Differential-Difference Iterative Domain Decomposition Methods for the Problems of Contact of Elastic Bodies with Nonlinear Winkler Surface Layers

We consider the problem of contact interaction of several elastic bodies with nonlinear Winkler surface layers. To solve a nonlinear variational equation with nondifferentiable operator corresponding to this contact problem, we propose to use implicit two-point combined differential-difference parallel iterative Robin-type domain decomposition algorithms. We propose software realization of these algorithms for the case of plane contact problems based on finite-element approximations. We compare the numerical efficiency of the two-point and one-point iterative domain decomposition methods for the problem of contact of two elastic bodies containing a groove through a nonlinear Winkler layer.