Dedner, Andreas, Müller, Eike and Scheichl, Robert (2015) Efficient multigrid preconditioners for atmospheric flow simulations at high aspect ratio. International Journal for Numerical Methods in Fluids, 80 (1). pp. 76-102. doi:10.1002/fld.4072 ISSN 0271-2091.

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Abstract

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in ‘flat’ domains. For example, in numerical weather and climate prediction, an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi‐implicit semi‐Lagrangian time stepping methods, which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor‐product approach originally analysed by Börm and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219–234]. We extend the analysis to three dimensions under slightly weakened assumptions and numerically demonstrate its efficiency for the solution of the elliptic PDE for the global pressure correction in atmospheric forecast models. For this, we compare the performance of different multigrid preconditioners on a tensor‐product grid with a semi‐structured and quasi‐uniform horizontal mesh and a one‐dimensional vertical grid. The code is implemented in the Distributed and Unified Numerics Environment, which provides an easy‐to‐use and scalable environment for algorithms operating on tensor‐product grids. Parallel scalability of our solvers on up to 20 480 cores is demonstrated on the HECToR supercomputer.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	International Journal for Numerical Methods in Fluids
Publisher:	John Wiley & Sons Ltd.
ISSN:	0271-2091
Official Date:	2 July 2015
Dates:	Date Event 2 July 2015 Available
Volume:	80
Number:	1
Page Range:	pp. 76-102
DOI:	10.1002/fld.4072
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Open Access Version:	ArXiv

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