# An Accelerated Uzawa Method for Application to Frictionless Contact Problem

## TL;DR

This paper introduces an accelerated version of the Uzawa method, improving convergence speed for solving frictionless contact problems in computational mechanics by applying an accelerated projected gradient approach.

## Contribution

The paper proposes a novel accelerated Uzawa method that enhances convergence speed for contact mechanics problems compared to the traditional approach.

## Key findings

- Faster convergence demonstrated in preliminary experiments
- Application of accelerated projected gradient to dual problem
- Potential for improved computational efficiency in contact mechanics

## Abstract

The Uzawa method is a method for solving constrained optimization problems, and is often used in computational contact mechanics. The simplicity of this method is an advantage, but its convergence is slow. This paper presents an accelerated variant of the Uzawa method. The proposed method can be viewed as application of an accelerated projected gradient method to the Lagrangian dual problem. Preliminary numerical experiments suggest that the convergence of the proposed method is much faster than the original Uzawa method.