Performance comparison of data-reordering algorithms for sparse matrix-vector multiplication in edge-based unstructured grid computations

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 3, 2006, Pages 431-460

  Coutinho, Alvaro L G A ^a   Martins, Marcos A D ^a   Sydenstricker, Rubens M ^a   Elias, Renato N ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Cache based machines; Data reordering; Edge based finite elements; Unstructured grids

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; VECTORS;

CACHE-BASED MACHINES; DATA REORDERING; EDGE-BASED FINITE ELEMENTS; UNSTRUCTURED GRIDS;

DATA STRUCTURES;

ALGORITHMS; COMPUTATIONAL METHODS; DATA STRUCTURES; FINITE ELEMENT METHOD; MATRIX ALGEBRA; VECTORS;

EID: 33645913852     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1557     Document Type: Article

References (31)

1. Hennessy JL, Patterson DA, Goldberg D. Computer Architecture: A Quantitative Approach (3rd edn). Morgan Kaufmann: Los Altos, CA, 2002.
2. www.top500.org, visited in November, 2004.
3. Feitelson DG. The supercomputer industry in light of the Top500 data. Computing in Science and Engineering, January/February, 2005; 42-47.
4. Burgess DA, Giles MB. Renumbering unstructured grids to improve the performance of codes on hierarchical memory machines. Advances in Engineering Software 1997; 28:189-201.
5. Oliker L, Li X, Heber G, Biswas R. Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforrns. IEEE Transactions on Parallel and Distributed Systems 2000; 11(9):931-940.
6. Biswas R, Oliker L, Shan H. Parallel computing strategies for irregular algorithms. In Annual Review of Scalable Computing, Kwong YC (ed.), vol. 5, Chapter 1. World Scientific Publishing Company Inc.: Singapore, 2003.
7. Oliker L, Li X, Heber G, Biswas R. Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems. Lecture Notes in Computer Science, vol. 1800, 2000; 497-503.
8. Oliker L, Li X, Husbands P, Biswas R. Effects of ordering strategies and programming paradigms on sparse matrix computations. SIAM Review 44(3):373-393.
9. Pinar A, Heath MT. Improving performance of sparse matrix-vector multiplication. Conference on High Performance Networking and Computing, Proceedings of the 1999 ACM/IEEE Conference on Supercomputing (CDROM), Portland, Oregon, U.S.A., 1999, Article No. 30, ISBN:1-58113-091-0.
10. Vuduc R, Demmel JW, Yelick KA, Kamil S, Nishtala R, Lee B. Performance optimizations and bounds for sparse matrix-vector multiply. Proceedings of the 2002 ACM/IEEE Conference on Supercomputing, Baltimore, MA, U.S.A., 16-22 November 2002; 1-35. CD-ROM ACM, 2002.
11. Douglas CC, Hu J, Kowarschik M, Rude U, Weiss C. Cache optimization for structured and unstructured grid multigrid. Electronic Transactions on Numerical Analysis 2000; 10:21-40.
12. Ferencz RM, Hughes TJR. Iterative finite element solutions in nonlinear solid mechanics. Handbook of Numerical Analysis, vol. 6. Elsevier Science: Amsterdam, 1998.
13. Gropp WD, Kaushik DK, Keyes DE, Smith BF. Performance modeling and tuning of an unstructured mesh CFD application. Proceedings of SC 2000, IEEE Computer Society, Dallas, TX, U.S.A., 2000, Article No. 34, ISBN:0-7803-9802-5.
14. Heras DB, Blanco V, Cabaleiro JC, Rivera FF. Modeling and improving locality for the sparse-matrix-vector product on cache machines. Future Generation Computer Systems 2001; 18:55-67.
15. Kennedy JG, Behr M, Kalro V, Tezduyar TE. Implementation of implicit finite element methods for incompressible flows on the CM-5. Computer Methods in Applied Mechanics and Engineering 1994; 119:95-111.
16. Löhner R, Galle M. Minimization of indirect addressing for edge-based field solvers. Communications in Numerical Methods in Engineering 2002; 18:335-343.
17. Löhner R. Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines. Computer Methods in Applied Mechanics and Engineering 1998; 163:95-109.
18. Löhner R. Some useful renumbering strategies for unstructured grids. International Journal for Numerical Methods in Engineering 1993; 36:3259-3270.
19. Löhner R. Edges, stars, superedges and chains. Computer Methods in Applied Mechanics and Engineering 1994; 111:255-263.
20. Martins MAD, Alves JLD, Coutinho ALGA. Parallel Edge-based Finite Techniques for Nonlinear Solid Mechanics. Lecture Notes on Computer Science, vol. 1981. Springer: Berlin, Heidelberg, 2001; 506-518.
21. Mavriplis D. Three-dimensional unstructured multigrid for the Euler equations. Paper AIAA-91-1549-CP, 1991.
22. Oliker L, Canning A, Carter J, Shalf J, Skinner D. Evaluation of cache-based superscalar and cacheless vector architectures for scientific computations. Proceedings of the 18th Annual International Conference on Supercomputing, Malo, France, 2004, ISBN:1-58113-839-3.
23. Ribeiro FLB, Coutinho ALGA. Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses. International Journal for Numerical Methods in Engineering 2005; 63(4):569-588.
24. Strout MM, Carter L, Ferrante J, Kreaseck B. Sparse tiling for stationary iterative methods. International Journal of High Performance Computing Applications 2004; 18(1):95-113.
25. Carey GF, Swift S, McLey RT. Maximizing sparse matrix-vector product performance on RISC based MIMD computers. Journal of Parallel and Distributed Computing 1996; 37:146-158.
26. Cuthill E, McKee J. Reducing the bandwidth of sparse symmetric matrices. Proceedings of the ACM Nature Conference, 1969; 157-172.
27. Dongarra J, Foster I, Fox G, Kennedy K, White A, Torczon L. Sourcebook of Parallel Computing. Morgan Kaufmann: Los Altos, CA, 2002.
28. Barth T. A 3-D upwind Euler solver for unstructured meshes. AIAA-91-1548-CP, 1991.
29. Sydenstricker RM, Martins MAD, Coutinho ALGA, Alves JLD. Edge-based Interface Elements for Solution of Three-dimensional Geomechanical Problems. Lecture Notes in Computer Science, vol. 2565, 2003; 53-64.
30. Coutinho ALGA, Martins MAD, Alves JLD, Landau L, Moraes A. Edge-based finite element techniques for nonlinear solid mechanics problems. International Journal for Numerical Methods in Engineering 2001; 50(9):2053-2068.
31. Web Site for 10th SPE Comparative Solution Project, http://www.spe.org/ csp, 10th February, 2004.