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\section{exch2: Extended Cubed Sphere Exchange} |
\section{Extended Cubed Sphere Exchange} |
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\label{sec:exch2} |
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\subsection{Introduction} |
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\subsection{Introduction} |
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The \texttt{exch2} package is an extension to the original cubed |
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sphere topological configuration that allows more flexible domain |
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decomposition and parallelization. Cube faces (also called |
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subdomains) may be divided into any number of tiles that divide evenly |
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into the grid point dimensions of the subdomain. Furthermore, the |
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individual tiles may be run on separate processors in different |
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combinations, and whether exchanges between particular tiles occur |
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between different processors is determined at runtime. This |
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flexibility provides for manual load balancing across a relatively |
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arbitrary number of processors. |
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The exchange parameters are declared in |
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\filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h} |
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and assigned in |
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\filelink{pkg/exch2/w2\_e2setup.F}{pkg-exch2-w2_e2setup.F}. The |
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validity of the cube topology depends on the \texttt{SIZE.h} file as |
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detailed below. Both files are generated by Matlab scripts in ?? |
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check these in already! and should not be edited. The default files |
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provided in the release configure a cubed sphere arrangement of six |
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tiles, one per subdomain, each with 32$\times$32 grid points, all |
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running on a single processor. Pregenerated examples of these files |
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with alternate topologies are provided in ??. |
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\subsection{Invoking exch2} |
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To use exch2 with the cubed sphere, the following conditions must be met: |
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- the exch2 package is included when \texttt{genmake2} is run. The |
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easiest way to do this is to add the line \texttt{exch2} to the |
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\texttt{profile.conf} file -- see Section \ref{sect:buildingCode} |
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for general details. \\ |
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- an example of \texttt{W2\_EXCH2\_TOPOLOGY.h} and |
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\texttt{w2\_e2setup.F} must reside in a directory containing code |
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linked when \texttt{genmake2} runs. The safest place to put these |
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is the directory indicated in the \texttt{-mods=DIR} command line |
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modifier (typically \texttt{../code}), or the build directory. The |
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default versions of these files reside in \texttt{pkg/exch2}, but |
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they should be left untouched to avoid breaking configurations other |
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than the one you intend to modify.\\ |
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- files containing grid parameters, named |
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\texttt{tile}xxx\texttt{.mitgrid} where xxx is \texttt{001} through |
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\texttt{006}, must be in the working directory when the MITgcm |
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executable is run. These files are provided in the example |
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experiments for cubed sphere configurations with 32$\times$32 cube |
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sides and are non-trivial to generate -- please contact MITgcm |
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support if you want to generate files for other configurations. |
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This is lame. ?? \\ |
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As of the time of writing the following examples use exch2 and may be |
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used for guidance: |
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\begin{verbatim} |
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verification/adjust_nlfs.cs-32x32x1 |
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verification/adjustment.cs-32x32x1 |
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verification/aim.5l_cs |
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verification/global_ocean.cs32x15 |
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verification/hs94.cs-32x32x5 |
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\end{verbatim} |
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\subsection{Generating Topology Files} |
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\subsection{Key Variables} |
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The descriptions of the variables are divided up into scalars, |
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one-dimensional arrays indexed to the tile number, and two and three |
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dimensional arrays indexed to tile number and neighboring tile. This |
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division actually reflects the functionality of these variables: the |
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scalars are common to every part of the topology, the tile-indexed |
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arrays to individual tiles, and the arrays indexed to tile and |
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neighbor to relationships between tiles and their neighbors. |
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\subsubsection{Scalars} |
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The number of tiles in a particular topology is set with the parameter |
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\texttt{NTILES}, and the maximum number of neighbors of any tiles by |
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\texttt{MAX\_NEIGHBOURS}. These parameters are used for defining the |
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size of the various one and two dimensional arrays that store tile |
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parameters indexed to the tile number.\\ |
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The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt} |
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and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number |
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of tiles in the x and y global indices. For example, the default |
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setup of six tiles has \texttt{exch2\_domain\_nxt=6} and |
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\texttt{exch2\_domain\_nyt=1}. A topology of twenty-four square (in |
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gridpoints) tiles, four (2x2) per subdomain, will have |
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\texttt{exch2\_domain\_nxt=12} and \texttt{exch2\_domain\_nyt=2}. |
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Note that these parameters express the tile layout to allow global |
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data files that are tile-layout-neutral and have no bearing on the |
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internal storage of the arrays. The tiles are internally stored in a |
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range from \texttt{1,bi} (in the x axis) and y-axis variable |
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\texttt{bj} is generally ignored within the package. |
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\subsubsection{Arrays Indexed to Tile Number} |
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The following arrays are of size \texttt{NTILES}, are indexed to the |
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tile number, and the indices are omitted in their descriptions. |
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The arrays \varlink{exch2\_tnx}{exch2_tnx} and |
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\varlink{exch2\_tny}{exch2_tny} express the x and y dimensions of each |
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tile. At present for each tile \texttt{exch2\_tnx=sNx} and |
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\texttt{exch2\_tny=sNy}, as assigned in \texttt{SIZE.h}. Future |
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releases of MITgcm are to allow varying tile sizes. |
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The location of the tiles' Cartesian origin within a subdomain are |
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determined by the arrays \varlink{exch2\_tbasex}{exch2_tbasex} and |
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\varlink{exch2\_tbasey}{exch2_tbasey}. These variables are used to |
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relate the location of the edges of the tiles to each other. As an |
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example, in the default six-tile topology (the degenerate case) each |
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index in these arrays are set to 0. The twenty-four, 32x32 cube face |
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case discussed above will have values of 0 or 16, depending on the |
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quadrant the tile falls within the subdomain. The array |
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\varlink{exch2\_myFace}{exch2_myFace} contains the number of the |
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cubeface/subdomain of each tile, numbered 1-6 in the case of the |
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standard cube topology. |
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The arrays \varlink{exch2\_txglobalo}{exch2_txglobalo} and |
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\varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to |
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\varlink{exch2\_tbasex}{exch2_tbasex} and |
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\varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the |
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global address space, similar to that used by global files. |
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The arrays \varlink{exch2\_isWedge}{exch2_isWedge}, |
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\varlink{exch2\_isEedge}{exch2_isEedge}, |
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\varlink{exch2\_isSedge}{exch2_isSedge}, and |
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\varlink{exch2\_isNedge}{exch2_isNedge} are set to 1 if the indexed |
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tile lies on the edge of a subdomain, 0 if not. The values are used |
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within the topology generator to determine the orientation of |
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neighboring tiles and to indicate whether a tile lies on the corner of |
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a subdomain. The latter case indicates special exchange and numerical |
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handling for the singularities at the eight corners of the cube. |
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\varlink{exch2\_nNeighbours}{exch2_nNeighbours} contains a count of |
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how many neighboring tiles each tile has, and is used for setting |
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bounds for looping over neighboring tiles. |
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\varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each |
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tile, and is used in interprocess communication. |
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\subsubsection{Arrays Indexed to Tile Number and Neighbor} |
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The following arrays are all of size \texttt{MAX\_NEIGHBOURS} $\times$ |
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\texttt{NTILES} and describe the orientations between the the tiles. |
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The array \texttt{exch2\_neighbourId(a,T)} holds the tile number for |
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each of the $n$ neighboring tiles. The neighbor tiles are indexed |
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\texttt{(1,MAX\_NEIGHBOURS} in the order right to left on the north |
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then south edges, and then top to bottom on the east and west edges. |
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Maybe throw in a fig here, eh? |
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The \texttt{exch2\_opposingSend\_record(a,T)} array holds the index c |
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in \texttt{exch2\_neighbourId(b,$T_{n}$)} that holds the tile number T. |
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In other words, |
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\begin{verbatim} |
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exch2_neighbourId( exch2_opposingSend_record(a,T), |
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exch2_neighbourId(a,T) ) = T |
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\end{verbatim} |
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and this provides a back-reference from the neighbor tiles. |
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The arrays \varlink{exch2\_pi}{exch2_pi}, |
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\varlink{exch2\_pj}{exch2_pj}, \varlink{exch2\_oi}{exch2_oi}, |
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\varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and |
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\varlink{exch2\_oj\_f}{exch2_oj_f} specify the transformations in |
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exchanges between the neighboring tiles. The dimensions of |
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\texttt{exch2\_pi(t,N,T)} and \texttt{exch2\_pj(t,N,T)} are the |
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neighbor ID \textit{N} and the tile number \textit{T} as explained |
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above, plus the transformation vector {\em t }, of length two. The |
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first element of the transformation vector indicates the factor by |
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which variables representing the same vector component of a tile will |
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be multiplied, and the second element indicates the transform to the |
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variable in the other direction. As an example, |
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\texttt{exch2\_pi(1,N,T)} holds the transform of the i-component of a |
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vector variable in tile \texttt{T} to the i-component of tile |
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\texttt{T}'s neighbor \texttt{N}, and \texttt{exch2\_pi(2,N,T)} hold |
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the component of neighbor \texttt{N}'s j-component. |
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Under the current cube topology, one of the two elements of |
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\texttt{exch2\_pi} or \texttt{exch2\_pj} for a given tile \texttt{T} |
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and neighbor \texttt{N} will be 0, reflecting the fact that the vector |
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components are orthogonal. The other element will be 1 or -1, |
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depending on whether the components are indexed in the same or |
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opposite directions. For example, the transform dimension of the |
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arrays for all tile neighbors on the same subdomain will be [1,0], |
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since all tiles on the same subdomain are oriented identically. |
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Vectors that correspond to the orthogonal dimension with the same |
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index direction will have [0,1], whereas those in the opposite index |
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direction will have [0,-1]. |
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{\footnotesize |
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\begin{verbatim} |
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C exch2_pi :: X index row of target to source permutation |
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C :: matrix for each neighbour entry. |
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C exch2_pj :: Y index row of target to source permutation |
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C :: matrix for each neighbour entry. |
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C exch2_oi :: X index element of target to source |
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C :: offset vector for cell-centered quantities |
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C :: of each neighbor entry. |
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C exch2_oj :: Y index element of target to source |
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C :: offset vector for cell-centered quantities |
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C :: of each neighbor entry. |
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C exch2_oi_f :: X index element of target to source |
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C :: offset vector for face quantities |
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C :: of each neighbor entry. |
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C exch2_oj_f :: Y index element of target to source |
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C :: offset vector for face quantities |
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C :: of each neighbor entry. |
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\end{verbatim} |
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} |
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