On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction

Abstract

In the paper, a variant of the semismooth${}^{\ast }$ Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild regularity requirement, the method exhibits (locally) superlinear convergence behavior. From the main conceptual algorithm, two implementable variants are derived whose efficiency is tested via a generalized equation modeling a discretized static contact problem with Coulomb friction.

Keywords: Generalized equation; Newton method; Signorini problem with Coulomb friction; Subspace containing derivative; semismoothness${}^{\ast }$.