This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Iterative Algorithms for Solution of Large Sparse Systems of Linear Equations on Hypercubes
December 1988 (vol. 37 no. 12)
pp. 1554-1568
Finite-element discretization produces linear equations in the form Ax=b, where A is large, sparse, and banded with proper ordering of the variables x. The solution of such equations on distributed-memory message-passing multiprocessors implementing the hypercube topology is addressed. Iterative algorithms based on the conjugate gradient method are developed for hypercubes designed for coarse-g

[1] G. A. Lyzenga, A. Raefsky, and G. H. Hager, "Finite elements and the method of conjugate gradients on a concurrent processor," inProc. ASME Int. Conf. Comput. Eng., 1985, pp. 393-399.
[2] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 22-33, Jan. 1985.
[3] J. M. Ortega and R. G. Voigt, "Solution of partial differential equations on vector and parallel computers,"SIAM Rev., vol. 27, pp. 149-240, 1985.
[4] R. Lucas, T. Blank, and J. Tiemann, "A parallel solution method for large sparse systems of equations,"IEEE Trans. Computer-Aided Design, vol. CAD-6, pp. 981-990, Nov. 1987.
[5] H. Jordan, "A special purpose architecture for finite element analysis," inProc. IEEE Int. Conf. Parallel Processing, Aug. 1978, pp. 263-266.
[6] J. A. George and J. Liu,Computer Solution of Large Sparse Positive Definite Systems. Englewood Cliffs, NJ: Prentice-Hall, 1981.
[7] J. P. Hayeset al., "A microprocessor-based hypercube supercomputer,"IEEE Micro, vol. 6, pp. 6-17, Oct. 1986.
[8] S. H. Bokhari, "On the mapping problem,"IEEE Trans. Comput., vol. C-30, pp. 207-214, Mar. 1981.
[9] Z. Cvetanovic, "The effect of problem partitioning, allocation, and granularity on the performance of multiple-processor systems,"IEEE Trans. Comput., vol. C-36, Apr. 1987.
[10] Y. Saad, "Practical use of polynomial preconditionings for the conjugate gradient method,"SIAM J. Scientif. Statist. Comput., vol. 6, pp. 865-881, Oct. 1985.
[11] D. Luenberger,Introduction to Linear and Nonlinear Programming. Reading, MA: Addison-Wesley, 1973.
[12] A. Jennings and C. Malek, "The solution of sparse linear equations by the conjugate gradient method,"Int. J. Numer. Meth. Eng., vol. 12, pp. 141-158, 1978.
[13] P. Sadayappan and F. Ercal, "Nearest-neighbor mappings of finite element graphs onto processor meshes,"IEEE Trans. Comput., vol. C-36, pp. 1408-1424, Dec. 1987.
[14] G. Meurant, "Multitasking the conjugate gradient method on the CRAY X-MP/48,"Parallel Comput., no. 5, pp. 267-280, 1987.
[15] C. Moler, "Matrix computations on distributed memory multiprocessors," inProc. SIAM First Conf. Hypercube Multiprocessors, 1986, pp. 181-195.

Index Terms:
parallel algorithms; iterative algorithms; large sparse systems; linear equations; hypercubes; distributed-memory; message-passing multiprocessors; hypercube topology; conjugate gradient method; finite element analysis; iterative methods; linear algebra; parallel algorithms.
Citation:
C. Aykanat, F. Ozguner, F. Ercal, P. Sadayappan, "Iterative Algorithms for Solution of Large Sparse Systems of Linear Equations on Hypercubes," IEEE Transactions on Computers, vol. 37, no. 12, pp. 1554-1568, Dec. 1988, doi:10.1109/12.9733
Usage of this product signifies your acceptance of the Terms of Use.