10 |
%% o automatically inserted at \section{Reference} |
%% o automatically inserted at \section{Reference} |
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12 |
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13 |
\section{exch2: Extended Cubed Sphere Exchange} |
\section{exch2: Extended Cubed Sphere \mbox{Topology}} |
14 |
\label{sec:exch2} |
\label{sec:exch2} |
15 |
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16 |
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17 |
\subsection{Introduction} |
\subsection{Introduction} |
18 |
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|
19 |
The exch2 package is an extension to the original cubed sphere exchanges |
The \texttt{exch2} package extends the original cubed sphere topology |
20 |
to allow more flexible domain decomposition and parallelization. Cube faces |
configuration to allow more flexible domain decomposition and |
21 |
(subdomains) may be divided into whatever number of tiles that divide evenly |
parallelization. Cube faces (also called subdomains) may be divided |
22 |
into the grid point dimensions of the subdomain. Furthermore, the individual |
into any number of tiles that divide evenly into the grid point |
23 |
tiles may be run on separate processors in different combinations, |
dimensions of the subdomain. Furthermore, the tiles can run on |
24 |
and whether exchanges between particular tiles occur between different |
separate processors individually or in groups, which provides for |
25 |
processors is determined at runtime. |
manual compile-time load balancing across a relatively arbitrary |
26 |
|
number of processors. \\ |
27 |
The exchange parameters are declared in {\em W2\_EXCH2\_TOPOLOGY.h} and |
|
28 |
assigned in {\em w2\_e2setup.F}, both in the |
The exchange parameters are declared in |
29 |
{\em pkg/exch2} directory. The validity of the cube topology depends |
\filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h} |
30 |
on the {\em SIZE.h} file as detailed below. Both files are generated by |
and assigned in |
31 |
Matlab scripts and |
\filelink{pkg/exch2/w2\_e2setup.F}{pkg-exch2-w2_e2setup.F}. The |
32 |
should not be edited. The default files provided in the release set up |
validity of the cube topology depends on the \file{SIZE.h} file as |
33 |
a cube sphere arrangement of six tiles, one per subdomain, each with 32x32 grid |
detailed below. The default files provided in the release configure a |
34 |
points, running on a single processor. |
cubed sphere topology of six tiles, one per subdomain, each with |
35 |
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32$\times$32 grid points, with all tiles running on a single processor. Both |
36 |
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files are generated by Matlab scripts in |
37 |
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\file{utils/exch2/matlab-topology-generator}; see Section |
38 |
|
\ref{sec:topogen} \sectiontitle{Generating Topology Files for exch2} |
39 |
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for details on creating alternate topologies. Pregenerated examples |
40 |
|
of these files with alternate topologies are provided under |
41 |
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\file{utils/exch2/code-mods} along with the appropriate \file{SIZE.h} |
42 |
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file for single-processor execution. |
43 |
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|
44 |
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\subsection{Invoking exch2} |
45 |
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|
46 |
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To use exch2 with the cubed sphere, the following conditions must be |
47 |
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met: \\ |
48 |
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|
49 |
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$\bullet$ The exch2 package is included when \file{genmake2} is run. |
50 |
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The easiest way to do this is to add the line \code{exch2} to the |
51 |
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\file{profile.conf} file -- see Section |
52 |
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\ref{sect:buildingCode} \sectiontitle{Building the code} for general |
53 |
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details. \\ |
54 |
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|
55 |
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$\bullet$ An example of \file{W2\_EXCH2\_TOPOLOGY.h} and |
56 |
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\file{w2\_e2setup.F} must reside in a directory containing files |
57 |
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symbolically linked when \file{genmake2} runs. The safest place to |
58 |
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put these is the directory indicated in the \code{-mods=DIR} command |
59 |
|
line modifier (typically \file{../code}), or the build directory. |
60 |
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The default versions of these files reside in \file{pkg/exch2} and |
61 |
|
are linked automatically if no other versions exist elsewhere in the |
62 |
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build path, but they should be left untouched to avoid breaking |
63 |
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configurations other than the one you intend to modify.\\ |
64 |
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|
65 |
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$\bullet$ Files containing grid parameters, named |
66 |
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\file{tile00$n$.mitgrid} where $n$=\code{(1:6)} (one per subdomain), |
67 |
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must be in the working directory when the MITgcm executable is run. |
68 |
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These files are provided in the example experiments for cubed sphere |
69 |
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configurations with 32$\times$32 cube sides |
70 |
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-- please contact MITgcm support if you want to generate |
71 |
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files for other configurations. \\ |
72 |
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|
73 |
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$\bullet$ As always when compiling MITgcm, the file \file{SIZE.h} must |
74 |
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be placed where \file{genmake2} will find it. In particular for |
75 |
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exch2, the domain decomposition specified in \file{SIZE.h} must |
76 |
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correspond with the particular configuration's topology specified in |
77 |
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\file{W2\_EXCH2\_TOPOLOGY.h} and \file{w2\_e2setup.F}. Domain |
78 |
|
decomposition issues particular to exch2 are addressed in Section |
79 |
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\ref{sec:topogen} \sectiontitle{Generating Topology Files for exch2} |
80 |
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and \ref{sec:exch2mpi} \sectiontitle{exch2, SIZE.h, and MPI}; a more |
81 |
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general background on the subject relevant to MITgcm is presented in |
82 |
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Section \ref{sect:specifying_a_decomposition} |
83 |
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\sectiontitle{Specifying a decomposition}.\\ |
84 |
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|
85 |
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At the time of this writing the following examples use exch2 and may |
86 |
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be used for guidance: |
87 |
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|
88 |
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\begin{verbatim} |
89 |
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verification/adjust_nlfs.cs-32x32x1 |
90 |
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verification/adjustment.cs-32x32x1 |
91 |
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verification/aim.5l_cs |
92 |
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verification/global_ocean.cs32x15 |
93 |
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verification/hs94.cs-32x32x5 |
94 |
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\end{verbatim} |
95 |
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|
96 |
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|
97 |
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|
98 |
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|
99 |
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\subsection{Generating Topology Files for exch2} |
100 |
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\label{sec:topogen} |
101 |
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|
102 |
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Alternate cubed sphere topologies may be created using the Matlab |
103 |
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scripts in \file{utils/exch2/matlab-topology-generator}. Running the |
104 |
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m-file |
105 |
|
\filelink{driver.m}{utils-exch2-matlab-topology-generator_driver.m} |
106 |
|
from the Matlab prompt (there are no parameters to pass) generates |
107 |
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exch2 topology files \file{W2\_EXCH2\_TOPOLOGY.h} and |
108 |
|
\file{w2\_e2setup.F} in the working directory and displays a figure of |
109 |
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the topology via Matlab -- figures \ref{fig:6tile}, \ref{fig:12tile}, |
110 |
|
and \ref{fig:24tile} are examples. The other m-files in the directory are |
111 |
|
subroutines of \file{driver.m} and should not be run ``bare'' except |
112 |
|
for development purposes. \\ |
113 |
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|
114 |
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The parameters that determine the dimensions and topology of the |
115 |
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generated configuration are \code{nr}, \code{nb}, \code{ng}, |
116 |
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\code{tnx} and \code{tny}, and all are assigned early in the script. \\ |
117 |
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|
118 |
|
The first three determine the size of the subdomains and |
119 |
|
hence the size of the overall domain. Each one determines the number |
120 |
|
of grid points, and therefore the resolution, along the subdomain |
121 |
|
sides in a ``great circle'' around each the three spatial axes of the cube. At the time |
122 |
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of this writing MITgcm requires these three parameters to be equal, |
123 |
|
but they provide for future releases to accomodate different |
124 |
|
resolutions around the axes to allow (for example) greater resolution |
125 |
|
around the equator.\\ |
126 |
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|
127 |
|
The parameters \code{tnx} and \code{tny} determine the width and height of |
128 |
|
the tiles into which the subdomains are decomposed, and must evenly |
129 |
|
divide the integer assigned to \code{nr}, \code{nb} and \code{ng}. |
130 |
|
The result is a rectangular tiling of the subdomain. Figure |
131 |
|
\ref{fig:24tile} shows one possible topology for a twenty-four-tile |
132 |
|
cube, and figure \ref{fig:12tile} shows one for twelve tiles. \\ |
133 |
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|
134 |
|
\begin{figure} |
135 |
|
\begin{center} |
136 |
|
\resizebox{4in}{!}{ |
137 |
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\includegraphics{part6/s24t_16x16.ps} |
138 |
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} |
139 |
|
\end{center} |
140 |
|
|
141 |
|
\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
142 |
|
divided into six 32$\times$32 subdomains, each of which is divided |
143 |
|
into four tiles of width \code{tnx=16} and height \code{tny=16} for a |
144 |
|
total of twenty-four tiles. The colored borders of the subdomains |
145 |
|
represent the parameters \code{nr} (red), \code{nb} (blue), and |
146 |
|
\code{ng} (green). } \label{fig:24tile} |
147 |
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\end{figure} |
148 |
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|
149 |
|
\begin{figure} |
150 |
|
\begin{center} |
151 |
|
\resizebox{4in}{!}{ |
152 |
|
\includegraphics{part6/s12t_16x32.ps} |
153 |
|
} |
154 |
|
\end{center} |
155 |
|
\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
156 |
|
divided into six 32$\times$32 subdomains of two tiles each |
157 |
|
(\code{tnx=16, tny=32}). |
158 |
|
} \label{fig:12tile} |
159 |
|
\end{figure} |
160 |
|
|
161 |
|
\begin{figure} |
162 |
|
\begin{center} |
163 |
|
\resizebox{4in}{!}{ |
164 |
|
\includegraphics{part6/s6t_32x32.ps} |
165 |
|
} |
166 |
|
\end{center} |
167 |
|
\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
168 |
|
divided into six 32$\times$32 subdomains with one tile each |
169 |
|
(\code{tnx=32, tny=32}). This is the default configuration. |
170 |
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} |
171 |
|
\label{fig:6tile} |
172 |
|
\end{figure} |
173 |
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|
174 |
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|
175 |
|
Tiles can be selected from the topology to be omitted from being |
176 |
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allocated memory and processors. This tuning is useful in ocean |
177 |
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modeling for omitting tiles that fall entirely on land. The tiles |
178 |
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omitted are specified in the file |
179 |
|
\filelink{blanklist.txt}{utils-exch2-matlab-topology-generator_blanklist.txt} |
180 |
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by their tile number in the topology, separated by a newline. \\ |
181 |
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|
182 |
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|
183 |
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|
184 |
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|
185 |
|
\subsection{exch2, SIZE.h, and multiprocessing} |
186 |
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\label{sec:exch2mpi} |
187 |
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|
188 |
|
Once the topology configuration files are created, the Fortran |
189 |
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\code{PARAMETER}s in \file{SIZE.h} must be configured to match. |
190 |
|
Section \ref{sect:specifying_a_decomposition} \sectiontitle{Specifying |
191 |
|
a decomposition} provides a general description of domain |
192 |
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decomposition within MITgcm and its relation to \file{SIZE.h}. The |
193 |
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current section specifies certain constraints the exch2 package |
194 |
|
imposes as well as describes how to enable parallel execution with |
195 |
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MPI. \\ |
196 |
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|
197 |
|
As in the general case, the parameters \varlink{sNx}{sNx} and |
198 |
|
\varlink{sNy}{sNy} define the size of the individual tiles, and so |
199 |
|
must be assigned the same respective values as \code{tnx} and |
200 |
|
\code{tny} in \file{driver.m}.\\ |
201 |
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|
202 |
|
The halo width parameters \varlink{OLx}{OLx} and \varlink{OLy}{OLy} |
203 |
|
have no special bearing on exch2 and may be assigned as in the general |
204 |
|
case. The same holds for \varlink{Nr}{Nr}, the number of vertical |
205 |
|
levels in the model.\\ |
206 |
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|
207 |
|
The parameters \varlink{nSx}{nSx}, \varlink{nSy}{nSy}, |
208 |
|
\varlink{nPx}{nPx}, and \varlink{nPy}{nPy} relate to the number of |
209 |
|
tiles and how they are distributed on processors. When using exch2, |
210 |
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the tiles are stored in a single dimension, and so |
211 |
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\code{\varlink{nSy}{nSy}=1} in all cases. Since the tiles as |
212 |
|
configured by exch2 cannot be split up accross processors without |
213 |
|
regenerating the topology, \code{\varlink{nPy}{nPy}=1} as well. \\ |
214 |
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|
215 |
|
The number of tiles MITgcm allocates and how they are distributed |
216 |
|
between processors depends on \varlink{nPx}{nPx} and |
217 |
|
\varlink{nSx}{nSx}. \varlink{nSx}{nSx} is the number of tiles per |
218 |
|
processor and \varlink{nPx}{nPx} the number of processors. The total |
219 |
|
number of tiles in the topology minus those listed in |
220 |
|
\file{blanklist.txt} must equal \code{nSx*nPx}. \\ |
221 |
|
|
222 |
|
The following is an example of \file{SIZE.h} for the twelve-tile |
223 |
|
configuration illustrated in figure \ref{fig:12tile} running on |
224 |
|
one processor: \\ |
225 |
|
|
226 |
|
\begin{verbatim} |
227 |
|
PARAMETER ( |
228 |
|
& sNx = 16, |
229 |
|
& sNy = 32, |
230 |
|
& OLx = 2, |
231 |
|
& OLy = 2, |
232 |
|
& nSx = 12, |
233 |
|
& nSy = 1, |
234 |
|
& nPx = 1, |
235 |
|
& nPy = 1, |
236 |
|
& Nx = sNx*nSx*nPx, |
237 |
|
& Ny = sNy*nSy*nPy, |
238 |
|
& Nr = 5) |
239 |
|
\end{verbatim} |
240 |
|
|
241 |
|
The following is an example for the twenty-four-tile topology in |
242 |
|
figure \ref{fig:24tile} running on six processors: |
243 |
|
|
244 |
|
\begin{verbatim} |
245 |
|
PARAMETER ( |
246 |
|
& sNx = 16, |
247 |
|
& sNy = 16, |
248 |
|
& OLx = 2, |
249 |
|
& OLy = 2, |
250 |
|
& nSx = 4, |
251 |
|
& nSy = 1, |
252 |
|
& nPx = 6, |
253 |
|
& nPy = 1, |
254 |
|
& Nx = sNx*nSx*nPx, |
255 |
|
& Ny = sNy*nSy*nPy, |
256 |
|
& Nr = 5) |
257 |
|
\end{verbatim} |
258 |
|
|
259 |
|
|
260 |
|
|
261 |
|
|
262 |
|
|
263 |
\subsection{Key Variables} |
\subsection{Key Variables} |
264 |
|
|
265 |
The descriptions of the variables are divided up into scalars, |
The descriptions of the variables are divided up into scalars, |
266 |
one-dimensional arrays indexed to the tile number, and two and three |
one-dimensional arrays indexed to the tile number, and two and |
267 |
dimensional |
three-dimensional arrays indexed to tile number and neighboring tile. |
268 |
arrays indexed to tile number and neighboring tile. This division |
This division reflects the functionality of these variables: The |
269 |
actually reflects the functionality of these variables: the scalars |
scalars are common to every part of the topology, the tile-indexed |
270 |
are common to every part of the topology, the tile-indexed arrays to |
arrays to individual tiles, and the arrays indexed by tile and |
271 |
individual tiles, and the arrays indexed to tile and neighbor to |
neighbor to relationships between tiles and their neighbors. \\ |
|
relationships between tiles and their neighbors. |
|
272 |
|
|
273 |
\subsubsection{Scalars} |
\subsubsection{Scalars} |
274 |
|
|
275 |
The number of tiles in a particular topology is set with the parameter |
The number of tiles in a particular topology is set with the parameter |
276 |
{\em NTILES}, and the maximum number of neighbors of any tiles by |
\code{NTILES}, and the maximum number of neighbors of any tiles by |
277 |
{\em MAX\_NEIGHBOURS}. These parameters are used for defining the size of |
\code{MAX\_NEIGHBOURS}. These parameters are used for defining the |
278 |
the various one and two dimensional arrays that store tile parameters |
size of the various one and two dimensional arrays that store tile |
279 |
indexed to the tile number. |
parameters indexed to the tile number and are assigned in the files |
280 |
|
generated by \file{driver.m}.\\ |
281 |
The scalar parameters {\em exch2\_domain\_nxt} and |
|
282 |
{\em exch2\_domain\_nyt} express the number of tiles in the x and y global |
The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt} |
283 |
indices. For example, the default setup of six tiles has |
and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number |
284 |
{\em exch2\_domain\_nxt=6} and {\em exch2\_domain\_nyt=1}. A topology of |
of tiles in the $x$ and $y$ global indices. For example, the default |
285 |
twenty-four square (in gridpoints) tiles, four (2x2) per subdomain, will |
setup of six tiles (Fig. \ref{fig:6tile}) has |
286 |
have {\em exch2\_domain\_nxt=12} and {\em exch2\_domain\_nyt=2}. Note |
\code{exch2\_domain\_nxt=6} and \code{exch2\_domain\_nyt=1}. A |
287 |
that these parameters express the tile layout to allow global data files that |
topology of twenty-four square tiles, four per subdomain (as in figure |
288 |
are tile-layout-neutral and have no bearing on the internal storage of the |
\ref{fig:24tile}), will have \code{exch2\_domain\_nxt=12} and |
289 |
arrays. The tiles are internally stored in a range from {\em 1,bi} (in the |
\code{exch2\_domain\_nyt=2}. Note that these parameters express the |
290 |
x axis) and y-axis variable {\em bj} is generally ignored within the package. |
tile layout to allow global data files that are tile-layout-neutral |
291 |
|
and have no bearing on the internal storage of the arrays. The tiles |
292 |
|
are stored internally in a range from \code{(1:\varlink{bi}{bi})} the |
293 |
|
$x$ axis, and the $y$ axis variable \varlink{bj}{bj} is assumed to |
294 |
|
equal \code{1} throughout the package. \\ |
295 |
|
|
296 |
\subsubsection{Arrays Indexed to Tile Number} |
\subsubsection{Arrays Indexed to Tile Number} |
297 |
|
|
298 |
The following arrays are of size {\em NTILES}, are indexed to the tile number, |
The following arrays are of length \code{NTILES} and are indexed to |
299 |
and the indices are omitted in their descriptions. |
the tile number, which is indicated in the diagrams with the notation |
300 |
|
\textsf{t}$n$. The indices are omitted in the descriptions. \\ |
301 |
|
|
302 |
|
The arrays \varlink{exch2\_tnx}{exch2_tnx} and |
303 |
|
\varlink{exch2\_tny}{exch2_tny} express the $x$ and $y$ dimensions of |
304 |
|
each tile. At present for each tile \texttt{exch2\_tnx=sNx} and |
305 |
|
\texttt{exch2\_tny=sNy}, as assigned in \file{SIZE.h} and described in |
306 |
|
section \ref{sec:exch2mpi} \sectiontitle{exch2, SIZE.h, and |
307 |
|
multiprocessing}. Future releases of MITgcm may allow varying tile |
308 |
|
sizes. \\ |
309 |
|
|
310 |
|
The location of the tiles' Cartesian origin within a subdomain are |
311 |
|
determined by the arrays \varlink{exch2\_tbasex}{exch2_tbasex} and |
312 |
|
\varlink{exch2\_tbasey}{exch2_tbasey}. These variables are used to |
313 |
|
relate the location of the edges of different tiles to each other. As |
314 |
|
an example, in the default six-tile topology (Fig. \ref{fig:6tile}) |
315 |
|
each index in these arrays is set to \code{0} since a tile occupies |
316 |
|
its entire subdomain. The twenty-four-tile case discussed above will |
317 |
|
have values of \code{0} or \code{16}, depending on the quadrant the |
318 |
|
tile falls within the subdomain. The elements of the arrays |
319 |
|
\varlink{exch2\_txglobalo}{exch2_txglobalo} and |
320 |
|
\varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to |
321 |
|
\varlink{exch2\_tbasex}{exch2_tbasex} and |
322 |
|
\varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the |
323 |
|
global address space, similar to that used by global output and input |
324 |
|
files. \\ |
325 |
|
|
326 |
|
The array \varlink{exch2\_myFace}{exch2_myFace} contains the number of |
327 |
|
the subdomain of each tile, in a range \code{(1:6)} in the case of the |
328 |
|
standard cube topology and indicated by \textbf{\textsf{f}}$n$ in |
329 |
|
figures \ref{fig:12tile} and |
330 |
|
\ref{fig:24tile}. \varlink{exch2\_nNeighbours}{exch2_nNeighbours} |
331 |
|
contains a count of the neighboring tiles each tile has, and is used |
332 |
|
for setting bounds for looping over neighboring tiles. |
333 |
|
\varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each |
334 |
|
tile, and is used in interprocess communication. \\ |
335 |
|
|
336 |
|
|
337 |
|
The arrays \varlink{exch2\_isWedge}{exch2_isWedge}, |
338 |
|
\varlink{exch2\_isEedge}{exch2_isEedge}, |
339 |
|
\varlink{exch2\_isSedge}{exch2_isSedge}, and |
340 |
|
\varlink{exch2\_isNedge}{exch2_isNedge} are set to \code{1} if the |
341 |
|
indexed tile lies on the respective edge of a subdomain, \code{0} if |
342 |
|
not. The values are used within the topology generator to determine |
343 |
|
the orientation of neighboring tiles, and to indicate whether a tile |
344 |
|
lies on the corner of a subdomain. The latter case requires special |
345 |
|
exchange and numerical handling for the singularities at the eight |
346 |
|
corners of the cube. \\ |
347 |
|
|
|
The arrays {\em exch2\_tnx} and {\em exch2\_tny} |
|
|
express the x and y dimensions of each tile. At present for each tile |
|
|
{\em exch2\_tnx = sNx} |
|
|
and {\em exch2\_tny = sNy}, as assigned in {\em SIZE.h}. Future releases of |
|
|
MITgcm are to allow varying tile sizes. |
|
|
|
|
|
The location of the tiles' Cartesian origin within a subdomain are determined |
|
|
by the arrays {\em exch2\_tbasex} and {\em exch2\_tbasey}. These variables |
|
|
are used to relate the location of the edges of the tiles to each other. As |
|
|
an example, in the default six-tile topology (the degenerate case) |
|
|
each index in these arrays are |
|
|
set to 0. The twenty-four, 32x32 cube face case discussed above will have |
|
|
values of 0 or 16, depending on the quadrant the tile falls within the |
|
|
subdomain. {\em exch2\_myFace} contains the number of the |
|
|
cubeface/subdomain of each tile, numbered 1-6 in the case of the standard |
|
|
cube topology. |
|
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|
|
|
The arrays {\em exch2\_txglobalo} and {\em exch2\_txglobalo} are similar to |
|
|
{\em exch2\_tbasex} and {\em exch2\_tbasey}, but locate the tiles within |
|
|
the global address space, similar to that used by global files. |
|
|
|
|
|
The arrays {\em exch2\_isWedge}, {\em exch2\_isEedge}, {\em exch2\_isSedge}, |
|
|
and {\em exch2\_isNedge} are set to 1 if the indexed tile lies on the edge |
|
|
of a subdomain, 0 if not. The values are used within the topology generator |
|
|
to determine the orientation of neighboring tiles and to indicate whether |
|
|
a tile lies on the corner of a subdomain. The latter case indicates |
|
|
special exchange and numerical handling for the singularities at the eight |
|
|
corners of the cube. {\em exch2\_isNedge} contains a count of how many |
|
|
neighboring tiles each tile has, and is used for setting bounds for looping |
|
|
over neighboring tiles. {\em exch2\_tProc} holds the process rank of each tile, |
|
|
and is used in interprocess communication. |
|
348 |
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|
349 |
\subsubsection{Arrays Indexed to Tile Number and Neighbor} |
\subsubsection{Arrays Indexed to Tile Number and Neighbor} |
350 |
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|
351 |
The following arrays are all of size {\em MAX\_NEIGHBOURS}x{\em NTILES} and |
The following arrays have vectors of length \code{MAX\_NEIGHBOURS} and |
352 |
describe the orientations between the the tiles. |
\code{NTILES} and describe the orientations between the the tiles. \\ |
|
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|
The array {\em exch2\_neighbourId(a,T)} holds the tile number $T_{n}$ for each tile |
|
|
{\em T}'s neighbor tile {\em a}, and {\em exch2\_opposingSend\_record(a,T)} holds |
|
|
the index c in {\em exch2\_neighbourId(b,$T_{n}$)} that holds the tile number T. |
|
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In other words, |
|
353 |
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|
354 |
\begin{verbatim} |
The array \code{exch2\_neighbourId(a,T)} holds the tile number |
355 |
exch2_neighbourId( exch2_opposingSend_record(a,T), exch2_neighbourId(a,T) ) = T |
\code{Tn} for each of the tile number \code{T}'s neighboring tiles |
356 |
|
\code{a}. The neighbor tiles are indexed |
357 |
|
\code{(1:exch2\_nNeighbours(T))} in the order right to left on the |
358 |
|
north then south edges, and then top to bottom on the east then west |
359 |
|
edges. \\ |
360 |
|
|
361 |
|
The \code{exch2\_opposingSend\_record(a,T)} array holds the |
362 |
|
index \code{b} of the element in \texttt{exch2\_neighbourId(b,Tn)} |
363 |
|
that holds the tile number \code{T}, given |
364 |
|
\code{Tn=exch2\_neighborId(a,T)}. In other words, |
365 |
|
\begin{verbatim} |
366 |
|
exch2_neighbourId( exch2_opposingSend_record(a,T), |
367 |
|
exch2_neighbourId(a,T) ) = T |
368 |
\end{verbatim} |
\end{verbatim} |
369 |
|
This provides a back-reference from the neighbor tiles. \\ |
370 |
|
|
371 |
% {\em exch2\_neighbourId(exch2\_opposingSend\_record(a,T),exch2\_neighbourId(a,T))=T}. |
The arrays \varlink{exch2\_pi}{exch2_pi} and |
372 |
% alternate version |
\varlink{exch2\_pj}{exch2_pj} specify the transformations of indices |
373 |
|
in exchanges between the neighboring tiles. These transformations are |
374 |
This is to provide a backreference from the neighbor tiles. |
necessary in exchanges between subdomains because the array index in |
375 |
|
one dimension may map to the other index in an adjacent subdomain, and |
376 |
|
may be have its indexing reversed. This swapping arises from the |
377 |
|
``folding'' of two-dimensional arrays into a three-dimensional |
378 |
|
cube. \\ |
379 |
|
|
380 |
|
The dimensions of \code{exch2\_pi(t,N,T)} and \code{exch2\_pj(t,N,T)} |
381 |
|
are the neighbor ID \code{N} and the tile number \code{T} as explained |
382 |
|
above, plus a vector of length \code{2} containing transformation |
383 |
|
factors \code{t}. The first element of the transformation vector |
384 |
|
holds the factor to multiply the index in the same axis, and the |
385 |
|
second element holds the the same for the orthogonal index. To |
386 |
|
clarify, \code{exch2\_pi(1,N,T)} holds the mapping of the $x$ axis |
387 |
|
index of tile \code{T} to the $x$ axis of tile \code{T}'s neighbor |
388 |
|
\code{N}, and \code{exch2\_pi(2,N,T)} holds the mapping of \code{T}'s |
389 |
|
$x$ index to the neighbor \code{N}'s $y$ index. \\ |
390 |
|
|
391 |
|
One of the two elements of \code{exch2\_pi} or \code{exch2\_pj} for a |
392 |
|
given tile \code{T} and neighbor \code{N} will be \code{0}, reflecting |
393 |
|
the fact that the two axes are orthogonal. The other element will be |
394 |
|
\code{1} or \code{-1}, depending on whether the axes are indexed in |
395 |
|
the same or opposite directions. For example, the transform vector of |
396 |
|
the arrays for all tile neighbors on the same subdomain will be |
397 |
|
\code{(1,0)}, since all tiles on the same subdomain are oriented |
398 |
|
identically. An axis that corresponds to the orthogonal dimension |
399 |
|
with the same index direction in a particular tile-neighbor |
400 |
|
orientation will have \code{(0,1)}. Those in the opposite index |
401 |
|
direction will have \code{(0,-1)} in order to reverse the ordering. \\ |
402 |
|
|
403 |
|
The arrays \varlink{exch2\_oi}{exch2_oi}, |
404 |
|
\varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and |
405 |
|
\varlink{exch2\_oj\_f}{exch2_oj_f} are indexed to tile number and |
406 |
|
neighbor and specify the relative offset within the subdomain of the |
407 |
|
array index of a variable going from a neighboring tile \code{N} to a |
408 |
|
local tile \code{T}. Consider \code{T=1} in the six-tile topology |
409 |
|
(Fig. \ref{fig:6tile}), where |
410 |
|
|
411 |
|
\begin{verbatim} |
412 |
|
exch2_oi(1,1)=33 |
413 |
|
exch2_oi(2,1)=0 |
414 |
|
exch2_oi(3,1)=32 |
415 |
|
exch2_oi(4,1)=-32 |
416 |
|
\end{verbatim} |
417 |
|
|
418 |
// |
The simplest case is \code{exch2\_oi(2,1)}, the southern neighbor, |
419 |
|
which is \code{Tn=6}. The axes of \code{T} and \code{Tn} have the |
420 |
|
same orientation and their $x$ axes have the same origin, and so an |
421 |
|
exchange between the two requires no changes to the $x$ index. For |
422 |
|
the western neighbor (\code{Tn=5}), \code{code\_oi(3,1)=32} since the |
423 |
|
\code{x=0} vector on \code{T} corresponds to the \code{y=32} vector on |
424 |
|
\code{Tn}. The eastern edge of \code{T} shows the reverse case |
425 |
|
(\code{exch2\_oi(4,1)=-32)}), where \code{x=32} on \code{T} exchanges |
426 |
|
with \code{x=0} on \code{Tn=2}. \\ |
427 |
|
|
428 |
|
The most interesting case, where \code{exch2\_oi(1,1)=33} and |
429 |
|
\code{Tn=3}, involves a reversal of indices. As in every case, the |
430 |
|
offset \code{exch2\_oi} is added to the original $x$ index of \code{T} |
431 |
|
multiplied by the transformation factor \code{exch2\_pi(t,N,T)}. Here |
432 |
|
\code{exch2\_pi(1,1,1)=0} since the $x$ axis of \code{T} is orthogonal |
433 |
|
to the $x$ axis of \code{Tn}. \code{exch2\_pi(2,1,1)=-1} since the |
434 |
|
$x$ axis of \code{T} corresponds to the $y$ axis of \code{Tn}, but the |
435 |
|
index is reversed. The result is that the index of the northern edge |
436 |
|
of \code{T}, which runs \code{(1:32)}, is transformed to |
437 |
|
\code{(-1:-32)}. \code{exch2\_oi(1,1)} is then added to this range to |
438 |
|
get back \code{(32:1)} -- the index of the $y$ axis of \code{Tn} |
439 |
|
relative to \code{T}. This transformation may seem overly convoluted |
440 |
|
for the six-tile case, but it is necessary to provide a general |
441 |
|
solution for various topologies. \\ |
442 |
|
|
|
\begin{verbatim} |
|
443 |
|
|
444 |
|
|
445 |
|
Finally, \varlink{exch2\_itlo\_c}{exch2_itlo_c}, |
446 |
|
\varlink{exch2\_ithi\_c}{exch2_ithi_c}, |
447 |
|
\varlink{exch2\_jtlo\_c}{exch2_jtlo_c} and |
448 |
|
\varlink{exch2\_jthi\_c}{exch2_jthi_c} hold the location and index |
449 |
|
bounds of the edge segment of the neighbor tile \code{N}'s subdomain |
450 |
|
that gets exchanged with the local tile \code{T}. To take the example |
451 |
|
of tile \code{T=2} in the twelve-tile topology |
452 |
|
(Fig. \ref{fig:12tile}): \\ |
453 |
|
|
454 |
C exch2_pi :: X index row of target to source permutation |
\begin{verbatim} |
455 |
C :: matrix for each neighbour entry. |
exch2_itlo_c(4,2)=17 |
456 |
C exch2_pj :: Y index row of target to source permutation |
exch2_ithi_c(4,2)=17 |
457 |
C :: matrix for each neighbour entry. |
exch2_jtlo_c(4,2)=0 |
458 |
C exch2_oi :: X index element of target to source |
exch2_jthi_c(4,2)=33 |
|
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. |
|
459 |
\end{verbatim} |
\end{verbatim} |
460 |
|
|
461 |
|
Here \code{N=4}, indicating the western neighbor, which is |
462 |
|
\code{Tn=1}. \code{Tn} resides on the same subdomain as \code{T}, so |
463 |
|
the tiles have the same orientation and the same $x$ and $y$ axes. |
464 |
|
The $x$ axis is orthogonal to the western edge and the tile is 16 |
465 |
|
points wide, so \code{exch2\_itlo\_c} and \code{exch2\_ithi\_c} |
466 |
|
indicate the column beyond \code{Tn}'s eastern edge, in that tile's |
467 |
|
halo region. Since the border of the tiles extends through the entire |
468 |
|
height of the subdomain, the $y$ axis bounds \code{exch2\_jtlo\_c} to |
469 |
|
\code{exch2\_jthi\_c} cover the height of \code{(1:32)}, plus 1 in |
470 |
|
either direction to cover part of the halo. \\ |
471 |
|
|
472 |
|
For the north edge of the same tile \code{T=2} where \code{N=1} and |
473 |
|
the neighbor tile is \code{Tn=5}: |
474 |
|
|
475 |
|
\begin{verbatim} |
476 |
|
exch2_itlo_c(1,2)=0 |
477 |
|
exch2_ithi_c(1,2)=0 |
478 |
|
exch2_jtlo_c(1,2)=0 |
479 |
|
exch2_jthi_c(1,2)=17 |
480 |
|
\end{verbatim} |
481 |
|
|
482 |
|
\code{T}'s northern edge is parallel to the $x$ axis, but since |
483 |
|
\code{Tn}'s $y$ axis corresponds to \code{T}'s $x$ axis, \code{T}'s |
484 |
|
northern edge exchanges with \code{Tn}'s western edge. The western |
485 |
|
edge of the tiles corresponds to the lower bound of the $x$ axis, so |
486 |
|
\code{exch2\_itlo\_c} \code{exch2\_ithi\_c} are \code{0}. The range of |
487 |
|
\code{exch2\_jtlo\_c} and \code{exch2\_jthi\_c} correspond to the |
488 |
|
width of \code{T}'s northern edge, plus the halo. \\ |
489 |
|
|
490 |
|
|
491 |
\subsection{Key Routines} |
\subsection{Key Routines} |
492 |
|
|
493 |
|
Most of the subroutines particular to exch2 handle the exchanges |
494 |
|
themselves and are of the same format as those described in |
495 |
|
\ref{sect:cube_sphere_communication} \sectiontitle{Cube sphere |
496 |
|
communication}. Like the original routines, they are written as |
497 |
|
templates which the local Makefile converts from RX into RL and RS |
498 |
|
forms. \\ |
499 |
|
|
500 |
|
The interfaces with the core model subroutines are |
501 |
|
\code{EXCH\_UV\_XY\_RX}, \code{EXCH\_UV\_XYZ\_RX} and |
502 |
|
\code{EXCH\_XY\_RX}. They override the standard exchange routines |
503 |
|
when \code{genmake2} is run with \code{exch2} option. They in turn |
504 |
|
call the local exch2 subroutines \code{EXCH2\_UV\_XY\_RX} and |
505 |
|
\code{EXCH2\_UV\_XYZ\_RX} for two and three-dimensional vector |
506 |
|
quantities, and \code{EXCH2\_XY\_RX} and \code{EXCH2\_XYZ\_RX} for two |
507 |
|
and three-dimensional scalar quantities. These subroutines set the |
508 |
|
dimensions of the area to be exchanged, call \code{EXCH2\_RX1\_CUBE} |
509 |
|
for scalars and \code{EXCH2\_RX2\_CUBE} for vectors, and then handle |
510 |
|
the singularities at the cube corners. \\ |
511 |
|
|
512 |
|
The separate scalar and vector forms of \code{EXCH2\_RX1\_CUBE} and |
513 |
|
\code{EXCH2\_RX2\_CUBE} reflect that the vector-handling subrouine |
514 |
|
needs to pass both the $u$ and $v$ components of the phsical vectors. |
515 |
|
This arises from the topological folding discussed above, where the |
516 |
|
$x$ and $y$ axes get swapped in some cases. This swapping is not an |
517 |
|
issue with the scalar version. These subroutines call |
518 |
|
\code{EXCH2\_SEND\_RX1} and \code{EXCH2\_SEND\_RX2}, which do most of |
519 |
|
the work using the variables discussed above. \\ |
520 |
|
|
|
|
|
|
\subsection{References} |
|