solve a nonlinear one-sided contact problem with a rigid body (Signorini problem) for one of the bodies, and a linear elasticity problem with Neumann [13,14,15] or Dirichlet [16,17,18] boundary conditions on the possible contact area for the other body, or require to solve nonlinear Signorini problems for both of the bodies [19,20,21]. Moreover, to increase the convergence rate of Neumann-Neumann and Robin-Robin algorithms, it is recommended to perform an additional iteration, in which the linear elasticity problems with Neumann boundary conditions have to be solved for both of the bodies [16,20].…”