An Optimization-Based Domain Decomposition Method for a Two-Body Contact Problem

Abstract

We study a domain decomposition method for the numerical simulation of a two-body contact problem in two-dimensional linear elasticity. The problem is restated as a decomposition-coordination problem by introducing a smooth fictitious rigid surface between the two elastic bodies. In the decomposition step, two independent problems are solved: a Signorini-like problem and a prescribed displacement problem. In the coordination step, the fictitious rigid surface is adjusted to minimize a auxiliary functional.

Keywords:

• Contact problem
• Domain decomposition
• Hierarchical optimization

Notes

^aWe use C as a generic strictly positive constant with different values in different places