Acceleration of the implicit-explicit non-hydrostatic unified model of the atmosphere (NUMA) on Manycore processors

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Author
Abdi, Daniel S.
Giraldo, Francis X.
Constantinescu, Emil M.
Carr, Lester E., III
Wilcox, Lucas C.
Warburton, Timothy C.
Date
2017Metadata
Show full item recordAbstract
We present the acceleration of an IMplicit-EXplicit (IMEX) non-hydrostatic atmospheric model on
manycore processors
such as GPUs and Intel’s 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 (HEVI)
1D-IMEX scheme that has a lower workload and potentially better scalability than 3D-IMEX; c) using
high-order polynomial preconditioners to reduce the condition number of the resulting system; 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 above mentioned
improvements. Finally, 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.
Description
The article of record as published may be found at http://dx.doi.org/10.1177/ToBeAssigned
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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