Development of exascale matrix solvers based on communication avoiding algorithms

Imamura, Toshiyuki*; Idomura, Yasuhiro   ; Ina, Takuya*; Yamashita, Susumu   ; Onodera, Naoyuki   ; Ali, Y.*; Yamada, Susumu  

Towards exascale computing on the Post-K computer, a novel matrix solvers are developed by using communication avoiding algorithms. In this talk, we review two main approaches used in the three-dimensional thermal hydraulic multi-phase CFD code, JUPITER. One is a communication avoiding Krylov sub-space method, in which multiple basis vectors are generated and orthogonalized at once to reduce global collective communications. The other is a Krylov sub-space method with multi-grid preconditioning, which dramatically improve convergence property and reduce the number of iterations, and thus, global collective communications. We compare these approaches on the latest many core platform.