Scalable TFETI algorithm for the solution of multibody contact problems of elasticity

Abstract

A Total FETI (TFETI)-based domain decomposition algorithm with preconditioning by a natural coarse grid of the rigid body motions is adapted to the solution of multibody contact problems of elasticity in 2D and 3D and proved to be scalable. The algorithm finds an approximate solution at the cost asymptotically proportional to the number of variables provided the ratio of the decomposition parameter and the discretization parameter is bounded. The analysis is based on the classical results by Farhat, Mandel, and Roux on scalability of FETI with a natural coarse grid for linear problems and on our development of optimal quadratic programming algorithms for bound and equality constrained problems. The algorithm preserves parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate a high efficiency of our algorithm. In addition, its performance is illustrated on a real-world problem of analysis of the ball bearing. Copyright © 2009 John Wiley & Sons, Ltd.