| Fast sparse matrix-vector multiplication on TeraFlop/s computers |
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| Gerhard Wellein - Computing Center - Friedrich Alexander University Erlangen Nuernberg Georg Hager - Computing Center - Friedrich Alexander University Erlangen Nuernberg Achim Basermann - C&C Research Laboratories, NEC Europe Holger Fehske - Institut fuer Physik, Ernst-Moritz-Arndt Universitaet Greifswald |
Eigenvalue problems involving very large sparse matrices are common to various fields in science. In general, the numerical core of iterative eigenvalue algorithms is a matrix-vector multiplication (MVM) involving the large sparse matrix. We present three different programming approaches for parallel MVM on present day supercomputers. In addition to a pure message-passing approach, two hybrid parallel implementations are introduced based on simultaneous use of message-passing and shared-memory programming models. For a modern SMP cluster (HITACHI SR8000) performance and scalability of the hybrid implementations are discussed and compared with the pure message-passing approach on massively-parallel systems (CRAY T3E), vector computers(NEC SX5e) and distributed shared-memory systems (SGI Origin3800). |