English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many problems in fluid modelling require the efficient solution of highlyanisotropic elliptic partial differential equations (PDEs) in "flat" domains.For example, in numerical weather- and climate-prediction an elliptic PDE forthe pressure correction has to be solved at every time step in a thin sphericalshell representing the global atmosphere. This elliptic solve can be one of thecomputationally most demanding components in semi-implicit semi-Lagrangian timestepping methods which are very popular as they allow for larger model timesteps and better overall performance. With increasing model resolution,algorithmically efficient and scalable algorithms are essential to run the codeunder tight operational time constraints. We discuss the theory and practicalapplication of bespoke geometric multigrid preconditioners for equations ofthis type. The algorithms deal with the strong anisotropy in the verticaldirection by using the tensor-product approach originally analysed by B\"{o}rmand Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend theanalysis to three dimensions under slightly weakened assumptions, andnumerically demonstrate its efficiency for the solution of the elliptic PDE forthe global pressure correction in atmospheric forecast models. For this wecompare the performance of different multigrid preconditioners on atensor-product grid with a semi-structured and quasi-uniform horizontal meshand a one dimensional vertical grid. The code is implemented in the Distributedand Unified Numerics Environment (DUNE), which provides an easy-to-use andscalable environment for algorithms operating on tensor-product grids. Parallelscalability of our solvers on up to 20,480 cores is demonstrated on the HECToRsupercomputer.

Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio