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

TL;DR

This paper develops a variant of the semismooth* Newton method for solving generalized equations involving SCD mappings, demonstrating local superlinear convergence and applying it to static contact problems with Coulomb friction.

Contribution

It introduces a new variant of the semismooth* Newton method tailored for SCD mappings and applies it to a practical contact problem with promising efficiency.

Findings

Method exhibits local superlinear convergence.

Two implementable variants tested successfully.

Effective for static contact problems with Coulomb friction.

Abstract

In the paper, a variant of the \ssstar 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.