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Next: 6.18.6 Key Routines
Up: 6.18 exch2: Extended Cubed
Previous: 6.18.4 exch2, SIZE.h, and
Contents
Subsections
The descriptions of the variables are divided up into scalars,
one-dimensional arrays indexed to the tile number, and two and
three-dimensional arrays indexed to tile number and neighboring tile.
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.
The number of tiles in a particular topology is set with the parameter
NTILES, and the maximum number of neighbors of any tiles by
MAX_NEIGHBOURS. These parameters are used for defining the
size of the various one and two dimensional arrays that store tile
parameters indexed to the tile number and are assigned in the files
generated by driver.m.
The scalar parameters exch2_domain_nxt
and exch2_domain_nyt
express the number
of tiles in the and global indices. For example, the default
setup of six tiles (Fig. 6.6) has
exch2_domain_nxt=6 and exch2_domain_nyt=1. A
topology of twenty-four square tiles, four per subdomain (as in figure
6.4), will have exch2_domain_nxt=12 and
exch2_domain_nyt=2. Note that these parameters express the
tile layout in order to allow global data files that are tile-layout-neutral.
They have no bearing on the internal storage of the arrays. The tiles
are stored internally in a range from bi=(1:NTILES) in the
axis, and the axis variable bj
is assumed to
equal 1 throughout the package.
The following arrays are of length NTILES and are indexed to
the tile number, which is indicated in the diagrams with the notation
t. The indices are omitted in the descriptions.
The arrays exch2_tnx
and
exch2_tny
express the and dimensions of
each tile. At present for each tile exch2_tnx=sNx and
exch2_tny=sNy, as assigned in SIZE.h and described in
Section 6.18.4 exch2, SIZE.h, and
Multiprocessing. Future releases of MITgcm may allow varying tile
sizes.
The arrays exch2_tbasex
and
exch2_tbasey
determine the tiles'
Cartesian origin within a subdomain
and locate the edges of different tiles relative to each other. As
an example, in the default six-tile topology (Fig. 6.6)
each index in these arrays is set to 0 since a tile occupies
its entire subdomain. The twenty-four-tile case discussed above will
have values of 0 or 16, depending on the quadrant of the
tile within the subdomain. The elements of the arrays
exch2_txglobalo
and
exch2_txglobalo
are similar to
exch2_tbasex
and
exch2_tbasey, but locate the tile edges within the
global address space, similar to that used by global output and input
files.
The array exch2_myFace
contains the number of
the subdomain of each tile, in a range (1:6) in the case of the
standard cube topology and indicated by f in
figures 6.5 and
6.4. exch2_nNeighbours
contains a count of the neighboring tiles each tile has, and sets
the bounds for looping over neighboring tiles.
exch2_tProc
holds the process rank of each
tile, and is used in interprocess communication.
The arrays exch2_isWedge,
exch2_isEedge,
exch2_isSedge, and
exch2_isNedge
are set to 1 if the
indexed tile lies on the edge of its 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 requires special
exchange and numerical handling for the singularities at the eight
corners of the cube.
The following arrays have vectors of length MAX_NEIGHBOURS and
NTILES and describe the orientations between the the tiles.
The array exch2_neighbourId(a,T) holds the tile number
Tn for each of the tile number T's neighboring tiles
a. The neighbor tiles are indexed
(1:exch2_nNeighbours(T)) in the order right to left on the
north then south edges, and then top to bottom on the east then west
edges.
The exch2_opposingSend_record(a,T) array holds the
index b of the element in exch2_neighbourId(b,Tn)
that holds the tile number T, given
Tn=exch2_neighborId(a,T). In other words,
exch2_neighbourId( exch2_opposingSend_record(a,T),
exch2_neighbourId(a,T) ) = T
This provides a back-reference from the neighbor tiles.
The arrays exch2_pi
and
exch2_pj
specify the transformations of indices
in exchanges between the neighboring tiles. These transformations are
necessary in exchanges between subdomains because a horizontal dimension
in one subdomain
may map to other horizonal dimension in an adjacent subdomain, and
may also have its indexing reversed. This swapping arises from the
``folding'' of two-dimensional arrays into a three-dimensional
cube.
The dimensions of exch2_pi(t,N,T) and exch2_pj(t,N,T)
are the neighbor ID N and the tile number T as explained
above, plus a vector of length 2 containing transformation
factors t. The first element of the transformation vector
holds the factor to multiply the index in the same dimension, and the
second element holds the the same for the orthogonal dimension. To
clarify, exch2_pi(1,N,T) holds the mapping of the axis
index of tile T to the axis of tile T's neighbor
N, and exch2_pi(2,N,T) holds the mapping of T's
index to the neighbor N's index.
One of the two elements of exch2_pi or exch2_pj for a
given tile T and neighbor N will be 0, reflecting
the fact that the two axes are orthogonal. The other element will be
1 or -1, depending on whether the axes are indexed in
the same or opposite directions. For example, the transform vector of
the arrays for all tile neighbors on the same subdomain will be
(1,0), since all tiles on the same subdomain are oriented
identically. An axis that corresponds to the orthogonal dimension
with the same index direction in a particular tile-neighbor
orientation will have (0,1). Those with the opposite index
direction will have (0,-1) in order to reverse the ordering.
The arrays exch2_oi,
exch2_oj, exch2_oi_f, and
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 T=1 in the six-tile topology
(Fig. 6.6), where
exch2_oi(1,1)=33
exch2_oi(2,1)=0
exch2_oi(3,1)=32
exch2_oi(4,1)=-32
The simplest case is exch2_oi(2,1), the southern neighbor,
which is Tn=6. The axes of T and Tn have the
same orientation and their axes have the same origin, and so an
exchange between the two requires no changes to the index. For
the western neighbor (Tn=5), code_oi(3,1)=32 since the
x=0 vector on T corresponds to the y=32 vector on
Tn. The eastern edge of T shows the reverse case
(exch2_oi(4,1)=-32)), where x=32 on T exchanges
with x=0 on Tn=2.
The most interesting case, where exch2_oi(1,1)=33 and
Tn=3, involves a reversal of indices. As in every case, the
offset exch2_oi is added to the original index of T
multiplied by the transformation factor exch2_pi(t,N,T). Here
exch2_pi(1,1,1)=0 since the axis of T is orthogonal
to the axis of Tn. exch2_pi(2,1,1)=-1 since the
axis of T corresponds to the axis of Tn, but the
index is reversed. The result is that the index of the northern edge
of T, which runs (1:32), is transformed to
(-1:-32). exch2_oi(1,1) is then added to this range to
get back (32:1) - the index of the axis of Tn
relative to 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, exch2_itlo_c,
exch2_ithi_c,
exch2_jtlo_c
and
exch2_jthi_c
hold the location and index
bounds of the edge segment of the neighbor tile N's subdomain
that gets exchanged with the local tile T. To take the example
of tile T=2 in the twelve-tile topology
(Fig. 6.5):
exch2_itlo_c(4,2)=17
exch2_ithi_c(4,2)=17
exch2_jtlo_c(4,2)=0
exch2_jthi_c(4,2)=33
Here N=4, indicating the western neighbor, which is
Tn=1. Tn resides on the same subdomain as T, so
the tiles have the same orientation and the same and axes.
The axis is orthogonal to the western edge and the tile is 16
points wide, so exch2_itlo_c and exch2_ithi_c
indicate the column beyond Tn's eastern edge, in that tile's
halo region. Since the border of the tiles extends through the entire
height of the subdomain, the axis bounds exch2_jtlo_c to
exch2_jthi_c cover the height of (1:32), plus 1 in
either direction to cover part of the halo.
For the north edge of the same tile T=2 where N=1 and
the neighbor tile is Tn=5:
exch2_itlo_c(1,2)=0
exch2_ithi_c(1,2)=0
exch2_jtlo_c(1,2)=0
exch2_jthi_c(1,2)=17
T's northern edge is parallel to the axis, but since
Tn's axis corresponds to T's axis, T's
northern edge exchanges with Tn's western edge. The western
edge of the tiles corresponds to the lower bound of the axis, so
exch2_itlo_c and exch2_ithi_c are 0, in the
western halo region of Tn. The range of
exch2_jtlo_c and exch2_jthi_c correspond to the
width of T's northern edge, expanded by one into the halo.
Next: 6.18.6 Key Routines
Up: 6.18 exch2: Extended Cubed
Previous: 6.18.4 exch2, SIZE.h, and
Contents
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