Accelerating iterative solution methods using reduced-order models as solution predictors

International Journal for Numerical Methods in Engineering

Volumn 68, Issue 5, 2006, Pages 525-541

  Markovinovic R ^a   Jansen, J D ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Empirical orthogonal functions; Iterative solvers; Karhunen Lo ve decomposition; Projection based model reduction; Proper orthogonal decomposition; Solution acceleration; Solution extrapolation

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; EXTRAPOLATION; MATHEMATICAL MODELS; TWO PHASE FLOW; VECTORS;

EMPIRICAL ORTHOGONAL DECOMPOSITION; IMPLICIT-PRESSURE EXPLICIT-SATURATION (IMPES) SCHEME; ITERATIVE SOLVERS; PROJECTION-BASED MODEL REDUCTION; PROPER ORTHOGONAL DECOMPOSITION; REDUCED-ORDER MODELS; SOLUTION ACCELERATION; SOLUTION EXTRAPOLATION;

ITERATIVE METHODS;

ALGORITHMS; COMPUTER SIMULATION; EXTRAPOLATION; ITERATIVE METHODS; MATHEMATICAL MODELS; TWO PHASE FLOW; VECTORS;

EID: 33750298127     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1721     Document Type: Article

References (22)

1. Axelson O. Iterative Solution Methods. Cambridge University Press: Cambridge, MA, 1994.
2. Saad Y, van der Vorst H. Iterative solution of linear systems in the 20th century. Journal of Computational and Applied Mathematics 2000; 123:1-33.
3. Vuik C, Segal A, Meijerink JA. An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients. Journal of Computational Physics 1999; 152:385-403.
4. Frank J, Vuik C. On the construction of deflation-based preconditioners. Journal on Scientific Computing 2001; 23:442-462.
5. Strakoš Z, Liesen J. On numerical stability in large scale linear algebraic computation. Zeitschrift fur Angewandte Mathematik und Mechanik 2005; 85:307-325.
6. Clemens M, Wilke M, Weiland T. Extrapolation strategies in numerical schemes for transient magnetic field simulations. IEEE Transactions on Magnetics 2003; 39:1171-1174.
7. Clemens M, Wilke M, Schumann R, Weiland T. Subspace projection extrapolation scheme for transient field simulations. IEEE Transactions on Magnetics 2004; 40:934-937.
8. Karhunen K. Zur Spektraltheorie stochastischer Prozesse. Annales Academiae Scientiarum Fennicae Series A1 1946; 34:1-7.
9. Holmes P, Lumley JL, Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press: Cambridge, MA, 1996.
10. Sirovich L. Turbulence and the dynamics of coherent structures. Part 1: Coherent structures. Quarterly Journal of Applied Mathematics 1987; 55:561-571.
11. Webb A. Statistical Pattern Recognition (2nd edn). Wiley: New York, 2002.
12. Kunisch K, Volkwein S. Control of Burgers equation by a reduced-order approach using proper orthogonal decomposition. Journal of Optimization Theory and Applications 1999; 102:345-371.
13. Meyer M, Matthies HG. Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods. Computational Mechanics 2003; 179-191.
14. Gharbi R, Smaoui N, Peters EJ. Prediction of unstable fluid displacements in porous media using the Karhunen-Loève decomposition. In Situ 1997; 21:331-356.
15. Heijn T, Markovinović R, Jansen JD. Generation of low-order reservoir models using system-theoretical concepts. SPE Journal 2004; 9:202-218.
16. Vermeulen PTM, Heemink AW, Te Stroet CBM. Reduced models for linear groundwater flow models using empirical orthogonal functions. Advances in Water Resources 2004; 27:57-69.
17. Van Doren JFM, Markovinović R, Jansen JD. Reduced-order optimal control of water flooding using Proper Orthogonal Decomposition. Computational Geosciences 2006, in press.
18. Aziz K, Settari A. Petroleum Reservoir Simulation. Elsevier: Amsterdam, 1979.
19. Audigane P, Blunt MJ. Dual mesh method for upscaling in waterflood simulation. Transport in Porous Media 2004; 55:71-89.
20. Brouwer DR, Jansen JD. Dynamic optimization of water flooding with smart wells using optimal control theory. SPE Journal 2004; 9:391-402.
21. Christie MA, Blunt MJ. Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reservoir Evaluation and Engineering 2001; 4:308-317.
22. Hall PM, Marshall AD, Martin RR. Incremental eigenanalysis for classification. Proceedings of Ninth British Machine Vision Conference, Southampton, 1998. http://www.bmva.ac.uk/bmvc/1998/papers/d186/h186.htm