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Parallel Sum Primal Spaces for Isogeometric Deluxe BDDC Preconditioners

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Domain Decomposition Methods in Science and Engineering XXIII

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

Abstract

In this paper, we study the adaptive selection of primal constraints in BDDC deluxe preconditioners applied to isogeometric discretizations of scalar elliptic problems. The main objective of this work is to significantly reduce the coarse space dimensions of the BDDC isogeometric preconditioners developed in our previous works, Beirão da Veiga et al. (Math Mod Meth Appl Sci 23, 1099–1142, 2013a) and Beirão da Veiga et al. (SIAM J Sci Comp 36, A1118–A1139, 2014b), while retaining their fast and scalable convergence rates.

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Acknowledgements

For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. The Authors would like to thank L. Dalcin for the 3D NURBS geometry.

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Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Via Cozzi 55, 20125, Milano, Italy

    L. Beirão da Veiga

  2. Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100, Pavia, Italy

    L. F. Pavarino

  3. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133, Milano, Italy

    S. Scacchi

  4. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    O. B. Widlund

  5. Extreme Computing Research Center, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

    S. Zampini

Authors
  1. L. Beirão da Veiga
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  2. L. F. Pavarino
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  3. S. Scacchi
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  4. O. B. Widlund
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  5. S. Zampini
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Corresponding author

Correspondence to L. F. Pavarino .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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da Veiga, L.B., Pavarino, L.F., Scacchi, S., Widlund, O.B., Zampini, S. (2017). Parallel Sum Primal Spaces for Isogeometric Deluxe BDDC Preconditioners. 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_2

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