Diff of /manual/s_phys_pkgs/text/exch2.tex

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--- manual/s_phys_pkgs/text/exch2.tex	2004/03/17 19:49:22	1.13
+++ manual/s_phys_pkgs/text/exch2.tex	2004/03/17 21:44:02	1.14
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.13 2004/03/17 19:49:22 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.14 2004/03/17 21:44:02 afe Exp $
 % $Name:  $
 
 %%  * Introduction
@@ -401,37 +401,72 @@
 orientation will have \code{(0,1)}, whereas those in the opposite
 index direction will have \code{(0,-1)}. \\
 
-
-\varlink{exch2\_oi}{exch2_oi},
+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}
+\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
+tile $T$.  Consider the six-tile case (Fig. \ref{fig:6tile}), where
+\code{exch2\_oi(1,1)=33}, \code{exch2\_oi(2,1)=0},
+\code{exch2\_oi(3,1)=32}, and \code{exch2\_oi(4,1)=-32}.  Each of these
+indicates the offset in the $x$ direction \\
+
+Finally, \varlink{exch2\_itlo\_c}{exch2_itlo_c},
+\varlink{exch2\_ithi\_c}{exch2_ithi_c},
+\varlink{exch2\_jtlo\_c}{exch2_jtlo_c} and
+\varlink{exch2\_jthi\_c}{exch2_jthi_c} hold the location and index
+bounds of the edge segment of the neighbor tile \code{N}'s subdomain
+that gets exchanged with the local tile \code{T}.  To take the example
+of tile \code{T=2} in the twelve-tile topology
+(Fig. \ref{fig:12tile}): \\
 
+\begin{verbatim}
+       exch2_itlo_c(4,2)=17
+       exch2_ithi_c(4,2)=17
+       exch2_jtlo_c(4,2)=0
+       exch2_jthi_c(4,2)=33
+\end{verbatim}
+ 
+Here \code{N=4}, indicating the western neighbor, which is \code{Tn=1}.
+\code{Tn=1} resides on the same subdomain as \code{T=2}, so the tiles
+have the same orientation and the same $x$ and $y$ axes.  The $i$
+component is orthogonal to the western edge and the tile is 16 points
+wide, so \code{exch2\_itlo\_c} and \code{exch2\_ithi\_c} indicate the
+column beyond \code{Tn=1}'s eastern edge, in that tile's 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
+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}:
 
+\begin{verbatim}
+       exch2_itlo_c(1,2)=0
+       exch2_ithi_c(1,2)=0
+       exch2_jtlo_c(1,2)=0
+       exch2_jthi_c(1,2)=17
+\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{T}'s northern edge exchanges with \code{Tn}'s western edge.
+The western edge of the tiles corresponds to the lower bound of the
+$x$ axis, so \code{exch2\_itlo\_c} \code{exch2\_ithi\_c} are \code{0}. The
+range of \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. \\
 
 
-{\footnotesize
-\begin{verbatim}
-C      exch2_pi          :: X index row of target to source permutation 
-C                        :: matrix for each neighbour entry.            
-C      exch2_pj          :: Y index row of target to source permutation 
-C                        :: matrix for each neighbour entry.            
-C      exch2_oi          :: X index element of target to source 
-C                        :: offset vector for cell-centered quantities  
-C                        :: of each neighbor entry.                     
-C      exch2_oj          :: Y index element of target to source 
-C                        :: offset vector for cell-centered quantities  
-C                        :: of each neighbor entry.                     
-C      exch2_oi_f        :: X index element of target to source 
-C                        :: offset vector for face quantities           
-C                        :: of each neighbor entry.                     
-C      exch2_oj_f        :: Y index element of target to source 
-C                        :: offset vector for face quantities           
-C                        :: of each neighbor entry.                     
-\end{verbatim}
-}
+
+
+
+
+
+
+
+
+This needs some diagrams. \\