Abstract
In this paper, BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithms with a change of basis for adaptive primal constraints are analyzed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
W.N. Anderson Jr., R.J. Duffin, Series and parallel addition of matrices. J. Math. Anal. Appl. 26, 576–594 (1969)
J.G. Calvo, O.B. Widlund, An adaptive choice of primal constraints for BDDC domain decomposition algorithms. Electron. Trans. Numer. Anal. 45, 524–544 (2016)
C.R. Dohrmann, C. Pechstein, Modern domain decomposition solvers: BDDC, deluxe scaling, and an algebraic approach, 2013. http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf
V. Dolean, F. Nataf, R. Scheichl, N. Spillane, Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps. Comput. Methods Appl. Math. 12(4), 391–414 (2012)
J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8(4), 1461–1483 (2010)
H.H. Kim, E. Chung, J. Wang, BDDC and FETI-DP mathods with enriched coarse spaces for elliptic problems with oscillatory and high contrast coefficients, in Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computer Science and Engineering, vol. 116 (Springer, Heidelberg, 2017), pp. 179–186
H.H. Kim, E. Chung, J. Wang, BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients. J. Comput. Phys. 349, 191–214 (2017)
H.H. Kim, E. Chung, J. Wang, Adaptive BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints, Electron. Trans. Numer. Anal. 49, 64–80 (2018)
A. Klawonn, O.B. Widlund, Dual-primal FETI methods for linear elasticity. Commun. Pure Appl. Math. 59(11), 1523–1572 (2006)
A. Klawonn, M. Kühn, O. Rheinbach, Adaptive coarse spaces for FETI-DP in three dimensions. SIAM J. Sci. Comput. 38(5), A2880–A2911 (2016)
J. Mandel, B. Sousedík, J. Šístek, Adaptive BDDC in three dimensions. Math. Comput. Simul. 82(10), 1812–1831 (2012)
N. Spillane, D.J. Rixen, Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms. Int. J. Numer. Methods Eng. 95(11), 953–990 (2013)
N. Spillane, V. Dolean, P. Hauret, F. Nataf, D.J. Rixen, Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method. C. R. Math. Acad. Sci. Paris 351(5–6), 197–201, 2013
Acknowledgements
The first author was supported by the National Research Foundation of Korea(NRF) grants funded by NRF20151009350, the second author was supported by the Hong Kong RGC General Research Fund (Project 14317516) and the CUHK Direct Grant for Research 2016–2017, and the third author was supported by the National Natural Science Foundation of China (Grant No. 11201398) and Open Foundation of Guangdong Provincial Engineering Technology Research Center for Data Science(2016KF07).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Kim, H.H., Chung, E.T., Wang, J. (2018). Adaptive BDDC and FETI-DP Methods with Change of Basis Formulation. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-319-93873-8_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93872-1
Online ISBN: 978-3-319-93873-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)