Analysis of multigrid algorithms on massively parallel computers: Architectural implications

Journal of Parallel and Distributed Computing

Volumn 33, Issue 1, 1996, Pages 33-43

  Matheson, Lesley R ^a   Tarjan, Robert E ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030600717     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.1996.0022     Document Type: Article

References (27)

1. [ALVE] Alverson, R., Callahan, D., Gumming, D., Koblenz, B., Porterfield, A., and Smith, B. The TERA computer system. Proc. ACM Symposium on Supercomputing, 1990, pp. 1-7.
2. [BRIG] Briggs, W. A Multigrid Tutuorial. SIAM, Philadelphia, 1987.
3. [BOZK] Bozkus, Z., Ranka, S., and Fox, G. Benchmarking the CM-5 multicomputer. Proc. of the Fourth Symposium on the Frontiers of Massively Parallel Computation (H. Siegel, Ed.), IEEE Computer Society Press, 1992, pp. 100-107.
4. [CHAN] Chan, T., and Tuminaro, R. Analysis of a parallel multigrid algorithm. Proc. of the Fourth Copper Mountain Conference on Multigrid Methods (S. McCormick, Ed.). 1989, pp. 66-86.
5. [CM200] The Connection Machine Series, Technical Summary. Thinking Machines, Inc., Cambridge, MA., 1992.
6. [CMS] CM5 Technical Summary. Thinking Machines Corporation, Cambridge, MA, 1991.
7. [CULL] Culler, D., Karp, R., Patterson, D., Sahay, A., Schauser, K., Santos, E., Subramonian, R., and von Eiken, T. LogP: Towards a realistic model of parallel computation. SIGPLAN Not. 28 (July 1993), 1-12.
8. [DALL] Dally, W. Express cubes: Improving performance of k-ary n-cube interconnection networks. IEEE Trans. Compu. 40 (1991), 1016-1023.
9. [DORW] Dorward, S., Matheson, L., and Tarjan, R. Unstructured multigrid strategies on massively parallel computers: A case for integrated design. Proc. of the Twenty-Seventh Annual Hawaii International Conference on System Sciences. IEEE Computer Society Press, 1994, pp. 169-179.
10. [FORS] Forsythe, G., and Wasow, W. Finite Difference Methods for Partial Differential Equations. Wiley, New York, 1960.
11. [GANN] Gannon, D., and Van Rosendale, J. On the structure of parallelism in a highly concurrent PDE solver. J. Parallel Distrib. Comput. 3, (1986), 106-135.
12. [GREE] Greenbaum, A. A multigrid method for multiprocessors. Appl. Math. Comput. 19 (1986), 75-88.
13. [HOCK] Hockney, R. The communications challenge for MPP: The intel paragon and the Meiko CS-2. Parallel Comput. 20 (Mar. 1994), 389-398.
14. Received May 9, 1994; revised December 27, 1994; accepted April 17, 1995
15. [JESP] Jesperson, D. Multigrid methods for partial differential equations. In Golub, G. (Ed.). Studies in Numerical Analysis. Math. Soc. of America, Washington, DC, 1984, pp. 270-318.
16. [LENO] Lenoski, D., Laudon, J., Joe, T., Nakahira, D., Stevens, L., Gupta, A., and Hennessy, J. The Stanford DASH prototype: Logic overhead and performance. IEEE Trans. Parallel Distrib. Systems 4 (Jan. 1993), 41-61.
17. [MART] Martinelli, L. Private communication. Department of Aerospace and Mechanical Engineering, Princeton University, 1994.
18. [MATH1] Matheson, L. Multigrid algorithms on massively parallel computers. Ph.D. dissertation, Department of Computer Science, Princeton University, 1994.
19. [MATH2] Matheson, L., and Tarjan, R. A critical analysis of multigrid methods on massively parallel computers. Contributions to Multigrid: A Selection of Contributions to the Fourth European Multigrid Conference. CWI, Amsterdam, to appear.
20. [PONN] Ponnusamy, R., Thakur, R., Choudhary, A., Velamakanni, K., Bozkus, Z., and Fox, G. Communications on the CM-5: An experimental performance evaluation. J. Parallel Distrib. Comput. 19 (Nov. 1993), 192-202.
21. [TOMA] Tomayo, P. Private communications. Applications Analyst, Thinking Machines, Inc., Cambridge, MA, 1992.
22. [SEIT] Seitz, C. Private communication. California Institute of Technology, 1992.
23. [SPER] Spertus, E., Goldstein, S., Schauser, K., von Eiken, T., Culler D., and Dally, W. Evaluation of mechanisms for fine-grained parallel programs in the J-machine and the CM-5. Proc. of the 20th Annual International Symposium on Computer Architecture, May 1993, pp. 302-313.
24. [T3D] T3D System Architecture Overview. #HP-04033, Cray Research, Inc., Egan, MN, 1993.
25. [VALI] Valiant, L. A bridging model for parallel computation. Comm. ACM 33 (Aug. 1990), 103-111.
26. [VARG] Varga, R. Matrix iterative analysis. Prentice-Hall, Englewood Cliffs, NJ, 1962.
27. [VONE] Von Eicken, T., Culler, D., Goldstein, S. Active messages: A mechanism for integrated communication and computation. Comput. Architecture News 20 (May 1992), 256-266.