Multi Level Parallelism of Multiple Implicitly/Explicitly Restarted Arnoldi Methods for Post-petascale Computing

The iterative methods are widely used to solve eigen problems in scientific computation. We focus on multiple restarted Arnoldi methods (MRAM) [4] which manage iterative co-methods to accelerate their convergence. These methods are considered as good candidate for emerging large scale computational systems thanks to their asynchronous communication schema, their potential load balancing and their multi-level parallelism. Both coarse grain parallelism between co-methods and fine grain parallelism inside each co-method need to be flexibly mapped to large scale distributed memory systems like hierarchical supercomputer, the cloud or P2P platforms. In this paper, we investigate such possibility in MRAMs by developing and executing them with a development and execution environment called FP2C (Framework for Post-Petascale Computing) [11]. The FP2C is a user-friendly and hierarchical-system-oriented development and execution environment based on workflow and distributed parallel methodologies. Our first goal is to show the feasibility of the approach FP2C to realize complex applications such as MRAMs. The next objective of the paper is to point out the adaptability of MRAMs to new generation of supercomputers (Petascale and futur Exascale). In addition, we show by our experiments that, collaboration of multiple iterative methods based on coarse grain parallelism accelerates convergence, and co-working processors within each iterative method based on fine grain parallelism accelerates the time per iteration.