Projection-based model reduction for contact problems

Maciej Balajewicz, David Amsallem, Charbel Farhat

Research output: Contribution to journalArticlepeer-review


To be feasible for computationally intensive applications such as parametric studies, optimization, and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that tend to dramatically increase computational complexity. Although significant progress has been achieved in the development of computational approaches for the reduction of nonlinear computational mechanics models, addressing the issue of contact remains a major hurdle. To this effect, this paper introduces a projection-based model reduction approach for both static and dynamic contact problems. It features the application of a non-negative matrix factorization scheme to the construction of a positive reduced-order basis for the contact forces, and a greedy sampling algorithm coupled with an error indicator for achieving robustness with respect to model parameter variations. The proposed approach is successfully demonstrated for the reduction of several two-dimensional, simple, but representative contact and self contact computational models.

Original languageEnglish (US)
Pages (from-to)644-663
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - May 25 2016


  • Contact
  • Greedy sampling method
  • Non-negative matrix factorization
  • Nonlinear model reduction
  • Reduced-order basis
  • Reduced-order model
  • Singular value decomposition

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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