A Parallel Two-Level Hybrid Method for Tridiagonal Systems and Its Application to Fast Poisson Solvers

IEEE Transactions on Parallel and Distributed Systems

Volumn 15, Issue 2, 2004, Pages 97-106

  Sun, Xian He ^a   Zhang, Wu ^b  

^a Illinois Institute of Technology   (United States)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Parallel processing; Poisson solver; Scalable computing; Tridiagonal systems

Indexed keywords

POISSON SOLVERS; SCALABLE COMPUTING; TRIDIAGONAL SYSTEMS;

COMPUTER SIMULATION; COMPUTER SYSTEMS; DATA COMMUNICATION SYSTEMS; MATRIX ALGEBRA; PARALLEL ALGORITHMS; POISSON EQUATION; PROGRAM PROCESSORS;

PARALLEL PROCESSING SYSTEMS;

EID: 1342282168     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2004.1264794     Document Type: Article

References (19)

1. I. Duff, A. Erisman, and J. Reid, Direct Methods for Sparse Matrices. Clarendon Press, Oxford, 1986.
2. O. Egecioglu, D. Koc, and A. Laub, "A Recursive Doubling Algorithm for Solution of Tridiagonal Systems on Hypercube Multiprocessors," J. Computational and Applied Math., vol. 27, 1989.
3. T.M. Edison and G. Erlebacher, "Implementation of a Fully-Balanced Periodic Tridiagonal Solver on a Parallel Distributed Memory Architecture, " Concurrency: Practics and Experience, 1995.
4. C. Ho and S. Johnsson, "Optimizing Tridiagonal Solvers for Alternating Direction Methods on Boolean Cube Multiprocessors," SIAM J. Scientific and Statistical Computing, vol. 11, no. 3, pp. 563-592, 1990.
5. R.W. Hockney, "A Fast Direct Solution of Poisson's Equation Using Fourier Analysis," J. ACM, vol. 12, pp. 95-113, 1965.
6. R.W. Hockney, Parallel Computers 2, Architecture, Programming and Algorithms. Adam Hilger, 1988.
7. IBM, Parallel Engineering and Scientific Subroutine Library for AIX, third ed. 1999, http://www.rs6000.ibm.com.
8. D. Lawrie and A. Sameh, "The Computation and Communication Complexity of a Parallel Banded System Solver," ACM Trans. Mathmatic Software, vol. 10, no. 2, pp. 155-195, June 1984.
9. J. Ortega and R. Voigt, "Solution of Partial Differential Equations on Vector and Parallel Computers," SIAM Rev., pp. 149-240, 1985.
10. J. Sherman and W. Morrison, "Adjustment of an Inverse Matrix Corresponding to Changes in the Elements of a Given Column or a Given Row of the Original Matrix," Ann. Math Statistics, vol. 20, p. 618, 1949.
11. H. Stone, "An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations," J. ACM, vol. 20, no. 1, pp. 27-38, Jan. 1973.
12. X.-H. Sun, "Application and Accuracy of the Parallel Diagonal Dominant Algorithm," Parallel Computing, vol. 18, pp. 1241-1267, 1995.
13. X.-H. Sun and S. Moitra, "Performance Comparison of a Set of Periodic and Nonperiodic Tridiagonal Solvers on SP2 and Paragon Parallel Computers," Concurrency: Practice and Experience, vol. 9, no. 8, pp. 781-801, 1997.
14. X.-H. Sun and D. Rover, "Scalability of Parallel Algorithm-Machine Combinations," IEEE Trans. Parallel Distributed Systems, pp. 599-613, June 1994.
15. X.-H. Sun, H. Zhang, and L. Ni, "Efficient Tridiagonal Solvers on Multicomputers," IEEE Trans. Computers, vol. 41, no. 3, pp. 286-296, 1992.
16. X.-H. Sun and J. Zhu, "Performance Considerations of Shared Virtual Memory Machines," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 11, pp. 1185-1194, Nov. 1995.
17. A.J. Walkraft and D.R. Moore, "The NRL Layered Ocean Model," Parallel Computing, vol. 23, pp. 2227-2242, 1997.
18. H. Wang, "A Parallel Method for Tridiagonal Equations," ACM Trans. Math Software, vol. 7, pp. 170-153, 1981.
19. P. Arbenz, A. Cleary, J. Dongarra, and M. Hegland, "A Comparison of Parallel Solvers for Diagonally Dominant and General Narrow Banded Linear Systems," Parallel and Distributed Computing Practices, vol. 2, pp. 385-400, 1999.