Scalable TFETI domain decomposition based contact algorithm

摘要

This paper is concerned with a novel algorithm for a solution to contact problems stemming from the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. The TFETI method is based on the idea that the compatibility between non-overlapping sub-domains, into which the original domain is partitioned, is enforced by the Lagrange multipliers. The distinctive feature of the TFETI consists of the fact that the method also enforces the Dirichlet boundary conditions by means of the Lagrange multipliers. The TFETI based technique converts the original contact problem to the quadratic programming one with the equalities and simple bound constraints. Moreover, it also results in more efficient preconditioning by an enriched natural coarse grid defined by a priory known kernels of the stiffness matrices. Our new algorithm exhibits both parallel and numerical scalabilities so that it enables us to effectively solve steady-state problems of deformable bodies undergoing contact, geometric and material nonlinear effects. In this paper we propose an algorithm with nested iteration strategy, where its inner part consists of a new version of our previously developed MPRGP and SMALBE algorithms and the outer loop iterates on the geometric and material non-linearities. Numerical experiments include solutions to steady-state problems with non-linear effects and their results document that the proposed algorithms are robust, highly accurate and exhibit both parallel and numerical scalabilities.