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Software concepts and numerical algorithms for a scalable adaptive parallel finite element method

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An Erratum to this article was published on 12 July 2016

Abstract

An efficient implementation of an adaptive finite element method on distributed memory systems requires an efficient linear solver. Most solver methods, which show scalability to a large number of processors make use of some geometric information of the mesh. This information has to be provided to the solver in an efficient and solver specific way. We introduce data structures and numerical algorithms which fulfill this task and allow in addition for an user-friendly implementation of a large class of linear solvers. The concepts and algorithms are demonstrated for global matrix solvers and domain decomposition methods for various problems in fluid dynamics, continuum mechanics and materials science. Weak and strong scaling is shown for up to 16.384 processors.

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Author notes

  1. T. Witkowski

    Present address: Institute of Scientific Computing, TU Dresden, 01062, Dresden, Germany

Authors and Affiliations

  1. Institute of Scientific Computing, TU Dresden, 01062, Dresden, Germany

    S. Ling, S. Praetorius & A. Voigt

Authors
  1. T. Witkowski
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  2. S. Ling
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  3. S. Praetorius
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  4. A. Voigt
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Correspondence to A. Voigt.

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Communicated by: Charlie Elliott

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Witkowski, T., Ling, S., Praetorius, S. et al. Software concepts and numerical algorithms for a scalable adaptive parallel finite element method. Adv Comput Math 41, 1145–1177 (2015). https://doi.org/10.1007/s10444-015-9405-4

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  • DOI: https://doi.org/10.1007/s10444-015-9405-4

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