Scalable Domain Decomposition Algorithms for Contact Problems: Theory, Numerical Experiments, and Real World Problems

Abstract

We review our results related to the development of theoretically supported scalable algorithms for the solution of large scale contact problems of elasticity. The algorithms combine the Total FETI/BETI based domain decomposition method adapted to the solution of 2D and 3D multibody contact problems of elasticity, both frictionless and with friction, with our in a sense optimal algorithms for the solution of resulting quadratic programming and QPQC problems. Rather surprisingly, the theoretical results are qualitatively the same as the classical results on scalability of FETI/BETI for linear elliptic problems. The efficiency of the method is demonstrated by results of parallel numerical experiments for contact problems of linear elasticity discretized by more than 11 million variables in 3D and 40 million variables in 2D. © Springer-Verlag Berlin Heidelberg 2013.