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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].

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
Software:
ParMETIS; PT-Scotch
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References:
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