Scalable total BETI based solver for 3D multibody frictionless contact problems in mechanical engineering

Abstract

A total BETI (TBETI) based domain decomposition algorithm with the preconditioning by a natural coarse grid of the rigid body motions is adapted for the solution of multibody frictionless contact problems of linear elastostatics and proved to be scalable, i.e., the cost of the solution is asymptotically proportional to the number of variables. The analysis admits floating bodies. The proofs combine the original results by Langer and Steinbach on the scalability of BETI for linear problems and our development of optimal quadratic programming algorithms for bound and equality constrained problems. The theoretical results are verified by numerical experiments. The power of the method is demonstrated on the analysis of ball bearings.