A theoretically supported scalable TFETI algorithm for the solution of multibody 3D contact problems with friction

A Total FETI (TFETI) based domain decomposition algorithm with preconditioning by a natural coarse grid defined by the rigid body motions of subdomains is adapted to the solution of multibody contact problems with friction in 3D and proved to be scalable for Tresca friction. The analysis admits “floating” bodies. The algorithm finds an approximate solution at the cost asymptotically proportional to the number of variables provided the ratio of the decomposition and the discretization parameters is bounded. The analysis is based on the classical results by Farhat et al. on scalability of FETI for linear problems and on our development of optimal quadratic programming algorithms. The algorithm preserves parallel scalability of the classical FETI method. Both theoretical results and numerical experiments indicate that our algorithm is effective. The effectiveness of the method in the inner loop of the fixed point iterations for the solution of the contact problems with Coulomb’s friction is illustrated on the analysis of a mine support.