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 non-diagonal, 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.
Original languageEnglish
Pages (from-to)2454-2476
Number of pages23
JournalJournal of Computational Physics
Volume149
Issue number755
Early online date23 Jun 2023
DOIs
Publication statusPublished - 1 Jul 2023

Bibliographical note

Funding Information:
This work was funded by two EPSRC Impact Acceleration Awards (grant numbers EP/R511547/1, EP/R51164X/1) and an EPSRC PostDoctoral Award (grant number EP/W522491/1) of Matthew Griffith.

Publisher Copyright:
© 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.

Keywords

  • atmosphere
  • dynamics
  • finite-element discretisation
  • hybridisation
  • linear solvers
  • multigrid
  • numerical methods and NWP
  • parallel scalability

ASJC Scopus subject areas

  • Atmospheric Science

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