Skip to main content

Parallel Sums and Adaptive BDDC Deluxe

  • Conference paper
  • First Online:
Book cover Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

  • 959 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • W.N. Anderson Jr., R.J. Duffin, Series and parallel addition of matrices. J. Math. Anal. Appl. 26, 576–594 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Klawonn, M. Kühn, O. Rheinbach, Adaptive coarse spaces for FETI–DP in three dimensions. SIAM J. Sci. Comput. (2016a, to appear)

    Google Scholar 

  • 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)

    MathSciNet  MATH  Google Scholar 

  • J. Li, O.B. Widlund, FETI–DP, BDDC, and block Cholesky methods. Int. J. Numer. Methods Eng. 66 (2), 250–271 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Mandel, B. Sousedík, J. Šístek, Adaptive BDDC in three dimensions. Math. Comput. Simul. 82 (10), 1812–1831 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • S. Zampini, PCBDDC: a class of robust dual-primal preconditioners in PETSc. SIAM J. Sci. Comput. 38 (5), S282–S306 (2016)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olof B. Widlund .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

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

Download citation

Publish with us

Policies and ethics