Improving scalability using hybrid asynchronous methods for non-Hermitian Eigen-problems

We propose an optimized implementation of the MERAM method and preliminary experiments to solve non-Hermitian Eigen-problems 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 3800 seconds is reduced to 4 seconds using 1200 Nehalem cores, and we achieve linear to super-linear 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. (authors)