Deflation AMG solvers for highly III-conditioned reservoir simulation problems

SPE Reservoir Simulation Symposium Proceedings

Volumn , Issue , 2007, Pages 43-51

  Klie, Hector ^a   Wheeler, Mary F ^a   Clees, Tanja ^b   Stüben, Klaus ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b SPE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AMG SOLVERS; DEFLATION; GENERALIZED GLOBAL BASIS (GGB) METHOD; NON-SYMMETRIC SYSTEMS;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LINEAR EQUATIONS; PROBLEM SOLVING;

PETROLEUM RESERVOIRS;

EID: 34249320499     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (31)

1. Parks, M.L., E. de Sturler, G. Mackey, D. D. Johnson, and S. Maiti, "Recycling Krylov Subspaces for Sequences of Linear Systems", SIAM J. Sci. Comput.5: pp. 1651-1674, 2006.
2. Frank, J. and Vuik, C. "On the Construction of Deflation-based Preconditioned". SIAM J. Sci. Comput. 13:2:442-462, 2001.
3. Morgan, R. "GMRES with Deflated Restarting". SIAM J. Sci. Comput 24:1:20-37, 2002.
4. Klie, H. and M.F. Wheeler, "Krylov-Secant Methods for Accelerating the Solution of Fully-Implicit Formulations", SPE Reservoir Simulation Symposium, SPE 92863, The Woodlands, Texas, Jan. 31-2 Feb., 2005.
5. Simoncini V. and D. B. Szyld, "Recent Computational Developments in Krylov Subspace Methods for Linear Systems", Research Report 05-9-25, Department of Mathematics, Temple University, September 2005 (revised May 2006). To appear in Numerical Linear Algebra with Applications.
6. L. Giraud and Gratton S. "On the Sensitivity of Some Spectral Preconditioners". SIAM J. Matrix Anal. Appl., Vol. 27, pp. 1089-1105, 2006
7. Stüben, K.: "An Introduction to Algebraic Multlgrid" Appendix in the book "Multigrid" by Trottenberg, U., Oosterlee C.W. and Schuller, A. Academic Press, pp. 413-532, 2001.
8. Stüben, K. "Review of Algebraic Multigrid", J. of Comp. and Appl. Math., 128, pp. 281-309, 2001.
9. Stüben K., Delaney P. and Chmakov, S. "Algebraic Multigrid (AMG) for Ground Water Flow and Oil Reservoir Simulation", Proceedings of the Conference "MODFLOW and More 2003: Understanding through Modeling", International Ground Water Modeling Center (IGWMC), Colorado School of Mines, Golden, Colorado, Sept 17-19, 2003.
10. Axelsson, O. "A Survey of Algebraic Multilevel Iteration (AMLI) Methods". BIT Num. Math. Vol. 43, pp. 863-879, 2003.
11. Brezina M., Falgout, R., Maclahan, S., Manteuffel, T., McCormick S. and Ruge, J. "Adaptive Smoothed Aggregation (aSA)". SIAM J. Sci. Comput. Vol. 25, N. 6, pp. 1896-1920, 2004.
12. Aarnes, J. and T.Y. Hou, "Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios", Acta Math. Appl., 2002, 18(1): 63-76.
13. Graham, I.G. and P.O. Lechner. "Domain Decomposition for Heterogeneous Media", Domain Decomposition Methods in Science and Engineering, XVI, Lecture Notes in Computational Science and Engineering, Vol. 55 O. Widlund and D. Keyes (Eds), 2006.
14. Nabben R. and C. Vuik. "A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow". SIAM J. Numer. Anal. Vol. 42, N. 4, pp. 1631-1647, 2004.
15. Nabben R. and C. Vuik. "A Comparison of Deflation and the Balancing Preconditioner". SIAM J. Sci. Comput. Vol. 27, N. 5, pp. 1742-1759, 2006.
16. Ruge J.W. and Stüben, K. "Algebraic Multigrid (AMG)", Multigrid Methods, S.F. McCormick ed., pp. 73-130, vol. 3 of Frontiers of Applied Mathematics, SIAM, Philadelphia, PA, 1987.
17. Waismann, H., J. Fish, R.S. Tuminaro and J. Shadid. "The Generalized Global Basis (GBB) Method". Int. J. Numer. Meth. Engng. Vol. 61, pp. 1243-1269, 2004.
18. Waismann, H., J. Fish, R.S. Tuminaro and J. Shadid. "Acceleration of the Generalized Global Basis (GBB) Method for Nonlinear Problems". J. Comp, Physics. Vol. 210, pp. 274-291, 2005.
19. Lehoucq, R., D. Sorensen and C. Yang. "ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicit Restarted Arnoldi Methods", SIAM Philadelphia, 1997.
20. Saad, Y. Iterative Methods for Sparse Linear Systems. SIAM, 2003. 2nd. edition.
21. Goossens S. and Roose, D. "Harmonic Ritz Values and the Convergence of FOM and GMRES". Numer. Lin. Alg., pp. 281-293, 1999.
22. Burrage, K and J. Erhel. "On the Performance of Various Adaptive Preconditioned GMRES Strategies", Numerical Linear Algebra with Applications, 5, pp. 101-121, 1998.
23. Carpentieri, B., I.S. Duff and L. Giraud. "A Class of Spectral Two-Level Preconditioners", SIAM J. Sci. Comput., 25, pp. 749-765, 2003.
24. Baglama J., D. Calvetti, G.K. Golub and L. Reichel. "Adoptively Preconditioned GMRES Algorithms", SIAM J. Sci. Comput., 20, pp. 243-269, 1998.
25. Sorensen, D.C. "Implicit Application of Polynomial Filters in a k-Step Arnoldi Method", SIAM J. Matrix Anal. Appl., 13, pp. 357-385, 1992.
26. Stüben, K. and Clees, T. "SAMG User's Manual", http//www.scai.fhg.de/samg.
27. Vuik, C. A. Segal and J.A. Meijerink. "A Comparison of Various Deflation Vectors Applied to Elliptic Problems with Discontinues Coefficients", Appl. Numer. Math., 41, pp. 219-233, 2002.
28. Anderson, E. et al. "LAPACK User's Guide", SIAM, Philadelphia, 1992.
29. Christie M.A. and Blunt, M.J.: "Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques", SPE Reservoir Simulation Symposium, SPE 72469, Houston, Feb 11-14, 2001.
30. Wheeler, J.: "IPARS User's Manual", Tech Report CSM, ICES, The University of Texas at Austin, Austin, TX, 2000.
31. Clees T. and L. Ganzer: "An Efficient Algebraic Multi-Grid Solver Strategy for Adaptive Implicit Methods in Oil Reservoir Simulation" paper SPE 105789 presented at the 2007 SPE Reservoir Simulation Symposium, Houston, TX, Feb. 26-28.