Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

Jörg Frohne, Timo Heister, Wolfgang Bangerth

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
Original languageEnglish (US)
Pages (from-to)416-439
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Aug 6 2015
Externally publishedYes


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