Acceleration of the IMplicit–EXplicit nonhydrostatic unified model of the atmosphere on manycore processors

Journal Article · 31 October 2017 · International Journal of High Performance Computing Applications

DOI: https://doi.org/10.1177/1094342017732395 · OSTI ID:1498290

Abdi, Daniel S. ^[1]; Giraldo, Francis X. ^[1]; Constantinescu, Emil M. ^[2]; Carr, III, Lester E. ^[1]; Wilcox, Lucas C. ^[1]; Warburton, Timothy C. ^[3]

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1. Naval Postgraduate School, Monterey, CA (United States)
2. Argonne National Lab. (ANL), Argonne, IL (United States)
3. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

We present the acceleration of an IMplicit-EXplicit (IMEX) nonhydrostatic atmospheric model on manycore processors such as graphic processing units (GPUs) and Intel's Many Integrated Core (MIC) architecture. IMEX time integration methods sidestep the constraint imposed by the Courant-Friedrichs-Lewy condition on explicit methods through corrective implicit solves within each time step. In this work, we implement and evaluate the performance of IMEX on manycore processors relative to explicit methods. Using 3D-IMEX at Courant number C = 15, we obtained a speedup of about 4x relative to an explicit time stepping method run with the maximum allowable C = 1. Moreover, the unconditional stability of IMEX with respect to the fast waves means the speedup can increase significantly with the Courant number as long as the accuracy of the resulting solution is acceptable. We show a speedup of 100x at C = 150 using 1D-IMEX to demonstrate this point. Several improvements on the IMEX procedure were necessary in order to outperform our results with explicit methods: (a) reducing the number of degrees of freedom of the IMEX formulation by forming the Schur complement, (b) formulating a horizontally explicit vertically implicit 1D-IMEX scheme that has a lower workload and better scalability than 3D-IMEX, (c) using high-order polynomial preconditioners to reduce the condition number of the resulting system, and (d) using a direct solver for the 1D-IMEX method by performing and storing LU factorizations once to obtain a constant cost for any Courant number. Without all of these improvements, explicit time integration methods turned out to be difficult to beat. We discuss in detail the IMEX infrastructure required for formulating and implementing efficient methods on manycore processors. Several parametric studies are conducted to demonstrate the gain from each of the abovementioned improvements. Lastly, we validate our results with standard benchmark problems in numerical weather prediction and evaluate the performance and scalability of the IMEX method using up to 4192 GPUs and 16 Knights Landing processors.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Department of the Navy, Office of Naval Research (ONR)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1498290
• Journal Information: International Journal of High Performance Computing Applications, Vol. 33, Issue 2; ISSN 1094-3420
• Publisher: SAGECopyright Statement
• Country of Publication: United States
• Language: English