/[MITgcm]/manual/s_phys_pkgs/text/exch2.tex

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  \subsection{Introduction}
- The \texttt{exch2} package extends the original cubed
+ The \texttt{exch2} package extends the original cubed sphere topology
- sphere topology configuration to allow more flexible domain
+ configuration to allow more flexible domain decomposition and
- decomposition and parallelization.  Cube faces (also called
+ parallelization.  Cube faces (also called subdomains) may be divided
- subdomains) may be divided into any number of tiles that divide evenly
+ into any number of tiles that divide evenly into the grid point
- into the grid point dimensions of the subdomain.  Furthermore, the
+ dimensions of the subdomain.  Furthermore, the tiles can run on
- individual tiles can run on separate processors in different
+ separate processors individually or in groups, which provides for
- combinations, and whether exchanges between particular tiles occur
+ manual compile-time load balancing across a relatively arbitrary
- between different processors is determined at runtime.  This
+ number of processors. \\
- flexibility provides for manual compile-time load balancing across a
- relatively arbitrary number of processors. \\
  The exchange parameters are declared in
  \filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h}
-Line 55 
 $\bullet$ The exch2 package is included
+Line 53 
 $\bullet$ The exch2 package is included
    details. \\
  $\bullet$ An example of \file{W2\_EXCH2\_TOPOLOGY.h} and
-   \file{w2\_e2setup.F} must reside in a directory containing code
+   \file{w2\_e2setup.F} must reside in a directory containing files
-   linked when \file{genmake2} runs.  The safest place to put these
+   symbolically linked when \file{genmake2} runs.  The safest place to
-   is the directory indicated in the \code{-mods=DIR} command line
+   put these is the directory indicated in the \code{-mods=DIR} command
-   modifier (typically \file{../code}), or the build directory.  The
+   line modifier (typically \file{../code}), or the build directory.
-   default versions of these files reside in \file{pkg/exch2} and are
+   The default versions of these files reside in \file{pkg/exch2} and
-   linked automatically if no other versions exist elsewhere in the
+   are linked automatically if no other versions exist elsewhere in the
-   link path, but they should be left untouched to avoid breaking
+   build path, but they should be left untouched to avoid breaking
    configurations other than the one you intend to modify.\\
  $\bullet$ Files containing grid parameters, named
-Line 84 
 $\bullet$ As always when compiling MITgc
+Line 82 
 $\bullet$ As always when compiling MITgc
    Section \ref{sect:specifying_a_decomposition}
    \sectiontitle{Specifying a decomposition}.\\
- As of the time of writing the following examples use exch2 and may be
+ At the time of this writing the following examples use exch2 and may
- used for guidance:
+ be used for guidance:
  \begin{verbatim}
  verification/adjust_nlfs.cs-32x32x1
-Line 129 
 The parameters \code{tnx} and \code{tny}
+Line 127 
 The parameters \code{tnx} and \code{tny}
  the tiles into which the subdomains are decomposed, and must evenly
  divide the integer assigned to \code{nr}, \code{nb} and \code{ng}.
  The result is a rectangular tiling of the subdomain.  Figure
- \ref{fig:24tile} shows one possible topology for a twentyfour-tile
+ \ref{fig:24tile} shows one possible topology for a twenty-four-tile
  cube, and figure \ref{fig:12tile} shows one for twelve tiles. \\
  \begin{figure}
-Line 140 
 cube, and figure \ref{fig:12tile} shows
+Line 138 
 cube, and figure \ref{fig:12tile} shows
  \end{center}
  \caption{Plot of a cubed sphere topology with a 32$\times$192 domain
- divided into six 32$\times$32 subdomains, each of which is divided into four tiles
+ divided into six 32$\times$32 subdomains, each of which is divided
- (\code{tnx=16, tny=16}) for a total of twentyfour tiles.
+ into four tiles (\code{tnx=16, tny=16}) for a total of twenty-four
- } \label{fig:24tile}
+ tiles.  } \label{fig:24tile}
  \end{figure}
  \begin{figure}
-Line 206 
 levels in the model.\\
+Line 204 
 levels in the model.\\
  The parameters \varlink{nSx}{nSx}, \varlink{nSy}{nSy},
  \varlink{nPx}{nPx}, and \varlink{nPy}{nPy} relate to the number of
  tiles and how they are distributed on processors.  When using exch2,
- the tiles are stored in single dimension, and so
+ the tiles are stored in a single dimension, and so
  \code{\varlink{nSy}{nSy}=1} in all cases.  Since the tiles as
  configured by exch2 cannot be split up accross processors without
  regenerating the topology, \code{\varlink{nPy}{nPy}=1} as well. \\
-Line 237 
 one processor: \\
+Line 235 
 one processor: \\
       &           Nr  =   5)
  \end{verbatim}
- The following is an example for the twentyfour-tile topology in figure
+ The following is an example for the twenty-four-tile topology in
- \ref{fig:24tile} running on six processors:
+ figure \ref{fig:24tile} running on six processors:
  \begin{verbatim}
        PARAMETER (
-Line 262 
 The following is an example for the twen
+Line 260 
 The following is an example for the twen
  \subsection{Key Variables}
  The descriptions of the variables are divided up into scalars,
- one-dimensional arrays indexed to the tile number, and two and three
+ one-dimensional arrays indexed to the tile number, and two and
- dimensional arrays indexed to tile number and neighboring tile.  This
+ three-dimensional arrays indexed to tile number and neighboring tile.
- division reflects the functionality of these variables: The
+ This division reflects the functionality of these variables: The
  scalars are common to every part of the topology, the tile-indexed
  arrays to individual tiles, and the arrays indexed by tile and
  neighbor to relationships between tiles and their neighbors. \\
-Line 288 
 topology of twenty-four square tiles, fo
+Line 286 
 topology of twenty-four square tiles, fo
  \code{exch2\_domain\_nyt=2}.  Note that these parameters express the
  tile layout to allow global data files that are tile-layout-neutral
  and have no bearing on the internal storage of the arrays.  The tiles
- are internally stored in a range from \code{(1:\varlink{bi}{bi})} the
+ are stored internally in a range from \code{(1:\varlink{bi}{bi})} the
- $x$ axis, and the $y$ axis variable \varlink{bj}{bj} is generally
+ $x$ axis, and the $y$ axis variable \varlink{bj}{bj} generally is
  ignored within the package. \\
  \subsubsection{Arrays Indexed to Tile Number}
- The following arrays are of length \code{NTILES}and are indexed to the
+ The following arrays are of length \code{NTILES} and are indexed to
- tile number, which is indicated in the diagrams with the notation
+ the tile number, which is indicated in the diagrams with the notation
  \textsf{t}$n$.  The indices are omitted in the descriptions. \\
  The arrays \varlink{exch2\_tnx}{exch2_tnx} and
-Line 312 
 determined by the arrays \varlink{exch2\
+Line 310 
 determined by the arrays \varlink{exch2\
  relate the location of the edges of different tiles to each other.  As
  an example, in the default six-tile topology (Fig. \ref{fig:6tile})
  each index in these arrays is set to \code{0} since a tile occupies
- its entire subdomain.  The twentyfour-tile case discussed above will
+ its entire subdomain.  The twenty-four-tile case discussed above will
  have values of \code{0} or \code{16}, depending on the quadrant the
  tile falls within the subdomain.  The elements of the arrays
  \varlink{exch2\_txglobalo}{exch2_txglobalo} and
  \varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to
  \varlink{exch2\_tbasex}{exch2_tbasex} and
  \varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the
- global address space, similar to that used by global files. \\
+ global address space, similar to that used by global output and input
+ files. \\
  The array \varlink{exch2\_myFace}{exch2_myFace} contains the number of
  the subdomain of each tile, in a range \code{(1:6)} in the case of the
  standard cube topology and indicated by \textbf{\textsf{f}}$n$ in
  figures \ref{fig:12tile} and
  \ref{fig:24tile}. \varlink{exch2\_nNeighbours}{exch2_nNeighbours}
- contains a count the  neighboring tiles each tile has, and is
+ contains a count of the neighboring tiles each tile has, and is used
- used for setting bounds for looping over neighboring tiles.
+ for setting bounds for looping over neighboring tiles.
  \varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each
  tile, and is used in interprocess communication.  \\
-Line 346 
 corners of the cube. \\
+Line 345 
 corners of the cube. \\
  \subsubsection{Arrays Indexed to Tile Number and Neighbor}
- The following arrays are all of size
+ The following arrays have vectors of length \code{MAX\_NEIGHBOURS} and
- \code{MAX\_NEIGHBOURS}$\times$\code{NTILES} and describe the
+ \code{NTILES} and describe the orientations between the the tiles. \\
- orientations between the the tiles. \\
  The array \code{exch2\_neighbourId(a,T)} holds the tile number
  \code{Tn} for each of the tile number \code{T}'s neighboring tiles
  \code{a}.  The neighbor tiles are indexed
- \code{(1:exch2\_NNeighbours(T))} in the order right to left on the
+ \code{(1:exch2\_nNeighbours(T))} in the order right to left on the
- north then south edges, and then top to bottom on the east and west
+ north then south edges, and then top to bottom on the east then west
- edges.  Maybe throw in a fig here, eh?  \\
+ edges.  \\
- \sloppy The \code{exch2\_opposingSend\_record(a,T)} array holds the
+  The \code{exch2\_opposingSend\_record(a,T)} array holds the
  index \code{b} of the element in \texttt{exch2\_neighbourId(b,Tn)}
  that holds the tile number \code{T}, given
  \code{Tn=exch2\_neighborId(a,T)}.  In other words,
-Line 373 
 in exchanges between the neighboring til
+Line 371 
 in exchanges between the neighboring til
  necessary in exchanges between subdomains because the array index in
  one dimension may map to the other index in an adjacent subdomain, and
  may be have its indexing reversed. This swapping arises from the
- ``folding'' of two-dimensional arrays into a three-dimensional cube.
+ ``folding'' of two-dimensional arrays into a three-dimensional
+ cube. \\
  The dimensions of \code{exch2\_pi(t,N,T)} and \code{exch2\_pj(t,N,T)}
  are the neighbor ID \code{N} and the tile number \code{T} as explained
-Line 402 
 The arrays \varlink{exch2\_oi}{exch2_oi}
+Line 401 
 The arrays \varlink{exch2\_oi}{exch2_oi}
  \varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and
  \varlink{exch2\_oj\_f}{exch2_oj_f} are indexed to tile number and
  neighbor and specify the relative offset within the subdomain of the
- array index of a variable going from a neighboring tile $N$ to a local
+ array index of a variable going from a neighboring tile \code{N} to a
- tile $T$.  Consider \code{T=1} in the six-tile topology
+ local tile \code{T}.  Consider \code{T=1} in the six-tile topology
  (Fig. \ref{fig:6tile}), where
  \begin{verbatim}
-Line 420 
 exchange between the two requires no cha
+Line 419 
 exchange between the two requires no cha
  the western neighbor (\code{Tn=5}), \code{code\_oi(3,1)=32} since the
  \code{x=0} vector on \code{T} corresponds to the \code{y=32} vector on
  \code{Tn}.  The eastern edge of \code{T} shows the reverse case
- (\code{exch2\_oi(4,1)=-32)}, where \code{x=32} on \code{T} exchanges
+ (\code{exch2\_oi(4,1)=-32)}), where \code{x=32} on \code{T} exchanges
- with \code{x=0} on \code{Tn=2}.  The most interesting case, where
+ with \code{x=0} on \code{Tn=2}. \\
- \code{exch2\_oi(1,1)=33} and \code{Tn=3}, involves a reversal of
- indices.  As in every case, the offset \code{exch2\_oi} is added to
+  The most interesting case, where \code{exch2\_oi(1,1)=33} and
- the original $x$ index of \code{T} multiplied by the transformation
+ \code{Tn=3}, involves a reversal of indices.  As in every case, the
- factor \code{exch2\_pi(t,N,T)}.  Here \code{exch2\_pi(1,1,1)=0} since
+ offset \code{exch2\_oi} is added to the original $x$ index of \code{T}
- the $x$ axis of \code{T} is orthogonal to the $x$ axis of \code{Tn}.
+ multiplied by the transformation factor \code{exch2\_pi(t,N,T)}.  Here
- \code{exch2\_pi(2,1,1)=-1} since the $x$ axis of \code{T} corresponds
+ \code{exch2\_pi(1,1,1)=0} since the $x$ axis of \code{T} is orthogonal
- to the $y$ axis of \code{Tn}, but the axes are reversed.  The result
+ to the $x$ axis of \code{Tn}.  \code{exch2\_pi(2,1,1)=-1} since the
- is that the index of the northern edge of \code{T}, which runs
+ $x$ axis of \code{T} corresponds to the $y$ axis of \code{Tn}, but the
- \code{(1:32)}, is transformed to
+ index is reversed.  The result is that the index of the northern edge
+ of \code{T}, which runs \code{(1:32)}, is transformed to
  \code{(-1:-32)}. \code{exch2\_oi(1,1)} is then added to this range to
- get back \code{(1:32)} -- the index of the $y$ axis of \code{Tn}.
+ get back \code{(32:1)} -- the index of the $y$ axis of \code{Tn}
- This transformation may seem overly convoluted for the six-tile case,
+ relative to \code{T}.  This transformation may seem overly convoluted
- but it is necessary to provide a general solution for various
+ for the six-tile case, but it is necessary to provide a general
- topologies. \\
+ solution for various topologies. \\
 Line 455 
 of tile \code{T=2} in the twelve-tile to
         exch2_jthi_c(4,2)=33
  \end{verbatim}
- Here \code{N=4}, indicating the western neighbor, which is \code{Tn=1}.
+ Here \code{N=4}, indicating the western neighbor, which is
- \code{Tn=1} resides on the same subdomain as \code{T=2}, so the tiles
+ \code{Tn=1}.  \code{Tn} resides on the same subdomain as \code{T}, so
- have the same orientation and the same $x$ and $y$ axes.  The $i$
+ the tiles have the same orientation and the same $x$ and $y$ axes.
- component is orthogonal to the western edge and the tile is 16 points
+ The $x$ axis is orthogonal to the western edge and the tile is 16
- wide, so \code{exch2\_itlo\_c} and \code{exch2\_ithi\_c} indicate the
+ points wide, so \code{exch2\_itlo\_c} and \code{exch2\_ithi\_c}
- column beyond \code{Tn=1}'s eastern edge, in that tile's halo
+ indicate the column beyond \code{Tn}'s eastern edge, in that tile's
- region. Since the border of the tiles extends through the entire
+ halo region. Since the border of the tiles extends through the entire
  height of the subdomain, the $y$ axis bounds \code{exch2\_jtlo\_c} to
- \code{exch2\_jthi\_c} cover the height, plus 1 in either direction to
+ \code{exch2\_jthi\_c} cover the height of \code{(1:32)}, plus 1 in
- cover part of the halo. \\
+ either direction to cover part of the halo. \\
  For the north edge of the same tile \code{T=2} where \code{N=1} and
  the neighbor tile is \code{Tn=5}:
 Line 477 
 the neighbor tile is \code{Tn=5}:
  \end{verbatim}
  \code{T}'s northern edge is parallel to the $x$ axis, but since
- \code{Tn}'s $y$ axis corresponds to \code{T}'s $x$ axis,
+ \code{Tn}'s $y$ axis corresponds to \code{T}'s $x$ axis, \code{T}'s
- \code{T}'s northern edge exchanges with \code{Tn}'s western edge.
+ northern edge exchanges with \code{Tn}'s western edge.  The western
- The western edge of the tiles corresponds to the lower bound of the
+ edge of the tiles corresponds to the lower bound of the $x$ axis, so
- $x$ axis, so \code{exch2\_itlo\_c} \code{exch2\_ithi\_c} are \code{0}. The
+ \code{exch2\_itlo\_c} \code{exch2\_ithi\_c} are \code{0}. The range of
- range of \code{exch2\_jtlo\_c} and \code{exch2\_jthi\_c} correspond to the
+ \code{exch2\_jtlo\_c} and \code{exch2\_jthi\_c} correspond to the
  width of \code{T}'s northern edge, plus the halo. \\
- This needs some diagrams. \\
  \subsection{Key Routines}
  Most of the subroutines particular to exch2 handle the exchanges
-Line 508 
 templates which the local Makefile conve
+Line 495 
 templates which the local Makefile conve
  forms. \\
  The interfaces with the core model subroutines are
- \code{EXCH\_UV\_XY\_RX}, \code{EXCH\_UV\_XYZ\_RX} and \code{EXCH\_XY\_RX}.
+ \code{EXCH\_UV\_XY\_RX}, \code{EXCH\_UV\_XYZ\_RX} and
- They override the standard exchange routines when \code{genmake2} is
+ \code{EXCH\_XY\_RX}.  They override the standard exchange routines
- run with \code{exch2} option.  They in turn call the local exch2
+ when \code{genmake2} is run with \code{exch2} option.  They in turn
- subroutines \code{EXCH2\_UV\_XY\_RX} and \code{EXCH2\_UV\_XYZ\_RX} for two
+ call the local exch2 subroutines \code{EXCH2\_UV\_XY\_RX} and
- and three dimensional vector quantities, and \code{EXCH2\_XY\_RX} and
+ \code{EXCH2\_UV\_XYZ\_RX} for two and three-dimensional vector
- \code{EXCH2\_XYZ\_RX} for two and three dimensional scalar quantities.
+ quantities, and \code{EXCH2\_XY\_RX} and \code{EXCH2\_XYZ\_RX} for two
- These subroutines set the dimensions of the area to be exchanged, call
+ and three-dimensional scalar quantities.  These subroutines set the
- \code{EXCH2\_RX1\_CUBE} for scalars and \code{EXCH2\_RX2\_CUBE} for
+ dimensions of the area to be exchanged, call \code{EXCH2\_RX1\_CUBE}
- vectors, and then handle the singularities at the cube corners. \\
+ for scalars and \code{EXCH2\_RX2\_CUBE} for vectors, and then handle
+ the singularities at the cube corners. \\
  The separate scalar and vector forms of \code{EXCH2\_RX1\_CUBE} and
- \code{EXCH2\_RX2\_CUBE} reflect that the vector-handling subrouine needs
+ \code{EXCH2\_RX2\_CUBE} reflect that the vector-handling subrouine
- to pass both the $x$ and $y$ components of the vectors.  This arises
+ needs to pass both the $u$ and $v$ components of the phsical vectors.
- from the topological folding discussed above, where the $x$ and $y$
+ This arises from the topological folding discussed above, where the
- axes get swapped in some cases.  This swapping is not an issue with
+ $x$ and $y$ axes get swapped in some cases.  This swapping is not an
- the scalar version. These subroutines call \code{EXCH2\_SEND\_RX1} and
+ issue with the scalar version. These subroutines call
- \code{EXCH2\_SEND\_RX2}, which do most of the work using the variables
+ \code{EXCH2\_SEND\_RX1} and \code{EXCH2\_SEND\_RX2}, which do most of
- discussed above. \\
+ the work using the variables discussed above. \\

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