×

Algebraic multilevel method AMG: comparison with the method BICGSTAB + ILU and its use in the method CPR. (English. Russian original) Zbl 1304.65124

Mosc. Univ. Math. Bull. 65, No. 4, 156-160 (2010); translation from Vest. Mosk. Univ. Mat. Mekh. 65, No. 4, 24-28 (2010).
Summary: The algebraic multilevel method AMG is compared with the method BICGSTAB+ILU on a model problem with a strong anisotropy. The method AMG was used as a part of the method CPR for solution of the filtration problems of a viscous compressible fluid flow in porous media. The algorithm CPR+AMG is compared with CPR+ILU on the base of this problem. The work of the CPR+AMG is analyzed by solving the problem for a model oil field.

MSC:

65F10 Iterative numerical methods for linear systems
86-08 Computational methods for problems pertaining to geophysics
86A20 Potentials, prospecting

Software:

IPARS; BiCGstab
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] G. I. Marchuk, Methods of Numerical Mathematics (Nauka, Moscow, 1989; Springer-Verlag, New York, 1982). · Zbl 0485.65003
[2] N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobelkov, Numerical Methods (Fizmatlit, Moscow, 2003) [in Russian].
[3] K. Stuben, A Review of Algebraic Multigrid (GMD Report 69, 1999).
[4] K. Stuben, Algebraic Multigrid (AMG): an Introduction with Applications (GMD Report 70, 1999).
[5] J. R. Wallis, Incomplete Gaussian Elimination as a Preconditioning for Generalized Conjugate Gradient Acceleration (SPE 12265, 1983).
[6] K. Aziz and A. Settari, Petroleum Reservoir Simulation (Kluwer Academic Publishers, 1979; Nedra, Moscow, 1982).
[7] Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, 2003). · Zbl 1031.65046
[8] S. Lacroix, Yu. Vassilevski, J. Wheeler, and M. Wheeler, ”Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly,” SIAM J. Sci. Comput. 25(3), 905 (2003). · Zbl 1163.65310
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.