## Scientific Computing, Applied and Industrial Mathematics (SCAIM) Seminar: Stephen Thomas

• Date: 10/30/2018
• Time: 12:30
Lecturer(s):
Stephen Thomas, National Renewable Energy Laboratory (NREL)
Location:

University of British Columbia

Topic:

Low Synchronization Gram-Schmidt and GMRES Algorithms

Description:

Communication-avoiding and pipelined variants of Krylov solvers are critical for the scalability of linear system solvers on future exascale architectures. We present low synchronization variants of iterated classical (CGS) and modified Gram-Schmidt (MGS) algorithms that require one and two global reduction communication steps.  Derivations of low synchronization algorithms are based on observations by Ruhe.  Our main contribution is to introduce a backward normalization lag into the compact $WY$ form of MGS resulting in a ${\cal O}(\eps)\kappa(A)$ stable GMRES algorithm that requires only one global synchronization per iteration.  The reduction operations are overlapped with computations and pipelined to increase speed. Further improvements in performance are achieved by accelerating GMRES BLAS-2 operations on GPUs. Extensions to re-cycled Krylov iterations are explored.

Co-authors/collaborators: Kasia Swirydowicz (NREL), Julien Langou (CU Denver), Shreyas Ananthan (NREL), Ulrike Yang (LLNL).

Other Information:

Location: ESB 4133 (PIMS lounge)