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Title: Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere

Abstract

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. Finally, 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 capturemore » 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.« less

Authors:
ORCiD logo [1];  [2];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Technical Univ. of Munich (Germany)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1581338
Alternate Identifier(s):
OSTI ID: 1703202
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 407; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Parallel-in-time integration; Multi-level spectral deferred corrections; Spherical harmonics; Shallow-water equations on the sphere; Atmospheric flows; Climate and weather simulations

Citation Formats

Hamon, François P., Schreiber, Martin, and Minion, Michael L. Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere. United States: N. p., 2019. Web. https://doi.org/10.1016/j.jcp.2019.109210.
Hamon, François P., Schreiber, Martin, & Minion, Michael L. Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere. United States. https://doi.org/10.1016/j.jcp.2019.109210
Hamon, François P., Schreiber, Martin, and Minion, Michael L. Tue . "Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere". United States. https://doi.org/10.1016/j.jcp.2019.109210. https://www.osti.gov/servlets/purl/1581338.
@article{osti_1581338,
title = {Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere},
author = {Hamon, François P. and Schreiber, Martin and Minion, Michael L.},
abstractNote = {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. Finally, 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.},
doi = {10.1016/j.jcp.2019.109210},
journal = {Journal of Computational Physics},
number = C,
volume = 407,
place = {United States},
year = {2019},
month = {12}
}

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