A parallel out-of-core multifrontal method: Storage of factors on disk and analysis of models for an out-of-core active memory

Parallel Computing

Volumn 34, Issue 6-8, 2008, Pages 296-317

  Agullo, Emmanuel ^a   Guermouche, Abdou ^b   L'Excellent, Jean Yves ^a  

^a UNIVERSITÉ DE LYON   (France)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Out of core; Parallel multifrontal method; Sparse direct solvers

Indexed keywords

DATA STORAGE EQUIPMENT; LINEAR EQUATIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

INDUSTRIAL GROUPS; PARALLEL MULTIFRONTAL METHODS; SPARSE DIRECT SOLVERS;

PARALLEL PROCESSING SYSTEMS;

EID: 44349090264     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2008.03.007     Document Type: Article

References (24)

1. The BCSLIB Mathematical/Statistical Library. .
2. E. Agullo, A. Guermouche, and J.-Y. L'Excellent, A preliminary out-of-core extension of a parallel multifrontal solver, in: EuroPar' 06 Parallel Processing, 2006, pp. 1053-1063.
3. E. Agullo, A. Guermouche, J.-Y. L'Excellent, Towards a parallel out-of-core multifrontal solver: preliminary study. Research report 6120, INRIA, 02 2007. Also appeared as LIP report RR2007-06.
4. P. Amestoy, I.S. Duff, A. Guermouche, Tz. Slavova. Analysis of the out-of-core solution phase of a parallel multifrontal approach. Research report RT/APO/07/3, ENSEEIHT, 04 2007. Also appeared as CERFACS and INRIA technical report.
5. Amestoy P.R., and Duff I.S. Memory management issues in sparse multifrontal methods on multiprocessors. International Journal of Supercomputer Applications 7 (1993) 64-82
6. Amestoy P.R., Duff I.S., Koster J., and L'Excellent J.-Y. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications 23 1 (2001) 15-41
7. Amestoy P.R., Duff I.S., and Vömel C. Task scheduling in an asynchronous distributed memory multifrontal solver. SIAM Journal on Matrix Analysis and Applications 26 2 (2005) 544-565
8. Amestoy P.R., Guermouche A., L'Excellent J.-Y., and Pralet S. Hybrid scheduling for the parallel solution of linear systems. Parallel Computing 32 2 (2006) 136-156
9. Ashcraft C., Grimes R.G., Lewis J.G., Peyton B.W., and Simon H.D. Progress in sparse matrix methods for large linear systems on vector computers. International Journal of Supercomputer Applications 1 4 (1987) 10-30
10. Choi J., Demmel J., Dhillon I., Dongarra J., Ostrouchov S., Petitet A., Stanley K., Walker D., and Whaley R.C. ScaLAPACK: a portable linear algebra library for distributed memory computers - design issues and performance. Computer Physics Communications 97 (1996) 1-15 (also LAPACK Working Note #95)
11. T.H. Cormen, E. Riccio Davidson, Siddhartha Chatterjee. Asyn chronous buffered computation design and engineering framework generator (abcdefg), in: 19th International Parallel and Distributed Processing Symposium (IPDPS'05), 2005.
12. F. Dobrian, External memory algorithms for factoring sparse matrices. Ph.D Thesis, Old Dominion University, 2001.
13. F. Dobrian, A. Pothen, Oblio: a sparse direct solver library for serial and parallel computations. Technical Report, Old Dominion University, 2000.
14. Duff I.S., and Reid J.K. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software 9 (1983) 302-325
15. Duff I.S., and Reid J.K. The multifrontal solution of unsymmetric sets of linear systems. SIAM Journal on Scientific and Statistical Computing 5 (1984) 633-641
16. John R. Gilbert, Sivan Toledo, High-performance out-of-core sparse LU factorization, in: Proceedings of the 9th SIAM Conference on Parallel Processing for Scientific Computing, 1999 (10 pages on CDROM).
17. G. Karypis, V. Kumar, MeTiS - A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Or-derings of Sparse Matrices - Version 4.0. University of Minnesota, September 1998.
18. Liu J.W.H. On the storage requirement in the out-of-core multifrontal method for sparse factorization. ACM Transactions on Mathematical Software 12 (1986) 127-148
19. Liu J.W.H. The role of elimination trees in sparse factorization. SIAM Journal on Matrix Analysis and Applications 11 (1990) 134-172
20. Rothberg E., and Schreiber R. Efficient methods for out-of-core sparse Cholesky factorization. SIAM Journal on Scientific Computing 21 1 (1999) 129-144
21. Rotkin V., and Toledo S. The design and implementation of a new out-of-core sparse Cholesky factorization method. ACM Transactions on Mathematical Software 30 1 (2004) 19-46
22. F. Schmuck, R. Haskin, GPFS: a shared-disk file system for large computing clusters, in: Proceedings of the First Conference on File and Storage Technologies, 2002.
23. Schulze J. Towards a tighter coupling of bottom-up and top-down sparse matrix ordering methods. BIT 41 4 (2001) 800-841
24. Takhur R., Gropp W., and Lusk E. On implementing MPI-IO portably and with high performance. Proceedings of the 6th Workshop on I/O in Parallel and Distributed Systems (1999), ACM Press 23-32