The role of multi-method linear solvers in PDE-based simulations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2667, Issue , 2003, Pages 828-839

  Bhowmick, S ^a   McInnes, L ^b   Norris, B ^b   Raghavan, P ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLICATION PROGRAMS; COMPUTATIONAL FLUID DYNAMICS; LINEAR SYSTEMS;

LINEAR SOLUTION; LINEAR SOLVER; LINEAR SYSTEM SOLUTION; MULTI METHODS; NON LINEAR PDE; NONLINEAR ITERATIONS; PRECONDITIONED ITERATIVE METHODS; SOLUTION METHODS;

ITERATIVE METHODS;

EID: 35248819657     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44839-x_87     Document Type: Article

References (18)

1. R. Armstrong, D. Cannon, A. Geist, K. Keahey, S. Kohn, L. C. Mclnnes, S. Parker, and B. Smolinski, Toward a Common Component Architecture for High-Performance Scientific Computing, Proceedings of High Performance Distributed Computing (1999) pp. 115-124, (see www.cca-forum.org).
2. O. Axelsson, A survey of preconditioned iterative methods for linear systems of equations, BIT, 25 (1987) pp. 166-187.
3. S. Balay, K. Buschelman, W. Gropp, D. Kaushik, M. Knepley, L.C. McInnes, B. Smith, and H. Zhang, PETSc users manual, Tech. Rep. ANL-95/11 - Revision 2.1.3, Argonne National Laboratory, 2002 (see www.mcs.anl.gov/petsc).
4. S. Balay, W. Gropp, L.C. McInnes, and B. Smith, Efficient management of parallelism in object oriented numerical software libraries, In Modern Software Tools in Scientific Computing (1997), E. Arge, A. M. Bruaset, and H. P. Langtangen, Eds., Birkhauser Press, pp. 163-202.
5. R. Barrett, M. Berry, J. Dongarra, V. Eijkhout, and C. Romine, Algorithmic Bombardment for the Iterative Solution of Linear Systems: A PolyIterative Approach. Journal of Computational and applied Mathematics, 74, (1996) pp. 91-110.
6. S. Bhowmick, P. Raghavan, and K. Teranishi, A Combinatorial Scheme for Developing Efficient Composite Solvers, Lecture Notes in Computer Science, Eds. P. M. A. Sloot, C.J. K. Tan, J. J. Dongarra, A. G. Hoekstra, 2330, Springer Verlag, Computational Science- ICCS 2002, (2002) pp. 325-334.
7. S. Bhowmick, P. Raghavan , L. McInnes, and B. Norris, Faster PDE-based simulations using robust composite linear solvers. Argonne National Laboratory preprint ANL/MCS-P993-0902, 2002. Also under review, Future Generation Computer Systems,
8. R. Bramley, D. Gannon, T. Stuckey, J. Villacis, J. Balasubramanian, E. Akman, F. Berg, S. Diwan, and M. Govindaraju, The Linear System Analyzer, Enabling Technologies for Computational Science, Kluwer, (2000).
9. T. S. Coffey, C. T. Kelley, and D. E. Keyes, Pseudo-Transient Continuation and Differential-Algebraic Equations, submitted to the open literature, 2002.
10. I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, 1986.
11. A. Ern, V. Giovangigli, D. E. Keyes, and M. D. Smooke, Towards Polyalgorithmic Linear System Solvers For Nonlinear Elliptic Problems, SIAM J. Sci. Comput., Vol. 15, No. 3, pp. 681-703.
12. R. Freund, G. H. Golub, and N. Nachtigal, Iterative Solution of Linear Systems, Acta Numerica, Cambridge University Press, (1992) pp. 57-100.
13. B. Fryxell, K. Olson, P. Ricker, F. Timmes, M. Zingale, D. Lamb, P. MacNeice, R. Rosner, J. Truran, and H. Tufo, FLASH: an Adaptive-Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes, Astrophysical Journal Supplement, 131 (2000) pp. 273-334, (see www.asci.uchicago.edu).
14. C. T. Kelley and D. E. Keyes, Convergence analysis of pseudo-transient continuation. SIAM Journal on Numerical Analysis 1998; 35:508-523.
15. L. McInnes, B. Norris, S. Bhowmick, and P. Raghavan, Adaptive Sparse Linear Solvers for Implicit CFD Using Newton-Krylov Algorithms, To appear in the Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, Massachusetts Institute of Technology, Boston, USA, June 17-20, 2003.
16. J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.
17. B. Norris, S. Balay, S. Benson, L. Freitag, P. Hovland, L. McInnes, and B. F. Smith, Parallel Components for PDEs and Optimization: Some Issues and Experiences, Parallel Computing, 28 (12) (2002), pp. 1811-1831.
18. X. Z. Tang, G. Y. Fu, S. C. Jardin, L. L. Lowe, W. Park, and H. R. Strauss, Resistive Magnetohydrodynamics Simulation of Fusion Plasmas, PPPL-3532, Princeton Plasma Physics Laboratory, 2001.