A Reverse Augmented Constraint preconditioner for Lagrange multiplier methods in contact mechanics

TL;DR

This paper introduces a novel reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics, improving computational efficiency and robustness in solving nonlinear frictional contact problems.

Contribution

It proposes a new reverse augmentation approach for constraint preconditioning that handles singular blocks and enhances efficiency over traditional methods.

Findings

Significantly cheaper than traditional methods

Effective for large-scale contact mechanics problems

Supports HPC implementation with Chronos

Abstract

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems. When contact is modeled with the aid of Lagrange multipliers, the impenetrability condition is enforced exactly, but the associated Jacobian matrix is indefinite and needs a special treatment for a fast numerical solution. In this work, a constraint preconditioner is proposed where the primal Schur complement is computed after augmenting the zero block. The name Reverse is used in contrast to the traditional approach where only the structural block undergoes an augmentation. Besides being able to address problems characterized by singular structural blocks, often arising in contact mechanics, it is shown that the proposed approach is significantly cheaper than traditional constraint preconditioning for this class of problems and it is suitable for an efficient HPC implementation through the Chronos parallel package. Our conclusions are supported by several numerical experiments on mid- and large-size problems from various applications. The source files implementing the proposed algorithm are freely available on GitHub.