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High Performance Computing and Applications pp 497–502Cite as

Development of a Scalable Solver for the Earth’s Core Convection

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5938))

Abstract

A scalable parallel solver is developed to simulate the Earth’s core convection. With the help from the “multiphysics” data structure and the restricted additive Schwarz preconditioning in PETSc the iterative solution of the linear solver converges rapidly at every time-step. The solver gains nearly 20 times speedup compared to a previous solver using least-squares polynomial preconditioning in Aztec. We show the efficiency and effectiveness of our new solver by giving numerical results obtained on a BlueGene/L supercomputer with thousands of processor cores.

Project supported by the National High Technology Research and Development Program of China (No. 2006AA01A125 and No. 2006AA01A102), the National Natural Science Foundation of China (No. 10801125 and No. 60533020) and the National Basic Research Program of China (No. 2005CB321702).

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References

  1. Arakawa, A., Lamb, V.: Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics 17, 174–267 (1977)

    MathSciNet  Google Scholar 

  2. Balay, S., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L., Smith, B., Zhang, H.: PETSc Users Manual, Argonne National Laboratory (2008)

    Google Scholar 

  3. Cai, X.-C., Sarkis, M.: A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21, 792–797 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chan, K., Li, L., Liao, X.: Modelling the core convection using finite element and finite difference methods. Phys. Earth Planet. Interiors 157, 124–138 (2006)

    Article  Google Scholar 

  5. Christensen, U., Aubert, J., et al.: A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25–34 (2001)

    Article  Google Scholar 

  6. Dukowicz, J., Dvinsky, A.: Approximate factorization as a high order splitting for the implicit incompressible flow equations. J. Comput. Phys. 102, 336–347 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Freund, R.W.: A Transpose-Free Quasi-Minimal Residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput. 14, 470–482 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Harlow, F., Welch, J.: Numerical calculatin of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189 (1965)

    Article  MATH  Google Scholar 

  9. Tuminaro, R., Heroux, M., Hutchinson, S., Shadid, J.: Official AZTEC Users Guide: Version 2.1 (1999)

    Google Scholar 

  10. van der Vorst, H.A.: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Chao Yang & Yunquan Zhang

  2. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, P.R. China

    Ligang Li

  3. State Key Lab. of Computer Science, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Yunquan Zhang

Authors
  1. Chao Yang
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  2. Ligang Li
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  3. Yunquan Zhang
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Editor information

Editors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, 200072, Shanghai, P.R. China

    Wu Zhang  & Weiqin Tong  & 

  2. Schulich School of Engineering, University of Calgary, T2N 1N4, Calgary, AB, Canada

    Zhangxin Chen

  3. Department of Mathematics, University of Wyoming, 1000 University Avenue, 82071-3036, Laramie, WY, USA

    Craig C. Douglas

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© 2010 Springer-Verlag Berlin Heidelberg

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Yang, C., Li, L., Zhang, Y. (2010). Development of a Scalable Solver for the Earth’s Core Convection. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_69

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  • DOI: https://doi.org/10.1007/978-3-642-11842-5_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11841-8

  • Online ISBN: 978-3-642-11842-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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