Um Esquema GMRES Precondicionado para Simulação de Reservatórios
DOI:
https://doi.org/10.5540/tema.2002.03.02.0063Abstract
Descrevemos um método GMRES precondicionado para a resolução de sistemas lineares que aparecem em Simulação de Reservatórios de Petróleo. Três esquemas de precondicionamento são propostos. Resultados numéricos e uma comparação com um simulador comercial são apresentados. Em particular, uma aplicação a um problema de determinação de parâmetros é discutida.References
[1] O. Axelsson, “Iterative Solution Methods”, Cambridge University Press, New York, 1994.
K. Aziz e A. Settari, “Petroleum Reservoir Simulation”, Applied Sci. Publ. , Londres, 1979.
L.M. Carvalho, F. Dickstein, J.R.P. Rodrigues e R.W. Santos, “Relatório Interno Petrobrás”, 2001.
T. Chan e W.L. Wan, Analysis of projection methods for solving linear systems with multiple right-hand sides, SIAM J. Sci. Comput., 18 (1997), 1698-1721.
G.H. Golub and C.F. Van Loan, “Matrix Computations”, Third Edition, Johns Hopkins Univ. Press, Baltimore, 1996.
C.T. Kelley, “Iterative Methods for Linear and Nonlinear Equations”, SIAM, Philadelphia, 1995.
B.N. Parlett, A new look at the Lanczos method for solving symmetric systems of linear equations, Linear Algebra Appl., 17 (1980), 323-346.
Y. Saad, On the Lanczos method for solving symmetric systems with several right-hand sides, Math Comp., 48 (1987), 651-662.
Y. Saad. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7(1986), 856-869.
Y. Saad. “Iterative Methods for Sparse Linear Sistems”, second edition with corrections, 2000.
V. Simoncini e E. Gallopoulos, An iterative method for nonsymmetric systems with multiple right-hand sides, SIAM J. Sci. Comput., 18 (1995), 917-933.
C.F. Smith, A.F. Peterson e R. Mittra, A conjugate gradient algorithm for the treatment of multiple incident eletromagnetic fields, IEEE Trans. on Antennas and Propag., 37, No. 11 (1989), 1490-1493.
H.A. Van der Vorst, An iterative solution method for solving f(A)x = b, using Krylov subspace information obtained for the symmetric positive matrix A, J. of Comput. and Appl. Math., 18 (1987), 249-263.
J. Wallis, “Incomplete Gaussian Elimination as a Preconditioning for Generalized Conjugate Gradient Acceleration”, SPE, 12265, 1983.
M.F. Wheeler, “Numerical Simulation in Oil Recovery”, Springer-Verlag, Nova Iorque, 1988.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.