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Dual-Primal Isogeometric Tearing and Interconnecting Methods

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Contributions to Partial Differential Equations and Applications

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 47))

Abstract

This paper generalizes the Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) method, that is well established as parallel solver for large-scale systems of finite element equations, to linear algebraic systems arising from the Isogemetric Analysis of elliptic diffusion problems with heterogeneous diffusion coefficients in two- and three-dimensional multipatch domains with \(C^0\) smoothness across the patch interfaces. We consider different scalings, and derive the expected polylogarithmic bound for the condition number of the preconditioned systems. The numerical results confirm these theoretical bounds, and show incredibly robustness with respect to large jumps in the diffusion coefficient across the interfaces.

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Acknowledgements

This research work was supported by the National Research Network (NFN) “Geometry + Simulation” funded by the Austrian Science Fund (FWF) under the grand S117-03.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, A-4040, Linz, Austria

    Christoph Hofer & Ulrich Langer

Authors
  1. Christoph Hofer
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  2. Ulrich Langer
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Correspondence to Christoph Hofer .

Editor information

Editors and Affiliations

  1. Keldysh Institute of Applied Mathematics (IPM), Moscow, Russia

    B. N. Chetverushkin

  2. College of Technology, University of Houston, Houston, TX, USA

    W. Fitzgibbon

  3. Department of Mathematics, University of Houston, Houston, TX, USA

    Y.A. Kuznetsov

  4. Department of Mathematical Information, University of Jyväskylä, Jyväskylä, Finland

    P. Neittaanmäki

  5. University of Jyväskylä, Jyväskylä, Finland

    J. Periaux

  6. LJLL-UPMC, Paris, France

    O. Pironneau

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Hofer, C., Langer, U. (2019). Dual-Primal Isogeometric Tearing and Interconnecting Methods. In: Chetverushkin, B., Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Periaux, J., Pironneau, O. (eds) Contributions to Partial Differential Equations and Applications. Computational Methods in Applied Sciences, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-78325-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-78325-3_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78324-6

  • Online ISBN: 978-3-319-78325-3

  • eBook Packages: EngineeringEngineering (R0)

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