Abstract
There has recently been a considerable activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants. The primal constraints of a BDDC or FETI-DP algorithm provide the global, coarse part of such a preconditioner and are of crucial importance for obtaining rapid convergence of these preconditioned conjugate gradient methods for the case of many subdomains.
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References
W.N. Anderson Jr., R.J. Duffin, Series and parallel addition of matrices. J. Math. Anal. Appl. 26, 576–594 (1969)
L. Beirão da Veiga, L.F. Pavarino, S. Scacchi, O.B. Widlund, S. Zampini, Adaptive selection of primal constraints for isogeometric BDDC deluxe preconditioners. SIAM J. Sci. Comput. (2017) (to appear)
J.G. Calvo, O.B. Widlund, An adaptive choice of primal constraints for BDDC domain decomposition algorithms. TR2015-979, Courant Institute, New York University, 2016
C.R. Dohrmann, C. Pechstein, Constraint and weight selection algorithms for BDDC. Slides for a talk by Dohrmann at DD21 in Rennes, France, June 2012 (2012), http://www.numa.uni-linz.ac.at/~clemens/dohrmann-pechstein-dd21-talk.pdf
C.R. Dohrmann, O.B. Widlund, A BDDC algorithm with deluxe scaling for three-dimensional H(curl) problems. Commun. Pure Appl. Math. 69 (4), 745–770 (2016)
H.H. Kim, E.T. Chung, J. Wang, BDDC and FETI-DP algorithms with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients (2015), http://arxiv.org/abs/1606.07560
A. Klawonn, O.B. Widlund, M. Dryja, Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal. 40 (1), 159–179 (2002)
A. Klawonn, M. Kühn, O. Rheinbach, Adaptive coarse spaces for FETI–DP in three dimensions. SIAM J. Sci. Comput. (2016a, to appear)
A. Klawonn, P. Radtke, O. Rheinbach, A comparison of adaptive coarse spaces for iterative substructuring in two dimensions. Electron. Trans. Numer. Anal. 46, 75–106 (2016b)
J. Li, O.B. Widlund, FETI–DP, BDDC, and block Cholesky methods. Int. J. Numer. Methods Eng. 66 (2), 250–271 (2006)
J. Mandel, B. Sousedík, Adaptive selection of face coarse degrees of freedom in the BDDC and the FETI-DP iterative substructuring methods. Comput. Methods Appl. Mech. Eng. 196 (8), 1389–1399 (2007)
J. Mandel, B. Sousedík, J. Šístek, Adaptive BDDC in three dimensions. Math. Comput. Simul. 82 (10), 1812–1831 (2012)
D.-S. Oh, O.B. Widlund, S. Zampini, C.R. Dohrmann, BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields. Math. Comput. (2017) (to appear)
C. Pechstein, C.R. Dohrmann, Modern domain decomposition methods, BDDC, deluxe scaling, and an algebraic approach. Talk by Pechstein in Linz, Austria, December 2013, http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf
C. Pechstein, C.R. Dohrmann, A unified framework for adaptive BDDC. Technical Report 2016-20, Johann Radon Institute for Computational and Applied Mathematics (RICAM) (2016), http://www.ricam.oeaw.ac.at/files/reports/16/rep16-20.pdf
Y. Tian, How to express a parallel sum of k matrices. J. Math. Anal. Appl. 266 (2), 333–341 (2002)
S. Zampini, PCBDDC: a class of robust dual-primal preconditioners in PETSc. SIAM J. Sci. Comput. 38 (5), S282–S306 (2016)
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Widlund, O.B., Calvo, J.G. (2017). Parallel Sums and Adaptive BDDC Deluxe. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_28
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DOI: https://doi.org/10.1007/978-3-319-52389-7_28
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