[Back]

S. Benkner, D. Kvasnicka, M. Lucka:
"Experiments with Cholesky Factorization on Clusters of SMPs";
in: "Proceedings of the Euro Conference NMCM2002 -- numerical methods and computational mechanics", Tagungsband, University of Miskolc, Miskolc, Hungary., 2002, 1.

Cholesky factorization of large dense matrices is an integral part of many applications in
science and engineering. In this paper we report on experiments with different parallel versions of Cholesky
factorization on modern high-performance computing architectures. For the parallelization of Cholesky factorization we
utilized various standard linear algebra software packages and present performance results on SMP clusters and
shared-memory cc-NUMA machines. Clusters of SMPs can be characterized as hybrid parallel architectures which combine the
main architectural features of distributed-memory and shared-memory parallel computers. Although the availability of SMP
clusters is increasing rapidly within the scientific computing community, currently no generally accepted programming
model exists for these machines. As a consequence, most application developers utilize pure distributed-memory
programming models, usually based on the message passing interface (MPI), and thus may miss a number of optimization
opportunities offered by the shared-memory available within the nodes of a cluster. In order to address these issues, we
have experimented with different parallelization strategies for Cholesky decomposition comparing pure message passing
strategies to a hybrid parallelization strategy that combines message passing with shared-memory paralleization based on
multi-threading.