Parallel implementation of multilevel BDDC In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method.

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  1. Jolivet, Pierre; Roman, Jose E.; Zampini, Stefano: KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners (2021)
  2. Hanek, Martin; Šístek, Jakub; Burda, Pavel: Multilevel BDDC for incompressible Navier-Stokes equations (2020)
  3. Widlund, Olof B.: BDDC domain decomposition algorithms (2020)
  4. Brown, Jed; He, Yunhui; Maclachlan, Scott: Local Fourier analysis of balancing domain decomposition by constraints algorithms (2019)
  5. Dohrmann, Clark R.; Pierson, Kendall H.; Widlund, Olof B.: Vertex-based preconditioners for the coarse problems of BDDC (2019)
  6. Eikeland, Erik; Marcinkowski, Leszek; Rahman, Talal: Overlapping Schwarz methods with adaptive coarse spaces for multiscale problems in 3D (2019)
  7. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver; Weber, Janine: Preconditioning the coarse problem of BDDC methods -- three-level, algebraic multigrid, and vertex-based preconditioners (2019)
  8. Sousedík, Bedřich: On adaptive BDDC for the flow in heterogeneous porous media. (2019)
  9. Badia, Santiago; Verdugo, Francesc: Robust and scalable domain decomposition solvers for unfitted finite element methods (2018)
  10. Marcinkowski, Leszek; Rahman, Talal: Additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems (2018)
  11. Hanek, Martin; Šístek, Jakub; Burda, Pavel: The effect of irregular interfaces on the BDDC method for the Navier-Stokes equations (2017)
  12. Klawonn, Axel; Lanser, Martin; Niehoff, Balthasar; Radtke, Patrick; Rheinbach, Oliver: Newton-Krylov-FETI-DP with adaptive coarse spaces (2017)
  13. Spillane, Nicole: Algebraic adaptive multipreconditioning applied to restricted additive Schwarz (2017)
  14. Zampini, Stefano; Tu, Xuemin: Multilevel balancing domain decomposition by constraints deluxe algorithms with adaptive coarse spaces for flow in porous media (2017)
  15. Badia, Santiago; Martín, Alberto F.; Principe, Javier: Multilevel balancing domain decomposition at extreme scales (2016)
  16. Hapla, Vaclav; Horak, David; Pospisil, Lukas; Cermak, Martin; Vasatova, Alena; Sojka, Radim: Solving contact mechanics problems with PERMON (2016)
  17. Klawonn, Axel; Kühn, Martin; Rheinbach, Oliver: Adaptive coarse spaces for FETI-DP in three dimensions (2016)
  18. Spillane, Nicole: An adaptive multipreconditioned conjugate gradient algorithm (2016)
  19. Subber, Waad; Matouš, Karel: Asynchronous space-time algorithm based on a domain decomposition method for structural dynamics problems on non-matching meshes (2016)
  20. Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices (2016)

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