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-revision 1.14 by afe,
Wed Mar 17 21:44:02 2004 UTC
+revision 1.17 by afe,
Fri Mar 19 21:25:45 2004 UTC
 Line 16
  \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 281 
 generated by \file{driver.m}.\\
+Line 279 
 generated by \file{driver.m}.\\
  The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt}
  and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number
  of tiles in the $x$ and $y$ global indices.  For example, the default
- setup of six tiles (Fig. \ref{fig:6tile}) has \code{exch2\_domain\_nxt=6} and
+ setup of six tiles (Fig. \ref{fig:6tile}) has
- \code{exch2\_domain\_nyt=1}.  A topology of twenty-four square tiles,
+ \code{exch2\_domain\_nxt=6} and \code{exch2\_domain\_nyt=1}.  A
- four per subdomain (as in figure \ref{fig:24tile}), will have
+ topology of twenty-four square tiles, four per subdomain (as in figure
- \code{exch2\_domain\_nxt=12} and \code{exch2\_domain\_nyt=2}.  Note
+ \ref{fig:24tile}), will have \code{exch2\_domain\_nxt=12} and
- that these parameters express the tile layout to allow global data
+ \code{exch2\_domain\_nyt=2}.  Note that these parameters express the
- files that are tile-layout-neutral and have no bearing on the internal
+ tile layout to allow global data files that are tile-layout-neutral
- storage of the arrays.  The tiles are internally stored in a range
+ and have no bearing on the internal storage of the arrays.  The tiles
- from \code{(1:\varlink{bi}{bi})} the $x$ axis, and $y$ axis variable
+ are stored internally in a range from \code{(1:\varlink{bi}{bi})} the
- \varlink{bj}{bj} is generally ignored within the package. \\
+ $x$ 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}, are indexed to the
+ The following arrays are of length \code{NTILES} and are indexed to
- tile number, and the indices are omitted in their descriptions. \\
+ 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
  \varlink{exch2\_tny}{exch2_tny} express the $x$ and $y$ dimensions of
 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 of how many 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 334 
 The arrays \varlink{exch2\_isWedge}{exch
+Line 335 
 The arrays \varlink{exch2\_isWedge}{exch
  \varlink{exch2\_isEedge}{exch2_isEedge},
  \varlink{exch2\_isSedge}{exch2_isSedge}, and
  \varlink{exch2\_isNedge}{exch2_isNedge} are set to \code{1} if the
- indexed tile lies on the edge of a subdomain, \code{0} if not.  The
+ indexed tile lies on the respective edge of a subdomain, \code{0} if
- values are used within the topology generator to determine the
+ not.  The values are used within the topology generator to determine
- orientation of neighboring tiles, and to indicate whether a tile lies
+ the orientation of neighboring tiles, and to indicate whether a tile
- on the corner of a subdomain.  The latter case requires special
+ lies on the corner of a subdomain.  The latter case requires special
  exchange and numerical handling for the singularities at the eight
  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:MAX\_NEIGHBOURS)}
+ \code{a}.  The neighbor tiles are indexed
- in the order right to left on the north then south edges, and then top
+ \code{(1:exch2\_nNeighbours(T))} in the order right to left on the
- to bottom on the east and west edges.  Maybe throw in a fig here, eh?
+ north then south edges, and then top to bottom on the east then west
- \\
+ edges.  \\
- \sloppy
+  The \code{exch2\_opposingSend\_record(a,T)} array holds the
- The \code{exch2\_opposingSend\_record(a,T)} array holds the index
+ index \code{b} of the element in \texttt{exch2\_neighbourId(b,Tn)}
- \code{b} in \texttt{exch2\_neighbourId(b,Tn)} that holds the tile
+ that holds the tile number \code{T}, given
- number \code{T}.  In other words,
+ \code{Tn=exch2\_neighborId(a,T)}.  In other words,
  \begin{verbatim}
     exch2_neighbourId( exch2_opposingSend_record(a,T),
                        exch2_neighbourId(a,T) ) = T
 Line 366 
 number \code{T}.  In other words,
  This provides a back-reference from the neighbor tiles. \\
  The arrays \varlink{exch2\_pi}{exch2_pi} and
- \varlink{exch2\_pj}{exch2_pj} specify the transformations of variables
+ \varlink{exch2\_pj}{exch2_pj} specify the transformations of indices
  in exchanges between the neighboring tiles.  These transformations are
- necessary in exchanges between subdomains because a physical vector
+ necessary in exchanges between subdomains because the array index in
- component in one direction may map to one in a different direction in
+ one dimension may map to the other index in an adjacent subdomain, and
- an adjacent subdomain, and may be have its indexing reversed. This
+ may be have its indexing reversed. This swapping arises from the
- swapping arises from the ``folding'' of two-dimensional arrays into a
+ ``folding'' of two-dimensional arrays into a three-dimensional
- three-dimensional cube.
+ 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
- above, plus a vector of length 2 containing transformation factors
+ above, plus a vector of length \code{2} containing transformation
- \code{t}.  The first element of the transformation vector indicates
+ factors \code{t}.  The first element of the transformation vector
- the factor \code{t} by which variables representing the same
+ holds the factor to multiply the index in the same axis, and the
- \emph{physical} vector component of a tile \code{T} will be multiplied
+ second element holds the the same for the orthogonal index.  To
- in exchanges with neighbor \code{N}, and the second element indicates
+ clarify, \code{exch2\_pi(1,N,T)} holds the mapping of the $x$ axis
- the transform to the physical vector in the other direction.  To
+ index of tile \code{T} to the $x$ axis of tile \code{T}'s neighbor
- clarify (hopefully), \code{exch2\_pi(1,N,T)} holds the transform of
+ \code{N}, and \code{exch2\_pi(2,N,T)} holds the mapping of \code{T}'s
- the $i$ component of a vector variable in tile \code{T} to the $i$
+ $x$ index to the neighbor \code{N}'s $y$ index. \\
- component of tile \code{T}'s neighbor \code{N}, and
- \code{exch2\_pi(2,N,T)} holds the transform of \code{T}'s $i$
- components to the neighbor \code{N}'s $j$ component. \\
- Under the current cube topology, one of the two elements of
+ One of the two elements of \code{exch2\_pi} or \code{exch2\_pj} for a
- \code{exch2\_pi} or \code{exch2\_pj} for a given tile \code{T} and
+ given tile \code{T} and neighbor \code{N} will be \code{0}, reflecting
- neighbor \code{N} will be \code{0}, reflecting the fact that the two
+ the fact that the two axes are orthogonal.  The other element will be
- vector components are orthogonal.  The other element will be \code{1}
+ \code{1} or \code{-1}, depending on whether the axes are indexed in
- or \code{-1}, depending on whether the components are indexed in the
+ the same or opposite directions.  For example, the transform vector of
- same or opposite directions.  For example, the transform vector of the
+ the arrays for all tile neighbors on the same subdomain will be
- arrays for all tile neighbors on the same subdomain will be
  \code{(1,0)}, since all tiles on the same subdomain are oriented
- identically.  A vector direction that corresponds to the orthogonal
+ identically.  An axis that corresponds to the orthogonal dimension
- dimension with the same index direction in a particular tile-neighbor
+ with the same index direction in a particular tile-neighbor
- orientation will have \code{(0,1)}, whereas those in the opposite
+ orientation will have \code{(0,1)}.  Those in the opposite index
- index direction will have \code{(0,-1)}. \\
+ direction will have \code{(0,-1)} in order to reverse the ordering. \\
  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 the six-tile case (Fig. \ref{fig:6tile}), where
+ local tile \code{T}.  Consider \code{T=1} in the six-tile topology
- \code{exch2\_oi(1,1)=33}, \code{exch2\_oi(2,1)=0},
+ (Fig. \ref{fig:6tile}), where
- \code{exch2\_oi(3,1)=32}, and \code{exch2\_oi(4,1)=-32}.  Each of these
- indicates the offset in the $x$ direction \\
+ \begin{verbatim}
+        exch2_oi(1,1)=33
+        exch2_oi(2,1)=0
+        exch2_oi(3,1)=32
+        exch2_oi(4,1)=-32
+ \end{verbatim}
+ The simplest case is \code{exch2\_oi(2,1)}, the southern neighbor,
+ which is \code{Tn=6}.  The axes of \code{T} and \code{Tn} have the
+ same orientation and their $x$ axes have the same origin, and so an
+ exchange between the two requires no changes to the $x$ index.  For
+ 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
+ with \code{x=0} on \code{Tn=2}. \\
+  The most interesting case, where \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 original $x$ index of \code{T}
+ multiplied by the transformation factor \code{exch2\_pi(t,N,T)}.  Here
+ \code{exch2\_pi(1,1,1)=0} since the $x$ axis of \code{T} is orthogonal
+ to the $x$ axis of \code{Tn}.  \code{exch2\_pi(2,1,1)=-1} since the
+ $x$ axis of \code{T} corresponds to the $y$ axis of \code{Tn}, but the
+ 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{(32:1)} -- the index of the $y$ axis of \code{Tn}
+ relative to \code{T}.  This transformation may seem overly convoluted
+ for the six-tile case, but it is necessary to provide a general
+ solution for various topologies. \\
  Finally, \varlink{exch2\_itlo\_c}{exch2_itlo_c},
  \varlink{exch2\_ithi\_c}{exch2_ithi_c},
-Line 427 
 of tile \code{T=2} in the twelve-tile to
+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 449 
 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
+ themselves and are of the same format as those described in
+ \ref{sect:cube_sphere_communication} \sectiontitle{Cube sphere
+ communication}.  Like the original routines, they are written as
+ templates which the local Makefile converts from RX into RL and RS
+ forms. \\
+ The interfaces with the core model subroutines are
+ \code{EXCH\_UV\_XY\_RX}, \code{EXCH\_UV\_XYZ\_RX} and
+ \code{EXCH\_XY\_RX}.  They override the standard exchange routines
+ when \code{genmake2} is run with \code{exch2} option.  They in turn
+ call the local exch2 subroutines \code{EXCH2\_UV\_XY\_RX} and
+ \code{EXCH2\_UV\_XYZ\_RX} for two and three-dimensional vector
+ quantities, and \code{EXCH2\_XY\_RX} and \code{EXCH2\_XYZ\_RX} for two
+ and three-dimensional scalar quantities.  These subroutines set the
+ dimensions of the area to be exchanged, call \code{EXCH2\_RX1\_CUBE}
+ 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 to pass both the $u$ and $v$ components of the phsical vectors.
+ This arises from the topological folding discussed above, where the
+ $x$ and $y$ axes get swapped in some cases.  This swapping is not an
+ issue with the scalar version. These subroutines call
+ \code{EXCH2\_SEND\_RX1} and \code{EXCH2\_SEND\_RX2}, which do most of
+ the work using the variables discussed above. \\
- \subsection{References}

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