Task scheduling in an asynchronous distributed memory multifrontal solver

SIAM Journal on Matrix Analysis and Applications

Volumn 26, Issue 2, 2005, Pages 544-565

  Amestoy, Patrick R ^a   Duff, Iain S ^b   Vömel, Christof ^c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b RAL   (United Kingdom)

^c CERFACS   (France)

Author keywords

Distributed memory code; High performance computing; Multifrontal Gaussian elimination; MUMPS; Sparse linear systems; Task scheduling

Indexed keywords

ALGORITHMS; DATA STORAGE EQUIPMENT; DATA STRUCTURES; DECISION MAKING; DISTRIBUTED COMPUTER SYSTEMS; MATRIX ALGEBRA; TREES (MATHEMATICS);

DISTRIBUTED MEMORY CODE; HIGH PERFORMANCE COMPUTING; MULTIFRONTAL GAUSSIAN ELIMINATION; MUMPS; SPARSE LINEAR SYSTEMS; TASK SCHEDULING;

LINEAR SYSTEMS;

EID: 17444367640     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802419877     Document Type: Article

References (34)

1. PARASOL test data, http://www.parallab.uib.no/parasol/data.html (last updated May 23, 2003).
2. P. R. AMESTOY AND I. S. DUFF, Memory management issues in sparse multifrontal methods on multiprocessors, Int. J. Supercomput. Appl., 7 (1993), pp. 64-82.
3. P. R. AMESTOY, I. S. DUFF, AND J. Y. L'EXCELLENT, Multifrontal parallel distributed symmetric and unsymmetric solvers, Comput. Methods in Appl. Mech. Engrg., 184 (2000), pp. 501-520.
4. P. R. AMESTOY, I. S. DUFF, J.-Y. L'EXCELLENT, AND J. KOSTER, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 15-41.
5. P. R. AMESTOY, I. S. DUFF, J. Y. L'EXCELLENT, AND X. S. LI, Analysis, tuning and comparison of two general sparse solvers for distributed memory computers, ACM Trans. Math. Software, 27 (2001), pp. 388-421.
6. P. R. AMESTOY, I. S. DUFF, S. PRALET, AND C. VÖMEL, Adapting a parallel sparse direct solver to architectures with clusters of SMPs, Parallel Comput., 29 (2003), pp. 1645-1668.
7. C. ASHCRAFT AND R. G. GRIMES, The influence of relaxed super-node partitions on the multifrontal method, ACM Trans. Math. Software, 15 (1989), pp. 291-309.
8. J. CHOI, J. DEMMEL, I. DHILLON, J. DONGARRA, S. OSTROUCHOV, A. PETITET, K. STANLEY, D. WALKER, AND R. C. WHALEY, ScaLAPACK: A portable linear algebra library for distributed memory computers: Design issues and performance, Comput. Phys. Comm., 97 (1996), pp. 1-15.
9. T. A. DAVIS, University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices (last updated August, 2004). NA Digest, 92 (42), October 16, 1994. NA Digest, 96 (28), July 23, 1996. NA Digest, 97 (23), June 7, 1997.
10. T. A. DAVIS, University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices (last updated August, 2004). NA Digest, 92 (42), October 16, 1994. NA Digest, 96 (28), July 23, 1996. NA Digest, 97 (23), June 7, 1997.
11. T. A. DAVIS, University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices (last updated August, 2004). NA Digest, 92 (42), October 16, 1994. NA Digest, 96 (28), July 23, 1996. NA Digest, 97 (23), June 7, 1997.
12. T. A. DAVIS, University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices (last updated August, 2004). NA Digest, 92 (42), October 16, 1994. NA Digest, 96 (28), July 23, 1996. NA Digest, 97 (23), June 7, 1997.
13. J. J. DONGARRA, I. S. DUFF, D. C. SORENSEN, AND H. A. VAN DER VORST, Numerical Linear Algebra on High-Performance Computers, Software Environ. Tools 7, SIAM, Philadelphia, 1998.
14. I. S. DUFF, A. M. ERISMAN, AND J. K. REID, Direct Methods for Sparse Matrices, Oxford University Press, London, 1986.
15. I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, The Rutherford-Boeing Sparse Matrix Collection, Technical report RAL-TR-97-031, Atlas Centre, Rutherford Appleton Laboratory, 1997. Also Technical report ISSTECH-97-017 from Boeing Information & Support Services and Report TR/PA/97/36 from CERFACS, Toulouse, France, http://www.cerfacs.fr/algor/reports/index.html.
16. I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, The Rutherford-Boeing Sparse Matrix Collection, Technical report RAL-TR-97-031, Atlas Centre, Rutherford Appleton Laboratory, 1997. Also Technical report ISSTECH-97-017 from Boeing Information & Support Services and Report TR/PA/97/36 from CERFACS, Toulouse, France, http://www.cerfacs.fr/algor/reports/index.html.
17. I. S. DUFF AND J. K. REID, The multifrontal solution of indefinite sparse symmetric linear systems, ACM Trans. Math. Software, 9 (1983), pp. 302-325.
18. I. S. DUFF AND J. K. REID, The multifrontal solution of unsymmetric sets of linear equations, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 633-641.
19. A. GEIST AND E. NG, Task scheduling for parallel sparse Cholesky factorization, Int. J. Parallel Program., 18 (1989), pp. 291-314.
20. A. GEORGE AND E. NG, SPARSPAK: Waterloo Sparse Matrix Package User's Guide for SPARSPAK-B, Research report CS-84-37, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 1984.
21. J. A. GEORGE, J. W. H. LIU, AND E. G.-Y. NG, Communication results for parallel sparse Cholesky factorization on a hypercube, Parallel Comput., 10 (1989), pp. 287-298.
22. A. GUPTA, Recent advances in direct methods for solving unsymmetric sparse systems of linear equations, ACM Trans. Math. Software, 28 (2002), pp. 301-324.
23. P. HÉNON, P. RAMET, AND J. ROMAN, PaStiX: A high-performance parallel direct solver for sparse symmetric definite systems, Parallel Comput., 28 (2002), pp. 301-321.
24. L. A. HALL, Approximation algorithms for scheduling, in Approximation Algorithms for NP-Hard Problems, D. Hochbaum, ed., PWS Publishing, Boston, 1996, pp. 1-45.
25. G. KARYPIS AND V. KUMAR, MeTis: A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices, Version 4.0, University of Minnesota, Minneapolis, 1998.
26. J. W. H. LIU, The role of elimination trees in sparse factorization, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 134-172.
27. J. W. H. LIU, The multifrontal method for sparse matrix solution: Theory and practice, SIAM Rev., 34 (1992), pp. 82-109.
28. J. W. H. LIU, E. G. NG, AND B. W. PEYTON, On finding super-nodes for sparse matrix computations, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 242-252.
29. E. G. NG AND P. RAGHAVAN, Performance of greedy ordering heuristics for sparse Cholesky factorization, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 902-914.
30. F. PELLEGRINI AND J. ROMAN, Sparse matrix ordering with Scotch, in Proceedings of High Performance Computing and Networking 1997, Vienna, Austria, Lecture Notes in Comput. Sci. 1225, Springer-Verlag, New York, 1997, pp. 370-378.
31. F. PELLEGRINI, J. ROMAN, AND P. AMESTOY, Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering, Concurrency: Practice and Experience, 12 (2000), pp. 69-84.
32. A. POTHEN AND C. SUN, A mapping algorithm for parallel sparse Cholesky factorization, SIAM J. Sci. Comput., 14 (1993), pp. 1253-1257.
33. P. RAGHAVAN, Distributed Sparse Matrix Factorization: QR and Cholesky Decompositions, Ph.D. thesis, Pennsylvania State University, University Park, PA, 1991.
34. E. ROTHBERG AND S. C. EISENSTAT, Node selection strategies for bottom-up sparse matrix ordering, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 682-695.