Title：On the Road to Exascale and Beyond,  Intelligent Restarted Linear Algebra Methods

　　Speaker：Prof. Serge G. Petition 

　　Time：2016-5-16 10:00 AM

　　Venue：Room A507, 5th Floor, Building #5, Institute of Software, CAS  

　　Abstract: 

　　Exascale hypercomputers are expected to have highly hierarchical architectures with nodes composed by lot-of-core processors and accelerators. The different programming levels (from clusters of processors loosely connected to tightly connected lot-of-core processors and/or accelerators) will generate new difficult algorithm issues. New methods should be defined and evaluated with respect to modern state-of-the-art of applied mathematics and scientific methods. 

　　Krylov linear methods such as GMRES and ERAM are now heavily used with success in various domains and industries despite their complexity. Their convergence and speed greatly depends on the hardware used and on the choice of the Krylov subspace size and other parameters which are difficult to determine efficiently in advance. Moreover, hybrid Krylov Methods would allow reducing the communications along all the cores, limiting the reduction only through subsets of these cores. Added to their numerical behaviours and their fault tolerance properties, these methods are interesting candidates for exascale/extreme matrix computing. Avoiding communication strategies may also be developed for each of the instance of these methods, generating complex methods but with high potential efficiencies. These methods have a lot of correlated parameter which may be optimized using auto/smart-tuning strategies to accelerate convergence, minimize storage space, data movements, and energy consumption.