52 lines
2.0 KiB
TeX
52 lines
2.0 KiB
TeX
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\begin{figure}
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\centering
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\includegraphics[width=14cm]{Pics/PUMA_alternate_grid.png}
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\caption[]{PUMA T21 horizontal grid sorted by index}
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\label{pumat21igrid}
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\end{figure}
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PUMA uses internally (other than the Planet Simulator and PUMA version 15) an alternating Gaussian grid.
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This feature is unimportant for users, who don't change source code - the output file
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will still contain the usual Gaussian grid with the latitude index running from the most Northern latitude
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to the most Southern one. But for those, who fiddle around with the code or want to implement additional
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arrays it is important to understand the internal structure.
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The alternating grid was introduced for two reasons:
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1) The number of values for Legendre polynomials could be reduced by a factor of two, because
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pairs of Northern and Southern latitudes with the same absolute value can be processed
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simultaneously. This is especially useful for very high resolution runs.
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E.g. a PUMA T1365 needs now ca. 45 GByte memory.
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2) The Legendre transformation was recoded to use symmetric and antisymmetric Fourier
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coefficients for these latitude pairs resulting in strict conservation of symmetry
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and antisymmetry properties.
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Figure \ref{pumat21igrid} shows how the elements of a horizontal grid
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are stored in computer memory. The restrictions for parallel execution
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using alternating grids are:
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Because a latitude pair must not be separated to different processes,
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the maximum number of processes is half of the number of latitudes.
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Also it not possible to use an odd number of processes.
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Figure \ref{pumat21lgrid} shows a horizontal grid sorted from North to South
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and its corresponding latitude indices.
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The subroutines ALT2REG and REG2ALT (in legsym.f90) may be used to convert from
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alternating to regular Gaussian grid and vice versa.
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\begin{figure}
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\centering
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\includegraphics[width=14cm]{Pics/PUMA_alternate_grid_geogr.png}
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\caption[]{PUMA T21 horizontal grid sorted from North to South}
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\label{pumat21lgrid}
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\end{figure}
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