A Full Multigrid Method for Linear Complementarity Problems arising from Elastic Normal Contact Problems

Abstract

This paper presents a full multigrid (FMG) technique, which combines a multigrid method, an active set algorithm and a nested iteration technique, to solve a linear complementarity problem (LCP) modeling elastic normal contact problems. The governing system in this LCP is derived from a Fredholm integral of the first kind, and its coefficient matrix is dense, symmetric and positive definite. One multigrid cycle is applied to solve this system approximately in each active set iteration. Moreover, this multigrid solver incorporates a special strategy to handle the complementarity conditions, including restricting both the defect and the contact area (active set) to the coarse grid, and setting all quantities outside contact to zero. The smoother is chosen by some analysis based on the eigenvectors of the iteration matrix. This method is applied to a Hertzian smooth contact and a rough surface contact problem.

Keywords:

• full multigrid
• linear complementarity problems
• integral equation
• normal contact problems
• active set algorithm

AMS Subject Classification:

• 65N55
• 65R20
• 49M30
• 35Q74