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Face-based selection of corners in 3D substructuring

Author

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  • Šístek, Jakub
  • Čertíková, Marta
  • Burda, Pavel
  • Novotný, Jaroslav

Abstract

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a ‘minimal’ set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.

Suggested Citation

  • Šístek, Jakub & Čertíková, Marta & Burda, Pavel & Novotný, Jaroslav, 2012. "Face-based selection of corners in 3D substructuring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1799-1811.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:10:p:1799-1811
    DOI: 10.1016/j.matcom.2011.06.007
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    References listed on IDEAS

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    1. Šístek, Jakub & Novotný, Jaroslav & Mandel, Jan & Čertíková, Marta & Burda, Pavel, 2010. "BDDC by a frontal solver and the stress computation in a hip joint replacement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1310-1323.
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    1. Mandel, Jan & Sousedík, Bedřich & Šístek, Jakub, 2012. "Adaptive BDDC in three dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1812-1831.
    2. Pultarová, Ivana, 2012. "Preconditioning of the coarse problem in the method of balanced domain decomposition by constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1788-1798.

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