Abstract
Semi-implicit time-stepping schemes for atmosphere and ocean models
require elliptic solvers that work efficiently on modern supercomputers.
This paper reports our study of the potential computational savings when
using mixed precision arithmetic in the elliptic solvers. Precision
levels as low as half (16 bits) are used and a detailed evaluation of
the impact of reduced precision on the solver convergence and the
solution quality is performed.
This study is conducted
in the context of a novel semi-implicit shallow-water model on the
sphere, purposely designed to mimic numerical intricacies of modern
all-scale weather and climate (W&C) models. The governing algorithm of
the shallow-water model is based on the non-oscillatory MPDATA methods
for geophysical flows, whereas the resulting elliptic problem employs a
strongly preconditioned non-symmetric Krylov-subspace solver GCR, proven
in advanced atmospheric applications. The classical longitude/latitude
grid is deliberately chosen to retain the stiffness of global W&C
models. The analysis of the precision reduction is done on a software
level, using an emulator, whereas the performance is measured on actual
reduced precision hardware. The reduced-precision experiments are
conducted for established dynamical-core test-cases, like the
Rossby-Haurwitz wavenumber 4 and a zonal orographic
flow.
The study shows that selected key components of
the elliptic solver, most
prominently the preconditioning and the application of the linear
operator, can be performed at the level of half precision. For these
components, the use of half precision is found to yield a speed-up of a
factor 4 compared to double precision for a wide range of problem sizes.