The RSCG algorithm on distributed memory architectures

In this paper, we demonstrate the scalability of the Reduced System Conjugate Gradient (RSCG) algorithm on distributed memory architectures. We present speed-up results obtained on the Intel iPSC/860 that compare one-, two-, and three-dimensional decompositions of the domain for both positive definite and positive semidefinite test problems. We develop a model for the RSCG algorithm to analyze computational and communication costs. The model is validated using experimental data and then used to examine and predict behavior of the RSCG algorithm as a function of architecture parameters including communication latency and transmission times and memory access costs.

[1]  E. Barszcz.  Intercube communication for the iPSC/860 , 1992, Proceedings Scalable High Performance Computing Conference SHPCC-92..

[2]  Shahid H. Bokhari.  Communication overhead on the Intel iPSC-860 hypercube , 1990 .

[3]  A. Sameh,et al.  The behavior of conjugate gradient algorithms on a multivector processor with a hierarchical memory , 1988 .

[4]  Thomas H. Dunigan,et al.  Performance of the Intel iPSC/860 and Ncube 6400 hypercubes , 1991, Parallel Comput..

[5]  S. R. Seidel,et al.  Concurrent Bidirectional Communication On The Intel iPSC/860 And iPSC/2 , 1991, The Sixth Distributed Memory Computing Conference, 1991. Proceedings.

[6]  Niel K. Madsen,et al.  Matrix Multiplication by Diagonals on a Vector/Parallel Processor , 1976, Inf. Process. Lett..

[7]  D. Young,et al.  Vector computations for sparse linear systems , 1986 .

[8]  William Gropp,et al.  A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation , 1985, PP.

[9]  David H. Bailey,et al.  Performance Results on the Intel Touchstone Gamma Prototype , 1990, Proceedings of the Fifth Distributed Memory Computing Conference, 1990..

[10]  David L. Harrar.  Conjugate gradient methods for red/black systems on vector computers , 1991 .

[11]  James M. Ortega,et al.  Solution of three-dimensional generalized Poisson equations on vector computers , 1990 .

[12]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[13]  J. M. Ortega,et al.  Parallel solution of the generalized Helmholtz equation , 1992, Proceedings Scalable High Performance Computing Conference SHPCC-92..

[14]  Steven A. Moyer,et al.  Performance of the IPSC/860 Node Architecture , 1991 .