|Fast sparse matrix-vector multiplication on TeraFlop/s computers|
|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).