期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 407, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.109210
关键词
Parallel-in-time integration; Multi-level spectral deferred corrections; Spherical harmonics; Shallow-water equations on the sphere; Atmospheric flows; Climate and weather simulations
资金
- U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program [DE-AC02-005CH11231]
- U.S. DOE [DE-AC02-05CH11231]
- NCAR
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps, even when the terms accounting for the propagation of fast atmospheric waves are treated implicitly. Therefore, the use of parallel-in-time integration schemes to reduce the time-to-solution is of increasing interest, particularly in the numerical weather forecasting field. We present a multi-level parallel-in-time integration method combining the Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial discretization based on Spherical Harmonics (SH). The iterative algorithm computes multiple time steps concurrently by interweaving parallel high-order fine corrections and serial corrections performed on a coarsened problem. To do that, we design a methodology relying on the spectral basis of the SH to coarsen and interpolate the problem in space. The methods are evaluated on the shallow-water equations on the sphere using a set of tests commonly used in the atmospheric flow community. We assess the convergence of PFASST-SH upon refinement in time. We also investigate the impact of the coarsening strategy on the accuracy of the scheme, and specifically on its ability to capture the high-frequency modes accumulating in the solution. Finally, we study the computational cost of PFASST-SH to demonstrate that our scheme resolves the main features of the solution multiple times faster than the serial schemes. (C) 2019 Elsevier Inc. All rights reserved.
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