A Nonlinear FETI-DP Method with an Inexact Coarse Problem

  • Axel Klawonn
  • Martin Lanser
  • Oliver RheinbachEmail author
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


A new nonlinear version of the well-known FETI-DP method (Finite Element Tearing and Interconnecting Dual-Primal) is introduced. In this method, the nonlinear problem is decomposed before linearization. Nonlinear approaches to domain decomposition can be viewed as a strategy to localize computational work for the efficient use with future extreme-scale supercomputers. As opposed to known nonlinear FETI-DP algorithms, in the new method the coarse solver can be replaced by a preconditioner, i.e., the coarse solve can be inexact. It is expected that the new method can show a superior parallel scalability if the number of subdomains is large. If the coarse solver is exact and the method is applied to linear problems then the method is equivalent to the standard FETI-DP method. Numerical results for up to 32,768 cores are presented using cycles of an algebraic multigrid for the coarse problem of the new method.


Domain Decomposition Domain Decomposition Method Newton Step Krylov Method Full Newton Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Satish Balay and Barry Smith, Argonne National Laboratory (ANL), USA, for the fruitful cooperation and the assistance on running the authors’ code on the MIRA Supercomputer (BG/P) at ANL. This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA). The authors acknowledge the use of the Cray XT6 computer at Universität Duisburg-Essen. The authors also gratefully acknowledge the SuperMUC Supercomputer at Leibniz-Rechenzentrum (


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany
  2. 2.Fakultät für Mathematik und InformatikInstitut für Numerische Mathematik und Optimierung, TU Bergakademie FreibergFreibergGermany

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