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**Block ILU-preconditioners for problems of filtration of a multicomponent mixture in a porous medium.**
*(English.
Russian original)*
Zbl 1304.65119

Mosc. Univ. Math. Bull. 64, No. 5, 195-201 (2009); translation from Vest. Mosk. Univ. Mat. Mekh. 64, No. 5, 19-25 (2009).

Summary: ILU class preconditioners (ILU(0), ILU(1), ILUT) are employed for iterative algorithms for asymmetric linear systems with sparse matrices are considered. Test matrices used in this study originate from discretization of systems of partial differential equations describing a multicomponent fluid flow in porous media. New algorithms for block storage of matrices and block based ILU-factorization are described. This new integrated approach was tested on a wide range of matrices resulted from actual hydrodynamic simulations of oil fields in Western Siberia and had demonstrated significant reduction of computational time.

### MSC:

65F08 | Preconditioners for iterative methods |

65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |

86-08 | Computational methods for problems pertaining to geophysics |

86A20 | Potentials, prospecting |

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\textit{K. Yu. Bogachev} and \textit{Ya. V. Zhabitskii}, Mosc. Univ. Math. Bull. 64, No. 5, 195--201 (2009; Zbl 1304.65119); translation from Vest. Mosk. Univ. Mat. Mekh. 64, No. 5, 19--25 (2009)

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### References:

[1] | Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, 2003). · Zbl 1031.65046 |

[2] | N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobelkov, Numerical Methods (Nauka, Moscow, 1987) [in Russian]. |

[3] | K. Yu. Bogachev, Computer Training. Solution Methods for Linear Systems and Eigenvalue Problems (Moscow State University, Moscow, 1999) [in Russian]. |

[4] | K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science Publishers, London, 1979). |

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