A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations

Nuclear Science and Engineering

Volumn 124, Issue 1, 1996, Pages 145-159

  Ashby, Steven F ^a   Falgout, Robert D ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; COMPUTER SIMULATION LANGUAGES; CONVERGENCE OF NUMERICAL METHODS; GROUNDWATER FLOW; PARALLEL PROCESSING SYSTEMS; PERFORMANCE; POROUS MATERIALS; PRESSURE;

COARSE GRID SOLVER STRATEGY; GEOSTATISTICAL PARAMETERS VARIATION; GRID RESOLUTION; HETEROGENEOUS POROUS MEDIA; MULTIGRID PRECONDITIONED CONJUGATE GRADIENT; PRESSURE HEAD; SCALABILITY; SUBSURFACE REALIZATION;

PARALLEL ALGORITHMS;

EID: 0030247884     PISSN: 00295639     EISSN: None     Source Type: Journal    
DOI: 10.13182/NSE96-A24230     Document Type: Article

References (23)

1. A. F. B. TOMPSON, S. F. ASHBY, R. D. FALGOUT, S. G. SMITH, T. W. FOGWELL, and G. A. LOOSMORE, "Use of High Performance Computing to Examine the Effectiveness of Aquifer Remediation," Proc, 10th Int. Conf. Computational Methods in Water Resources, Heidelberg, Germany, July 19-22, 1994, Vol. 2, A. PETERS, G- WITTUM, B. HERRLING, U. MEISSNER, C. BREBBIA, W. GRAY, and G. PINDER, Eds., Kluwer Academic Publishers, Dordrecht, The Netherlands (1994); see also UCRL-JC-115374, Lawrence Livermore National Laboratory.
2. R. ABABOU, D. B. MCLAUGHLIN, L. W. GELHAR, and A. F. B, TOMPSON, "Numerical Simulation of Three-Dimensional Saturated Flow in Randomly Heterogeneous Porous Media," Transport in Porous Media, Vol. 4, p. 549 (1989).
3. S. F. ASHBY, W. J. BOSL, R. D. FALGOUT, S. G. SMITH, A. F. B. TOMPSON, and T. J. WILLIAMS, "A Numerical Simulation of Groundwater Flow and Contaminant Transport on the CRAY T3D and C90 Supercomputers," Proc. 34th Cray User Group Conf., p. 275, Tours, France, October 10-14, 1994, Cray User Group (1994); see also UCRL-JC-118635, Lawrence Livermore National Laboratory.
4. A. F. B. TOMPSON, R. ABABOU, and L. W. GELHAR, "Implementation of the Three-Dimensional Turning Bands Random Field Generator," Water Resour. Res., 25, 2227 (1989).
5. S. F. ASHBY, R. D. FALGOUT, S. G. SMITH, and A. F. B. TOMPSON, "The Parallel Performance of a Groundwater Flow Code on the CRAY T3D," Proc. 7th SIAM Conf. Parallel Processing for Scientific Computing, p. 131, San Francisco, California, February 15-17, 1995, Society for Industrial and Applied Mathematics (1995); see also UCRL-JC-118604, Lawrence Livermore National Laboratory.
6. M. R. HESTENES and E. STIEFEL, "Methods of Conjugate Gradients for Solving Linear Systems," J. Res. Natl. Bur. Standards, 49, 409 (1952).
7. P. CONCUS, G. H. GOLUB, and D. P. O'LEARY, "A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations," Sparse Matrix Computations, p. 309, J. R. BUNCH and D. J. ROSE, Eds., Academic Press, New York (1976).
8. P. D. MEYER, A. J. VALOCCHI, S. F. ASHBY, and P. E. SAYLOR, "A Numerical Investigation of the Conjugate Gradient Method as Applied to Three-Dimensional Groundwater Flow Problems in Randomly Heterogeneous Porous Media." Water Resour. Res., 25, 1440 (1989).
9. G. H. GOLUB and J. M. ORTEGA, Scientific Computing: An Introduction with Parallel Computing, Academic Press, San Diego, California (1993).
10. J. E. DENDY and C. C. TAZARTES, "Grandchild of the Frequency Decomposition Multigrid Method," SIAM J. Sci. Comput., 16, 307 (1995).
11. W. HACKBUSCH, "The Frequency Decomposition Multigrid Method, Part I: Application to Anisotropic Equations," Numer. Math., 56, 229 (1989).
12. N. H. NAIK and J. R. ROSENDALE, "The Improved Robustness of Multigrid Elliptic Solvers Based on Multiple Semicoarsened Grids," SIAM J. Numer. Anal., 30, 215 (1993).
13. S. SCHAFFER, "A Semi-Coarsening Multigrid Method for Elliptic Partial Differential Equations with Highly Discontinuous and Anisotropic Coefficients," SIAM J. Sci. Comput. (to be published).
14. R. E. ALCOUFFE, A. BRANDT, J. E. DENDY, and J. W. PAINTER, "The Multi-Grid Method for the Diffusion Equation with Strongly Discontinuous Coefficients," SIAM J. Sci. Stat. Comput., 2, 430 (1981).
15. J. E. DENDY, "Black Box Multigrid," J. Comput. Phys., 48, 366 (1982).
16. T. W. FOGWELL and F. BRANKHAGEN, "Multigrid Method for the Solution of Porous Media Multiphase Flow Equations," Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications, Vol. 24, p. 139, Notes on Numer. Fluid Mech., Vieweg, Braunschweig (1989).
17. S. F. ASHBY, T. A. MANTEUFFEL, and P. E. SAYIOR, "A Taxonomy for Conjugate Gradient Methods," SIAM J. Numer. Anal., 27, 1542 (1990).
18. O. TATEBE, "The Multigrid Preconditioned Conjugate Gradient Method," Proc. 6th Copper Mountain Conf. Multigrid Methods, Hampton, Virginia, 1993, Vol. CP 3224, p. 621, N. D. MELSON, T. A. MANTEUFFEL, and S. F. MCCORMICK, Eds., U.S. National Aeronautics and Space Administration.
19. J. E. DENDY, "Black Box Multigrid for Nonsymmetric Problems," Appl. Math. Comput., 13, 261 (1983).
20. D. J. MAVRIPLIS and A. JAMESON, "Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes," Multigrid Methods: Theory, Applications, and Supercomputing, Vol. 110, p. 413. S. F. MCCORMICK, Ed., Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York (1988).
21. W. L. BRIGGS, L. HART, S. F. MCCORMICK, and D. QUINLAN, "Multigrid Methods on a Hypercube," Multigrid Methods: Theory, Applications, and Supercomputing, S. F. MCCORMICK, Ed., Vol. 110, p. 63, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York (1988).
22. T. F. CHAN and R. S. TUMINARO, "Design and Implementation of Parallel Multigrid Algorithms," Proc. 3rd Copper Mountain Conf. Multigrid Methods, S. F. MCCORMICK, Ed., p. 101, Marcel Dekker, New York (1987).
23. S. F. ASHBY, R. D. FALGOUT, S. G. SMITH, and T. W. FOGWELL, "Multigrid Preconditioned Conjugate Gradients for the Numerical Simulation of Groundwater Flow on the CRAY T3D," Proc. Int. Conf. Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, Oregon, April 30-May 4, 1995, p. 405, American Nuclear Society (1995).