Istituto di Matematica Applicata e Tecnologie Informatiche     
Fornasari N., Lanucara P., Rovida S. Parallel Iterative Methods on Distributed Shared Memory Systems. Technical report ercim.cnr.ian//1998-1079, 1998.
It is well known that Conjugate--Gradients algorithms are wildly used for the solution of large--scale linear systems as they are competitive among the available fast iterative schemes and their parallelization appears to be straightforward since there is a potential parallelism to be exploited at each step. In this paper we present a parallel implementation, on distributed shared memory architectures using the SPMD programming paradigm, of two Conjugate--Gradients algorithms: the CGS and the BiCGSTAB methods associated with some algebraic preconditioners. We analyze the programming environment supplied by an SMP cluster of 4 AlphaServer 4100 with 4 processors each, interconnected with Memory Channel to handle data communication and data distribution. We compare the performance of different implementations of the algorithms: one based on the PVM message passing interface and the other one based on the mix of PVM for message passing among different machines and GUIDE from KAP/Pro Toolset to exploit parallelism within each SMP machine through the use of directives. In particular we address the tradeoff between minimizing interprocessor communication and exploiting the available parallelism by a suitable data distribution.
Subject Parallel Computing, Conjugate-Gradients, Multilevel Parallelism

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