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Copyright by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. SCI. COMPUT. c 2007 Society for Industrial and Applied Mathematics
 

Summary: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM J. SCI. COMPUT. c 2007 Society for Industrial and Applied Mathematics
Vol. 29, No. 4, pp. 1683­1709
PARTITIONING SPARSE MATRICES FOR PARALLEL
PRECONDITIONED ITERATIVE METHODS
BORA UC¸AR AND CEVDET AYKANAT
Abstract. This paper addresses the parallelization of the preconditioned iterative methods
that use explicit preconditioners such as approximate inverses. Parallelizing a full step of these
methods requires the coefficient and preconditioner matrices to be well partitioned. We first show
that different methods impose different partitioning requirements for the matrices. Then we develop
hypergraph models to meet those requirements. In particular, we develop models that enable us
to obtain partitionings on the coefficient and preconditioner matrices simultaneously. Experiments
on a set of unsymmetric sparse matrices show that the proposed models yield effective partitioning
results. A parallel implementation of the right preconditioned BiCGStab method on a PC cluster
verifies that the theoretical gains obtained by the models hold in practice.
Key words. matrix partitioning, preconditioning, iterative method, parallel computing
AMS subject classifications. 05C50, 05C65, 65F10, 65F35, 65F50, 65Y05
DOI. 10.1137/040617431
1. Introduction. We consider the parallelization of the preconditioned itera-
tive methods that use explicit preconditioners such as approximate inverses or fac-

  

Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University
Uçar, Bora - Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon

 

Collections: Computer Technologies and Information Sciences