Improving Scalability Using Hybrid Asynchronous Methods For Non-Hermitian Eigenproblems

We propose an optimized implementation of the MERAM method and preliminary experiments to solve non-Hermitian eigenproblems faster using this asynchronous hybrid method. We focus on improving the communication pattern by providing an entity called the collector as well as an optimized communication scheme using MPI-2 one-sided communications. The scalability of the parallelization is discussed and experiments are done to show how well our implementation scales to a large number of nodes. The one 8 cores node computing time of 3800seconds is reduced to 4seconds using 1200 Nehalem cores, and we achieve linear to superlinear speed-ups thanks to our efficient communication pattern and the coarse-grained parallel nature of MERAM. Our approach achieved an optimal performance on more than a thousand cores for the first time with MERAM. We conclude that hybrid asynchronous methods like MERAM with a good communication patter offer tremendous possibilities for high performance computing