Research Period: April, 2011〜March, 2016 Research Director: Tetsuya Sakurai（University of Tsukuba・Professor） Research Area: CREST「Development of System Software Technologies for post-Peta Scale High Performance Computing」 In many cases, numerical computation arising in many fields such from fundamental science to industrial applications finally will return to solve very large eigenvalue problems. Various algorithms have been proposed, as most of them are implemented recursively or designed based on one parallel hierarchical mode, it is difficult to efficiently perform those algorithms for post-petascale machines with hierarchical architecture. The aim of this research is to develop a massively parallel eigenvalue analysis engine for post-petascale machines with a hierarchical parallel structure. The developed engine is based on newly designed algorithms created to address issues of scalability and fault tolerance that have plagued conventional eigenvalue methods. For high performance and practical applications, a variety of techniques need to be developed, such as sparse-dense hybrid methods, Krylov subspace methods, construction of performance modeling and its evaluation, implementation techniques for multi-cores and real applications etc. This analysis engine will open new doors for cutting-edge science and engineering simulations on scales that have never been feasible in the past, and then create a potential for stimulating technological innovation across a broad range of areas in science and industry.