Algoritmi di tipo Gradiente Coniugato su Sistemi Distribuiti a Memoria Condivisa

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 the BiCGSTAB algorithm associated with some algebraic preconditioners. We analyze the programming environment supplied by an SMP cluster of 4 Digital 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 MPI message passing interface and the other one based on the mix of MPI for message passing among different nodes and GUIDE from KAP/Pro Toolset to exploit parallelism within each SMP node through the use of standard OpenMP directives. This multilevel parallelism can be also obtained with a combination of MPI and the Digital Extended Math Library Pthreads, a multi-threaded version of the BLAS, LAPACK routines, available on the considered architecture.