Projects per year
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 language | English |
---|---|
Pages (from-to) | 2454-2476 |
Number of pages | 23 |
Journal | Journal of Computational Physics |
Volume | 149 |
Issue number | 755 |
Early online date | 23 Jun 2023 |
DOIs | |
Publication status | Published - 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
Fingerprint
Dive into the research topics of 'Hybridised multigrid preconditioners for a compatible finite element dynamical core'. Together they form a unique fingerprint.Projects
- 3 Finished
-
Research and development of a multigrid preconditioner for the LFRic hybridized solver
Mueller, E. (PI) & Griffith, M. (Researcher)
1/12/21 → 31/03/22
Project: Central government, health and local authorities
-
Maths Research Associates 2021
Milewski, P. (PI)
Engineering and Physical Sciences Research Council
1/10/21 → 30/06/24
Project: Research council
-
IAA – Accelerating climate- and weather-forecasts with faster multigrid solvers
Mueller, E. (PI) & Griffith, M. (Researcher)
Engineering and Physical Sciences Research Council
1/06/21 → 30/06/22
Project: Research council
File