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

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

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph


Revision 1.8 - (hide annotations) (download) (as text)
Tue Feb 17 21:58:56 2004 UTC (21 years, 5 months ago) by edhill
Branch: MAIN
Changes since 1.7: +129 -121 lines
File MIME type: application/x-tex
 o cleanup formatting and fix errors in exch2

1 edhill 1.8 % $Header: /u/u3/gcmpack/manual/part6/exch2.tex,v 1.7 2004/02/11 20:48:14 afe Exp $
2 afe 1.1 % $Name: $
3    
4     %% * Introduction
5     %% o what it does, citations (refs go into mitgcm_manual.bib,
6     %% preferably in alphabetic order)
7     %% o Equations
8     %% * Key subroutines and parameters
9     %% * Reference material (auto generated from Protex and structured comments)
10     %% o automatically inserted at \section{Reference}
11    
12    
13 edhill 1.8 \section{Extended Cubed Sphere Exchange}
14 afe 1.3 \label{sec:exch2}
15    
16 afe 1.1
17     \subsection{Introduction}
18 afe 1.2
19 edhill 1.8 The \texttt{exch2} package is an extension to the original cubed
20     sphere exchanges to allow more flexible domain decomposition and
21     parallelization. Cube faces (subdomains) may be divided into whatever
22     number of tiles that divide evenly into the grid point dimensions of
23     the subdomain. Furthermore, the individual tiles may be run on
24     separate processors in different combinations, and whether exchanges
25     between particular tiles occur between different processors is
26     determined at runtime.
27    
28     The exchange parameters are declared in
29     \filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h}
30     and assigned in
31     \filelink{pkg/exch2/w2\_e2setup.F}{pkg-exch2-w2_e2setup.F}, both in
32     the \texttt{pkg/exch2} directory. The validity of the cube topology
33     depends on the \texttt{SIZE.h} file as detailed below. Both files are
34     generated by Matlab scripts and should not be edited. The default
35     files provided in the release set up a cube sphere arrangement of six
36     tiles, one per subdomain, each with 32x32 grid points, running on a
37     single processor.
38 afe 1.4
39     \subsection{Key Variables}
40    
41     The descriptions of the variables are divided up into scalars,
42 edhill 1.8 one-dimensional arrays indexed to the tile number, and two and three
43     dimensional arrays indexed to tile number and neighboring tile. This
44     division actually reflects the functionality of these variables: the
45     scalars are common to every part of the topology, the tile-indexed
46     arrays to individual tiles, and the arrays indexed to tile and
47     neighbor to relationships between tiles and their neighbors.
48 afe 1.4
49     \subsubsection{Scalars}
50    
51     The number of tiles in a particular topology is set with the parameter
52 edhill 1.8 \texttt{NTILES}, and the maximum number of neighbors of any tiles by
53     \texttt{MAX\_NEIGHBOURS}. These parameters are used for defining the
54     size of the various one and two dimensional arrays that store tile
55     parameters indexed to the tile number.
56    
57     The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt}
58     and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number
59     of tiles in the x and y global indices. For example, the default
60     setup of six tiles has \texttt{exch2\_domain\_nxt=6} and
61     \texttt{exch2\_domain\_nyt=1}. A topology of twenty-four square (in
62     gridpoints) tiles, four (2x2) per subdomain, will have
63     \texttt{exch2\_domain\_nxt=12} and \texttt{exch2\_domain\_nyt=2}.
64     Note that these parameters express the tile layout to allow global
65     data files that are tile-layout-neutral and have no bearing on the
66     internal storage of the arrays. The tiles are internally stored in a
67     range from \texttt{1,bi} (in the x axis) and y-axis variable
68     \texttt{bj} is generally ignored within the package.
69 afe 1.4
70 afe 1.6 \subsubsection{Arrays Indexed to Tile Number}
71 afe 1.4
72 edhill 1.8 The following arrays are of size \texttt{NTILES}, are indexed to the
73     tile number, and the indices are omitted in their descriptions.
74 afe 1.4
75 edhill 1.8 The arrays \varlink{exch2\_tnx}{exch2_tnx} and
76     \varlink{exch2\_tny}{exch2_tny} express the x and y dimensions of each
77     tile. At present for each tile \texttt{exch2\_tnx=sNx} and
78     \texttt{exch2\_tny=sNy}, as assigned in \texttt{SIZE.h}. Future
79     releases of MITgcm are to allow varying tile sizes.
80    
81     The location of the tiles' Cartesian origin within a subdomain are
82     determined by the arrays \varlink{exch2\_tbasex}{exch2_tbasex} and
83     \varlink{exch2\_tbasey}{exch2_tbasey}. These variables are used to
84     relate the location of the edges of the tiles to each other. As an
85     example, in the default six-tile topology (the degenerate case) each
86     index in these arrays are set to 0. The twenty-four, 32x32 cube face
87     case discussed above will have values of 0 or 16, depending on the
88     quadrant the tile falls within the subdomain. The array
89     \varlink{exch2\_myFace}{exch2_myFace} contains the number of the
90     cubeface/subdomain of each tile, numbered 1-6 in the case of the
91     standard cube topology.
92    
93     The arrays \varlink{exch2\_txglobalo}{exch2_txglobalo} and
94     \varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to
95     \varlink{exch2\_tbasex}{exch2_tbasex} and
96     \varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the
97     global address space, similar to that used by global files.
98    
99     The arrays \varlink{exch2\_isWedge}{exch2_isWedge},
100     \varlink{exch2\_isEedge}{exch2_isEedge},
101     \varlink{exch2\_isSedge}{exch2_isSedge}, and
102     \varlink{exch2\_isNedge}{exch2_isNedge} are set to 1 if the indexed
103     tile lies on the edge of a subdomain, 0 if not. The values are used
104     within the topology generator to determine the orientation of
105     neighboring tiles and to indicate whether a tile lies on the corner of
106     a subdomain. The latter case indicates special exchange and numerical
107     handling for the singularities at the eight corners of the cube.
108     \varlink{exch2\_nNeighbours}{exch2_nNeighbours} contains a count of
109     how many neighboring tiles each tile has, and is used for setting
110     bounds for looping over neighboring tiles.
111     \varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each
112     tile, and is used in interprocess communication.
113 afe 1.4
114 afe 1.6 \subsubsection{Arrays Indexed to Tile Number and Neighbor}
115 afe 1.4
116 edhill 1.8 The following arrays are all of size \texttt{MAX\_NEIGHBOURS} $\times$
117     \texttt{NTILES} and describe the orientations between the the tiles.
118 afe 1.5
119 edhill 1.8 The array \texttt{exch2\_neighbourId(a,T)} holds the tile number for
120     each of the $n$ neighboring tiles. The neighbor tiles are indexed
121     \texttt{(1,MAX\_NEIGHBOURS} in the order right to left on the north
122     then south edges, and then top to bottom on the east and west edges.
123     Maybe throw in a fig here, eh?
124    
125     The \texttt{exch2\_opposingSend\_record(a,T)} array holds the index c
126     in \texttt{exch2\_neighbourId(b,$T_{n}$)} that holds the tile number T.
127     In other words,
128     \begin{verbatim}
129     exch2_neighbourId( exch2_opposingSend_record(a,T),
130     exch2_neighbourId(a,T) ) = T
131 afe 1.5 \end{verbatim}
132 edhill 1.8 and this provides a back-reference from the neighbor tiles.
133 afe 1.5
134 edhill 1.8 The arrays \varlink{exch2\_pi}{exch2_pi},
135     \varlink{exch2\_pj}{exch2_pj}, \varlink{exch2\_oi}{exch2_oi},
136     \varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and
137     \varlink{exch2\_oj\_f}{exch2_oj_f} specify the transformations in
138     exchanges between the neighboring tiles. The dimensions of
139     \texttt{exch2\_pi(t,N,T)} and \texttt{exch2\_pj(t,N,T)} are the
140     neighbor ID \textit{N} and the tile number \textit{T} as explained
141     above, plus the transformation vector {\em t }, of length two. The
142     first element of the transformation vector indicates the factor by
143     which variables representing the same vector component of a tile will
144     be multiplied, and the second element indicates the transform to the
145     variable in the other direction. As an example,
146     \texttt{exch2\_pi(1,N,T)} holds the transform of the i-component of a
147     vector variable in tile \texttt{T} to the i-component of tile
148     \texttt{T}'s neighbor \texttt{N}, and \texttt{exch2\_pi(2,N,T)} hold
149     the component of neighbor \texttt{N}'s j-component.
150    
151     Under the current cube topology, one of the two elements of
152     \texttt{exch2\_pi} or \texttt{exch2\_pj} for a given tile \texttt{T}
153     and neighbor \texttt{N} will be 0, reflecting the fact that the vector
154     components are orthogonal. The other element will be 1 or -1,
155     depending on whether the components are indexed in the same or
156     opposite directions. For example, the transform dimension of the
157     arrays for all tile neighbors on the same subdomain will be [1,0],
158     since all tiles on the same subdomain are oriented identically.
159     Vectors that correspond to the orthogonal dimension with the same
160     index direction will have [0,1], whereas those in the opposite index
161     direction will have [0,-1].
162 afe 1.5
163 afe 1.4
164 edhill 1.8 {\footnotesize
165 afe 1.4 \begin{verbatim}
166     C exch2_pi :: X index row of target to source permutation
167     C :: matrix for each neighbour entry.
168     C exch2_pj :: Y index row of target to source permutation
169     C :: matrix for each neighbour entry.
170     C exch2_oi :: X index element of target to source
171     C :: offset vector for cell-centered quantities
172     C :: of each neighbor entry.
173     C exch2_oj :: Y index element of target to source
174     C :: offset vector for cell-centered quantities
175     C :: of each neighbor entry.
176     C exch2_oi_f :: X index element of target to source
177     C :: offset vector for face quantities
178     C :: of each neighbor entry.
179     C exch2_oj_f :: Y index element of target to source
180     C :: offset vector for face quantities
181     C :: of each neighbor entry.
182     \end{verbatim}
183 edhill 1.8 }
184 afe 1.1
185    
186    
187     \subsection{Key Routines}
188    
189    
190    
191     \subsection{References}

  ViewVC Help
Powered by ViewVC 1.1.22