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Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

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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

A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

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References

  • X.-C. Cai, D.E. Keyes, Nonlinearly preconditioned inexact Newton algorithms. SIAM J. Sci. Comput. 24 (1), 183–200 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • X.-C. Cai, D.E. Keyes, L. Marcinkowski, Nonlinear additive Schwarz preconditioners and application in computational fluid dynamics. Int. J. Numer. Methods Fluids 40 (12), 1463–1470 (2002a)

    Article  MathSciNet  MATH  Google Scholar 

  • X.-C. Cai, D.E. Keyes, D.P. Young, A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flows, in Domain Decomposition Methods in Science and Engineering (Lyon, 2000) (CIMNE, Barcelona, 2002b), pp. 345–352

    MATH  Google Scholar 

  • G. De Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution. Int. J. Numer. Methods Fluids 3 (3), 249–264 (1983)

    Article  MATH  Google Scholar 

  • J.E. Dennis, Jr., R.B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations, Classics in Applied Mathematics, vol. 16 (SIAM, Philadelphia, 1996)

    Book  MATH  Google Scholar 

  • S.C. Eisenstat, H.F. Walker, Globally convergent inexact Newton methods. SIAM J. Optim. 4 (2), 393–422 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • F.-N. Hwang, X.-C. Cai, A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. J. Comput. Phys. 204 (2), 666–691 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • D.A. Knoll, D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2), 357–397 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • L. Liu, D.E. Keyes, Field-split preconditioned inexact Newton algorithms. SIAM J. Sci. Comput. 37 (3), A1388–A1409 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems. SIAM J. Sci. Comput. 19 (1), 302–318 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • J.O. Skogestad, E. Keilegavlen, J.M. Nordbotten, Domain decomposition strategies for nonlinear flow problems in porous media. J. Comput. Phys. 234, 439–451 (2013)

    Article  MathSciNet  Google Scholar 

  • C.-H. Zhang, W. Zhang, G. Xi, A pseudospectral multidomain method for conjugate conduction-convection in enclosures. Numer. Heat. Tr. B-FUND 57 (4), 260–282 (2010)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors acknowledge support from KAUST’s Extreme Computing Research Center and the PETSc group of Argonne National Laboratory.

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Authors and Affiliations

  1. Institute of Computational Science, Università della Svizzera italiana (USI), 6900, Lugano, Switzerland

    Lulu Liu

  2. Program in Mechanical Engineering, King Abdullah University of Science and Technology (KAUST), 23955-6900, Thuwal, Saudi Arabia

    Wei Zhang

  3. Program in Applied Mathematics and Computational Science and Extreme Computing Research Center, King Abdullah University of Science and Technology (KAUST), 23955-6900, Thuwal, Saudi Arabia

    David E. Keyes

Authors
  1. Lulu Liu
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  2. Wei Zhang
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  3. David E. Keyes
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Corresponding author

Correspondence to Lulu Liu .

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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Liu, L., Zhang, W., Keyes, D.E. (2017). Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow. 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_22

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