Hybridised multigrid preconditioners for a compatible finite-element dynamical core
Author(s)
Type
Journal Article
Abstract
Compatible finite-element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear equations. Preconditioning this system is challenging, since the velocity mass matrix is nondiagonal, leading to a dense Schur complement. Hybridisable discretisations overcome this issue: weakly enforcing continuity of the velocity field with Lagrange multipliers leads to a sparse system of equations, which has a similar structure to the pressure Schur complement in traditional approaches. We describe how the hybridised sparse system can be preconditioned with a non-nested two-level preconditioner. To solve the coarse system, we use the multigrid pressure solver that is employed in the approximate Schur complement method previously proposed by the some of the authors. Our approach significantly reduces the number of solver iterations. The method shows excellent performance and scales to large numbers of cores in the Met Office next-generation climate and weather prediction model LFRic.
Date Issued
2023-07
Date Acceptance
2023-06-13
Citation
Quarterly Journal of the Royal Meteorological Society, 2023, 149 (755), pp.2454-2476
ISSN
0035-9009
Publisher
Wiley
Start Page
2454
End Page
2476
Journal / Book Title
Quarterly Journal of the Royal Meteorological Society
Volume
149
Issue
755
Copyright Statement
© 2023 Crown Copyright and The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of Royal Meteorological Society. This article is published with the permission of the Controller of HMSO and the King's Printer for Scotland.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:001026587800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
atmosphere
dynamics
EXPLICIT
EXTERIOR CALCULUS
finite-element discretisation
H(DIV)
hybridisation
linear solvers
Meteorology & Atmospheric Sciences
MODEL
multigrid
numerical methods and NWP
parallel scalability
Physical Sciences
Science & Technology
WEATHER
Publication Status
Published
Date Publish Online
2023-07-12