The HTFETI Method Variant Gluing Cluster Subdomains by Kernel Matrices Representing the Rigid Body Motions

  • Alexandros MarkopoulosEmail author
  • Lubomír ŘíhaEmail author
  • Tomáš Brzobohatý
  • Ondřej Meca
  • Radek Kučera
  • Tomáš Kozubek
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


The proposed algorithm called the Hybrid Total Finite Element Tearing and Interconnecting method (HTFETI) is a variant of the TFETI domain decomposition method suitable for large-scale problems with hundreds of thousands of subdomains. The floating subdomains are gathered into several groups belonging to individual clusters. We use the new idea consisting in gluing the cluster subdomains using kernel matrices defined by the rigid body motions. This technique reduces the size of the coarse problem. While the size of the coarse problem depends linearly on the number of subdomains in the classical TFETI method, it depends linearly on the number of clusters in the HTFETI method. The zero weighted averages across the interfaces of neighbouring subdomains (an alternative to the constraints enforcing the continuity across the corners used, e.g., in the FETI-DP method) improve conditioning of the resulting system of linear equations.



This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science - LQ1602” and from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center – LM2015070”.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alexandros Markopoulos
    • 1
    Email author
  • Lubomír Říha
    • 1
    Email author
  • Tomáš Brzobohatý
    • 1
  • Ondřej Meca
    • 1
  • Radek Kučera
    • 1
  • Tomáš Kozubek
    • 1
  1. 1.IT4Innovations National Supercomputing CenterVŠB - Technical University of OstravaOstravaCzech Republic

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