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Data Structure and Parallel Decomposition Considerations on a Fibonacci GridThe Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.
Document ID
20060054444
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Michalakes, John
(Argonne National Lab. United States)
Purser,James
(National Centers for Environmental Prediction United States)
Swinbank, Richard
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Date Acquired
August 23, 2013
Publication Date
January 1, 1999
Subject Category
Computer Systems
Meeting Information
Meeting: 13th Conference on NWP
Location: Denver, CO
Country: United States
Start Date: September 13, 1999
End Date: September 17, 1999
Distribution Limits
Public
Copyright
Other

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