zbMATH — the first resource for mathematics

Relaxing the roles of corners in BDDC by perturbed formulation. (English) Zbl 1367.65047
Lee, Chang-Ock (ed.) et al., Domain decomposition methods in science and engineering XXIII. Proceedings of the 23rd international conference, Jeju Island, Korea, July 6–10, 2015. Cham: Springer (ISBN 978-3-319-52388-0/hbk; 978-3-319-52389-7/ebook). Lecture Notes in Computational Science and Engineering 116, 397-405 (2017).
Summary: We present a perturbed formulation of the BDDC method where the invertibility of the global coarse matrix is automatically guaranteed and positive direct solvers can be used without corner constraints or a change of basis. The perturbed method has the same polylogarithmic bounds for the precondition number and is weakly scalable. It is suitable for large scale simulations as small coarse spaces associated with only edge or/and face constraints can be used. In addition, it offers extra robustness when there are disconnected subdomains or in other situations where constraints fails to fix a small number of rigid body modes.
For the entire collection see [Zbl 1371.65003].

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
ParMETIS; PT-Scotch
Full Text: DOI
[1] O. Axelsson, G. Lindskog, On the rate of convergence of the preconditioned conjugate gradient method. Numer. Math. 48 (5), 499–523 (1986) · Zbl 0564.65017 · doi:10.1007/BF01389448
[2] S. Badia, H. Nguyen, Balancing domain decomposition by constraints and perturbation, SIAM J. Numer. Anal. 54 (6), 3436–3464 (2016) · Zbl 1354.65262 · doi:10.1137/15M1045648
[3] S. Badia, A.F. Martín, J. Principe, A highly scalable parallel implementation of balancing domain decomposition by constraints. SIAM J. Sci. Comput. 36 (2), C190–C218 (2014) · Zbl 1296.65177 · doi:10.1137/130931989
[4] C. Chevalier, F. Pellegrini, PT-Scotch: a tool for efficient parallel graph ordering. Parallel Comput. 34 (6–8), 318–331 (2008). Parallel Matrix Algorithms and Applications · doi:10.1016/j.parco.2007.12.001
[5] C.R. Dohrmann, A preconditioner for substructuring based on constrained energy minimization. SIAM J. Sci. Comput. 25 (1), 246–258 (2003) · Zbl 1038.65039 · doi:10.1137/S1064827502412887
[6] C.R. Dohrmann, An approximate BDDC preconditioner. Numer. Linear Algebra Appl. 14 (2), 149–168 (2007) · Zbl 1199.65088 · doi:10.1002/nla.514
[7] G. Karypis, K. Schloegel, V. Kumar, ParMETIS: parallel graph partitioning and sparse matrix ordering library, Technical Report, Department of Computer Science and Engineering, University of Minnesota, 1997
[8] A. Klawonn, O.B. Widlund, Dual-primal FETI methods for linear elasticity. Commun. Pure Appl. Math. 59 (11), 1523–1572 (2006) · Zbl 1110.74053 · doi:10.1002/cpa.20156
[9] M. Lesoinne, A FETI-DP corner selection algorithm for three-dimensional problems, in Domain Decomposition Methods in Science and Engineering XIV, ed. by I. Herrera, D.E. Keyes, O.B. Widlund, R. Yates (National Autonomous University of Mexico (UNAM), Mexico City, Mexico, 2003), pp. 217–224
[10] J. Li, O.B. Widlund, FETI-DP, BDDC, and block Cholesky methods. Int. J. Numer. Methods Eng. 66 (2), 250–271 (2006) · Zbl 1114.65142 · doi:10.1002/nme.1553
[11] J. Mandel, Balancing domain decomposition. Commun. Numer. Methods Eng. 9 (3), 233–241 (1993) · Zbl 0796.65126 · doi:10.1002/cnm.1640090307
[12] J. Šístek, M. Čertíková, P. Burda, J. Novotný, Face-based selection of corners in 3D substructuring. Math. Comput. Simul. 82 (10), 1799–1811 (2012) · doi:10.1016/j.matcom.2011.06.007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.