Communication cost reduction for Krylov methods on parallel computers
On large distributed memory parallel computers the global communication cost of inner products seriously limits the performance of Krylov subspace methods . We consider improved algorithms to reduce this communication overhead, and we analyze the performance by experiments on a 400-processor parallel computer and with a simple performance model.
KeywordsCommunication Overhead Krylov Subspace Method Krylov Method Communication Cost Reduction Measured Runtimes
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- 1.Z. Bai, D. Hu, and L. Reichel. A Newton basis GMRES implementation. Technical Report 91-03, University of Kentucky, 1991.Google Scholar
- 2.J. W. Demmel, M. T. Heath, and H.A. van der Vorst. Parallel numerical linear algebra. Acta Numerica Vol 2, Cambridge Press, New York, 1993Google Scholar
- 3.E. De Sturler. A parallel restructured version of GMRES(m). Technical Report 91-85, Delft University of Technology, Delft, 1991.Google Scholar
- 4.E. De Sturler. A parallel variant of GMRES(m). In R. Vichnevetsky, J. H. H. Miller, editors, Proc. of the 13th IMACS World Congress on Computation and Applied Mathematics, IMACS, Criterion Press Dublin 1991, pp 682–683.Google Scholar
- 5.E. De Sturler and H. A. Van der Vorst. Reducing the effect of global communication in GMRES (m) and CG on Parallel Distributed Memory Computers. Technical Report 832, Mathematical Institute, University of Utrecht, Utrecht, 1993Google Scholar
- 6.M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand., 49:409–436, 1954.Google Scholar
- 7.Y. Saad and M. H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 7:856–869, 1986.Google Scholar