Dohrmann, Clark R.; Pierson, Kendall H.; Widlund, Olof B. Vertex-based preconditioners for the coarse problems of BDDC. (English) Zbl 1425.65044 SIAM J. Sci. Comput. 41, No. 5, A3021-A3044 (2019). Summary: We present a family of approximate BDDC preconditioners based on inexact solvers for the coarse problem. The basic idea is to replace the direct solver for a standard BDDC coarse problem by a preconditioner which requires much less computation and memory. The focus in this study is on scalar elliptic and linear elasticity problems in three dimensions. The preconditioner for the coarse problem employs a standard two-level additive Schwarz approach in which the coarse problem dimension is either one or six times the number of subdomain vertices. We show, under certain assumptions on the coefficients, that favorable BDDC condition number estimates also hold for the approximate preconditioners. Numerical examples are presented to confirm the theory and to demonstrate the computational advantages of the approach. Cited in 3 Documents MSC: 65F08 Preconditioners for iterative methods 65F10 Iterative numerical methods for linear systems 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs Keywords:elliptic equations; linear elasticity; finite elements; domain decomposition; BDDC algorithms; small coarse spaces Software:Trilinos; BDDC; METIS; CUBIT; BDDCML; PCBDDC PDFBibTeX XMLCite \textit{C. R. Dohrmann} et al., SIAM J. Sci. Comput. 41, No. 5, A3021--A3044 (2019; Zbl 1425.65044) Full Text: DOI References: [1] S. Badia, A. F. Martín, and J. Principe, Multilevel balancing domain decomposition at extreme scale, SIAM J. Sci. Comput., 38 (2016), pp. C22-C52, https://doi.org/10.1137/15M1013511. [2] T. Blacker, S.-J. Owen, M. L. Staten, W. R. 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