Algebraic Multigrid Methods (AMG) for the efficient solution of fully implicit formulations in reservoir simulation

SPE Reservoir Simulation Symposium Proceedings

Volumn , Issue , 2007, Pages 59-69

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

^a SPE

^b FRAUNHOFER INSTITUTE FOR ALGORITHMS AND SCIENTIFIC COMPUTING SCAI   (Germany)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC MULTIGRID METHODS (AMG); HIERARCHICAL METHODS; INDUSTRIAL OIL RESERVOIRS; PRESSURE SUBSYSTEMS; SUBSYSTEMS;

ALGEBRA; GLOBAL OPTIMIZATION; HIERARCHICAL SYSTEMS; ITERATIVE DECODING; NUMERICAL METHODS; SIMULATORS;

LINEAR SYSTEMS;

EID: 34249303482     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (39)

1. Behie G. and Vinsome, P.: "Block Iterative Methods for Fully Implicit Reservoir Simulation", SPEJ, pp 658-668, 1982.
2. Behie, A. and Forsyth, P.A.: "Multigrid Solution of the Pressure Equation in Reservor Simulation", SPE AIME SPE 10492, pp. 623-636, 1983.
3. Dendy Jr., J.E., MeCormiek, S.F., Ruge, J.W., Russdl, T.F. and Schaffer, S.: "Multigrid Methods for Three-Dimensional Petroleum Reservoir Simulation", SPE Symposium on Reservoir Simulation, SPE 18409, Houston, TX, Feb. 6-8, 1989.
4. Wallis, J.R., Kendall, R.P. and Little, L.E.: "Constrained Residual Acceleration of Conjugate Residual Methods", SPE Reservoir Simulation Symposium, SPE 13536, Dallas, Texas, Feb 10-13, 1985.
5. Mattax, C. and Dalton, R.: "Reservoir Simulation", SPE Monograph Series, 1990.
6. Cao, H., Tchelepi, H.A. and Wallis, J.: "Parallel Scalable Unstructured CPR-type Linear Solver for Reservoir Simulation", SPE Annual Technical Conference and Exhibition, SPE 96809, Dallas, Texas, Oct. 9-12, 2005.
7. Dogru, A.H., Sunaidi, H.A., Fung, L.S., Habiballah, W.A., Al-Zamel, N. and U, K.G.: "A Parallel Simulator for Large-Scale Reservoir Simulation", SPE Reservoir Evaluation and Engineering, SPE N. 75805-PA,Vol.5, N. 1, pp. 11-23. 2002.
8. DeBaun, D. et al.: "An Extensible Architecture for Next Generation Scalable Parallel Reservoir Simulation", SPE Reservoir Simulation Symposium, SPE 93274, The Woodlands, Texas, Jan 31-Feb 2, 2005.
9. Watts J.W. and Shaw, J.S.: "New Method for Solving Implicit Reservoir Simulation Matrix Equation", SPE Reservoir Simulation Symposium, SPE 93068-MS, The Woodlands, Texas, Jan 31-Feb 2, 2005.
10. Fung, L.K, Su, H., Tan, C.T., Hemanthkumar, K. and Pita, J.: "Fully-Implicit Fully-coupled Well Model for Parallel MegaCell Reservoir Simulation ", SPE Technical Symposium of Saudi Arabia Section, SPE 106331, Dhahran, Saudi Arabia, May 14-16, 2005.
11. Fjerstad, P.A., Sikandar, A.S., Cao, H. and Liu, J.: "Next Generation Parallel Computing for Large-Scale Reservoir Simulation", SPE International Improved Oil Recovery Conference in Asia Pacific, SPE 97358, Kuala Lampur, Malaysia, Dec. 2005.
12. Becker, B.L., Usadi, A.K., Ray, M.B. and Diyankov, O.V.: "Next Generation Reservoir Simulation Using Russian Linear Solvers", SPE Russian Oil and Gas Technical Conference and Exhibition, SPE 103578-MS, Moscow, Russia, Oct 3-6, 2006.
13. Klie, H.: "Krylov-Secant Methods for Solving Large Scale Systems of Coupled Nonlinear Parabolic Equations", PhD thesis, Dept. of Computational and Applied Mathematics, Rice University, Houston, TX, 1996.
14. Axelsson, O.: "Iterative Solution Methods", Cambridge University Press, 1994.
15. Chen, K.: "Matrix Preconditioning Techniques and Applications", Cambridge University Press, 2005.
16. Stüben, K.: "An Introduction to Algebraic Multigrid", Appendix in the book "Multigrid" by Trottenberg, U., Oosterlee, C.W., Schüller, A., Academic Press, 2001, pp. 413-532.
17. Clees, T.: "AMG Strategies for PDE Systems with Applications in Industrial Semiconductor Simulation", Ph.D. Thesis, University of Cologne, Nov 2004; Shaker, Aachen, Germany, 2005.
18. Lu, B.: Iterative Coupling Techniques for Reservoir Simulation with Multiphase Flow. Ph.D. Thesis, Center for Subsurface Modeling, ICES, The University of Texas at Austin, 2006 (in progress).
19. Elman H., Silvester, D. and Wathen, A.: "Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics", Oxford Science Publications, 2005.
20. Behie, G. and Forsyth, P.: "Incomplete Factorization Methods for Fully-Implicit Simulation of Enhanced Oil Recovery", SIAM J. Sci. Statist. Comput., Vol. 5, pp. 543-561, 1984.
21. Wallis, J.: "Two-step Preconditioning", Private Communication, 1993.
22. Dawson, C., Klíe, H., Wheeler, M.F. and Woodward, C.: "A Parallel, Implicit, Cell-Centered Method for Two-Phase Flow with a Preconditioned Newton-Krylov Solver", Comp. Geosciences 1, pp. 215-249, 1997.
23. Lacroix, S., Vassileski, Yu., Wheeler, J. and Wheeler, M.F.: "Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully-Implicitly", SIAM J. Sci. Comput. 25, pp.905-926, 2003.
24. Scheichl, R., Masson, R. and Wendebourg, J.: "Decoupling and Block Preconditioning for Sedimentary Basin Simulations", Comp. Geosciences 7, pp.295-318, 2003.
25. Monteagudo, J.E.P. and Firoozabadi, A.: "Numerical Simulation of Water Injection in Disconnected and Connected Fracture Media Using Jacobian-Free Fully Implicit Control Volume Method", SPE/DOE Fourteenth Symposium on Improved Oil Recovery, SPE 89449, Tulsa, Oklahoma, April 17-21, 2004.
26. Bastian, P. and Helmig, R.: "Efficient Fully-coupled solution Techniques For Two-Phase Flow In Porous Media: Parallel Multigrid Solution and Large Computations", Advances in Water Res. 23, pp. 199-216, 1999.
27. Bank, R., Chan, T., Coughan, W. and Smith, K.: "The Alternate-Block-Factorization Procedure for Systems of Partial Differential Equations", BIT 29, pp. 938-954, 1989.
28. Wang, Z.V., Wu, K.C. and Dutton, R.W.: "An Approach to Construct Preconditioning Matrices for Block Iteration of linear Equations", IEEE Trans. on Computer Aided Design 11, pp. 1334-1343, 1992.
29. Fan, Q., Forsyth, P.A., McMaclcen, J.R.F. and Tang, W.P.; "Performance Issues for Iterative Solvers in Device Simulation" , SIAM J. Sci. Comp. 17, pp. 100-117, 1996.
30. Trottenberg, U., Oosterlee, C.W., Schuller, A.: " Multigrid", Academic Press, 2001.
31. Ruge, J.W. and Stuben. K.: "Algebraic Multigrid (AMG)" in "Multigrid Methods" (McCormick, S.F., ed.), SIAM, Frontiers in Applied Mathematics, Vol. 5, Philadelphia, 1986.
32. Stuben, K.: "Review of Algebraic Multigrid", J. of Comp. and Appl. Math. 128, pp. 281-309, 2001.
33. Füllenbach, T. and StUben, K.: "Algebraic multigrid for selected PDE systems", Proceedings of the Fourth European Conference on Elliptic and Parabolic Problems, Rolduc (The Netherlands) and Gaeta (Italy), 2001. World Scientific, New Jersey, London, pp. 399-410, 2002.
34. Clees, T. and Stüben, K.: "Algebraic multigrid for industrial semiconductor device simulation". Proceedings of the First International Conference on Challenges in Scientific Computing, Berlin, Germany, Oct 2-5, 2002. Lecture Notes in Computational Science and Engineering, Springer, Heidelberg, Berlin, 2003.
35. Stüben, K. and Clees, T.. "SAMG User's Manual", Release 22c, Fraunhofer Institute SCAI, June 2005. Can be downloaded from http://www.scai.fhg.de/samg.
36. Clees, T. and Ganzer, L.: "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.
37. 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.
38. Wheeler, J.: "IPARS User's Manual", Tech Report CSM, ICES, The University of Texas at Austin, Austin, TX, 2000.
39. Bank, R. and Wagner, Ch.: "Multilevel ILU decomposition" Numer. Math. 82, No.4, pp. 543-576, 1999.