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Comparing Two-Level Preconditioners for Solving Petroleum Reservoir Simulation Problems

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Mathematical Modeling and Computational Intelligence in Engineering Applications

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Abstract

Domain decomposition ideas (proven suitable for parallelization) are combined with incomplete factorizations (which are standard in reservoir simulation) at subdomain level, with the ultimate goal of designing a scalable parallel preconditioner for addressing reservoir simulation problems. An ILU(k)-based two-level domain decomposition preconditioner is introduced, and its performance is compared with a two-level ILU(k)-block Jacobi preconditioner.

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References

  1. Balay, S., Brown, J., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L., Smith, B., Zhang, H.: PETSc Web page (2013). http://www.mcs.anl.gov/petsc/

    Google Scholar 

  2. Cai, X.C., Sarkis, M.: A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput. 21 (2), 792–797 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Carvalho, L., Giraud, L., Le Tallec, P.: Algebraic two-level preconditioners for the Schur complement method. SIAM J. Sci. Comput. 22 (6), 1987–2005 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Christie, M., Blunt, M., et al.: Tenth SPE comparative solution project: a comparison of upscaling techniques. In: The Society of Petroleum Engineers (ed.) SPE Reservoir Simulation Symposium (2001)

    Google Scholar 

  5. Golub, G., van Loan, C.: Matrix Computations, 4th edn. Johns Hopkins University Press, Baltimore (2013)

    MATH  Google Scholar 

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Acknowledgements

The third author thanks the financial support of FAPERJ, through the APQ5 2014/01 Program, E-26/111.007/2014.

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Authors and Affiliations

  1. Petrobras/CENPES, Avenida Horácio Macedo, 950 - Ilha do Fundão, Rio de Janeiro, RJ, CEP 21940-915, Brazil

    José R. P. Rodrigues

  2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ, CEP 21941-909, Brazil

    Paulo Goldfeld

  3. Departamento de Matemática Aplicada, Universidade do Estado do Rio de Janeiro (UERJ), Rua São Francisco Xavier, 524, sala 6029D, Rio de Janeiro, RJ, CEP 20559-900, Brazil

    Luiz M. Carvalho

Authors
  1. José R. P. Rodrigues
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  2. Paulo Goldfeld
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  3. Luiz M. Carvalho
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Corresponding author

Correspondence to Luiz M. Carvalho .

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Editors and Affiliations

  1. Universidade do Estado do Rio de Janeiro, Instituto Politécnico, Nova Friburgo, Brazil

    Antônio José da Silva Neto

  2. Dpto. de Automática y Computación, Instit. Sup. Polit. José Antonio Echeverría (CUJAE), Havana, Cuba

    Orestes Llanes Santiago

  3. Universidade Estadual Paulista - UNESP IBILCE, São José do Rio Preto, Brazil

    Geraldo Nunes Silva

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© 2016 Springer International Publishing Switzerland

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Rodrigues, J.R.P., Goldfeld, P., Carvalho, L.M. (2016). Comparing Two-Level Preconditioners for Solving Petroleum Reservoir Simulation Problems. In: Silva Neto, A., Llanes Santiago, O., Silva, G. (eds) Mathematical Modeling and Computational Intelligence in Engineering Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-38869-4_10

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