The Semi-Smooth Netwon Method for Solving 2D and 3D Contact Problems with Tresca and Coulomb Friction

Abstract

The thesis analyzes the semi-smooth Newton method applied to 2D and 3D contact problems with the Tresca and the Coulomb friction. The starting point is the primal-dual formulation of a contact problem, in which contact conditions are reformulated by nonsmooth systems. The semi-smooth Newton method is implemented as an active set algorithm. The conjugate and biconjugate gradient methods are used for inexact solving of inner linear systems. In 2D, we propose the globally convergent variant of the algorithm and we prove its R-linear rate of convergence. Moreover, we combine the semismooth Newton method with the TFETI domain decomposition method. Finally, we present an implementation in 3D. The performance of different algorithms is illustrated by numerical experiments.