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Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems

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Abstract

We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into \(m\times m\times m\) subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to m. The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with \(m^6\) while the number of iterations increases only proportionally to \(\sqrt{m}\). Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Zdeněk Dostál, Oldřich Vlach & Marie Sadowská

  2. IT4Innovations, National Supercomputing Center, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Zdeněk Dostál, Tomáš Brzobohatý, Oldřich Vlach & Ondřej Meca

Authors
  1. Zdeněk Dostál
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  2. Tomáš Brzobohatý
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  3. Oldřich Vlach
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  4. Ondřej Meca
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  5. Marie Sadowská
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Correspondence to Zdeněk Dostál.

Additional information

To the memory of Alexandros Markopoulos, our student, colleague, and friend, who carried out some early experiments with hybrid TFETI in 3D and drew our attention to this interesting method.

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This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPS II) project IT4Innovations excellence in science—LQ1602 and by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project IT4Innovations National Supercomputing Center—LM2015070.

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Dostál, Z., Brzobohatý, T., Vlach, O. et al. Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems. Comput Mech 71, 333–347 (2023). https://doi.org/10.1007/s00466-022-02242-2

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  • DOI: https://doi.org/10.1007/s00466-022-02242-2

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