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

by   Andrea Franceschini, et al.

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.


A survey of numerical methods for hemivariational inequalities with applications to Contact Mechanics

In this paper we present an abstract nonsmooth optimization problem for ...

Numerical integration in celestial mechanics: a case for contact geometry

Several dynamical systems of interest in celestial mechanics can be writ...

A preconditioned mixed-FE scheme with stabilized Lagrange multiplier for frictional contact mechanics of crossing fractures in porous media

Simulation of contact mechanics in fractured media is of paramount impor...

The TR-BDF2 method for second order problems in structural mechanics

The application of the TR-BDF2 method to second order problems typical o...

New directions for contact integrators

Contact integrators are a family of geometric numerical schemes which gu...

A Physics-Based Model Reduction Approach for Node-to-Segment Contact Problems in Linear Elasticity

The paper presents a new reduction method designed for dynamic contact p...

An efficient implicit constraint resolution scheme for interactive FE simulations

This paper presents a novel implicit scheme for the constraint resolutio...

Please sign up or login with your details

Forgot password? Click here to reset