Asynchronous Schwarz methods applied to constrained mechanical structures in grid environment

•We characterize the solution of the obstacle problem by various ways.•We consider discretization schemes arising convergence of iterative algorithms.•We consider parallel solution of discrete problem by asynchronous Schwarz method.•Parallel experiments show the interest of asynchronous algorithms.•Tests are performed on grid architecture on distant and heterogeneous machines. This paper deals with the parallel solution of the stationary obstacle problem with convection–diffusion operator. The obstacle problem can be formulated by various ways and in the present study it is formulated like a multivalued problem. Another formulation by complementary problem is also considered. Appropriate discretization schemes are considered for the numerical solution on decentralised memory machines by using parallel synchronous and asynchronous Schwarz alternating algorithms. The considered discretization schemes ensure the convergence of the parallel synchronous or asynchronous Schwarz alternating methods on one hand for the solution of the multivalued problem and on the other hand for the solution of the complementary problem. Finally the implementation of the algorithms is described and the results of parallel simulations are presented.