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% $Header: /u/u3/gcmpack/manual/part6/exch2.tex,v 1.12 2004/03/16 21:52:15 afe Exp $ |
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% $Name: $ |
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%% * Introduction |
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%% o what it does, citations (refs go into mitgcm_manual.bib, |
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%% preferably in alphabetic order) |
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%% o Equations |
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%% * Key subroutines and parameters |
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%% * Reference material (auto generated from Protex and structured comments) |
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%% o automatically inserted at \section{Reference} |
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\section{exch2: Extended Cubed Sphere \mbox{Topology}} |
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\label{sec:exch2} |
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|
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|
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\subsection{Introduction} |
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|
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The \texttt{exch2} package extends the original cubed |
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sphere topology configuration to allow more flexible domain |
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decomposition and parallelization. Cube faces (also called |
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subdomains) may be divided into any number of tiles that divide evenly |
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into the grid point dimensions of the subdomain. Furthermore, the |
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individual tiles can run on separate processors in different |
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combinations, and whether exchanges between particular tiles occur |
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between different processors is determined at runtime. This |
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flexibility provides for manual compile-time load balancing across a |
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relatively arbitrary number of processors. \\ |
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|
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The exchange parameters are declared in |
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\filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h} |
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and assigned in |
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\filelink{pkg/exch2/w2\_e2setup.F}{pkg-exch2-w2_e2setup.F}. The |
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validity of the cube topology depends on the \file{SIZE.h} file as |
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detailed below. The default files provided in the release configure a |
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cubed sphere topology of six tiles, one per subdomain, each with |
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32$\times$32 grid points, all running on a single processor. Both |
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files are generated by Matlab scripts in |
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\file{utils/exch2/matlab-topology-generator}; see Section |
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\ref{sec:topogen} \sectiontitle{Generating Topology Files for exch2} |
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for details on creating alternate topologies. Pregenerated examples |
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of these files with alternate topologies are provided under |
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\file{utils/exch2/code-mods} along with the appropriate \file{SIZE.h} |
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file for single-processor execution. |
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|
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\subsection{Invoking exch2} |
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|
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To use exch2 with the cubed sphere, the following conditions must be |
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met: \\ |
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|
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$\bullet$ The exch2 package is included when \file{genmake2} is run. |
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The easiest way to do this is to add the line \code{exch2} to the |
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\file{profile.conf} file -- see Section |
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\ref{sect:buildingCode} \sectiontitle{Building the code} for general |
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details. \\ |
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|
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$\bullet$ An example of \file{W2\_EXCH2\_TOPOLOGY.h} and |
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\file{w2\_e2setup.F} must reside in a directory containing code |
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linked when \file{genmake2} runs. The safest place to put these |
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is the directory indicated in the \code{-mods=DIR} command line |
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modifier (typically \file{../code}), or the build directory. The |
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default versions of these files reside in \file{pkg/exch2} and are |
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linked automatically if no other versions exist elsewhere in the |
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link path, but they should be left untouched to avoid breaking |
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configurations other than the one you intend to modify.\\ |
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|
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$\bullet$ Files containing grid parameters, named |
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\file{tile00$n$.mitgrid} where $n$=\code{(1:6)} (one per subdomain), |
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must be in the working directory when the MITgcm executable is run. |
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These files are provided in the example experiments for cubed sphere |
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configurations with 32$\times$32 cube sides and are non-trivial to |
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generate -- please contact MITgcm support if you want to generate |
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files for other configurations. \\ |
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|
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$\bullet$ As always when compiling MITgcm, the file \file{SIZE.h} must |
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be placed where \file{genmake2} will find it. In particular for |
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exch2, the domain decomposition specified in \file{SIZE.h} must |
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correspond with the particular configuration's topology specified in |
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\file{W2\_EXCH2\_TOPOLOGY.h} and \file{w2\_e2setup.F}. Domain |
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decomposition issues particular to exch2 are addressed in Section |
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\ref{sec:topogen} \sectiontitle{Generating Topology Files for exch2} |
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and \ref{sec:exch2mpi} \sectiontitle{exch2, SIZE.h, and MPI}; a more |
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general background on the subject relevant to MITgcm is presented in |
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Section \ref{sect:specifying_a_decomposition} |
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\sectiontitle{Specifying a decomposition}.\\ |
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|
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As of the time of writing the following examples use exch2 and may be |
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used for guidance: |
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|
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\begin{verbatim} |
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verification/adjust_nlfs.cs-32x32x1 |
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verification/adjustment.cs-32x32x1 |
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verification/aim.5l_cs |
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verification/global_ocean.cs32x15 |
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verification/hs94.cs-32x32x5 |
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\end{verbatim} |
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|
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|
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|
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|
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\subsection{Generating Topology Files for exch2} |
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\label{sec:topogen} |
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|
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Alternate cubed sphere topologies may be created using the Matlab |
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scripts in \file{utils/exch2/matlab-topology-generator}. Running the |
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m-file |
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\filelink{driver.m}{utils-exch2-matlab-topology-generator_driver.m} |
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from the Matlab prompt (there are no parameters to pass) generates |
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exch2 topology files \file{W2\_EXCH2\_TOPOLOGY.h} and |
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\file{w2\_e2setup.F} in the working directory and displays a figure of |
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the topology via Matlab. The other m-files in the directory are |
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subroutines of \file{driver.m} and should not be run ``bare'' except |
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for development purposes. \\ |
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|
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The parameters that determine the dimensions and topology of the |
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generated configuration are \code{nr}, \code{nb}, \code{ng}, |
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\code{tnx} and \code{tny}, and all are assigned early in the script. \\ |
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|
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The first three determine the size of the subdomains and |
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hence the size of the overall domain. Each one determines the number |
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of grid points, and therefore the resolution, along the subdomain |
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sides in a ``great circle'' around an axis of the cube. At the time |
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of this writing MITgcm requires these three parameters to be equal, |
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but they provide for future releases to accomodate different |
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resolutions around the axes to allow (for example) greater resolution |
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around the equator.\\ |
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|
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The parameters \code{tnx} and \code{tny} determine the dimensions of |
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the tiles into which the subdomains are decomposed, and must evenly |
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divide the integer assigned to \code{nr}, \code{nb} and \code{ng}. |
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The result is a rectangular tiling of the subdomain. Figure |
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\ref{fig:24tile} shows one possible topology for a twentyfour-tile |
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cube, and figure \ref{fig:12tile} shows one for twelve tiles. \\ |
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|
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\begin{figure} |
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\begin{center} |
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\resizebox{4in}{!}{ |
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\includegraphics{part6/s24t_16x16.ps} |
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} |
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\end{center} |
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|
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\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
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divided into six 32$\times$32 subdomains, each of which is divided into four tiles |
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(\code{tnx=16, tny=16}) for a total of twentyfour tiles. |
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} \label{fig:24tile} |
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\end{figure} |
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|
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\begin{figure} |
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\begin{center} |
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\resizebox{4in}{!}{ |
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\includegraphics{part6/s12t_16x32.ps} |
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} |
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\end{center} |
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\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
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divided into six 32$\times$32 subdomains of two tiles each |
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(\code{tnx=16, tny=32}). |
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} \label{fig:12tile} |
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\end{figure} |
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|
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\begin{figure} |
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\begin{center} |
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\resizebox{4in}{!}{ |
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\includegraphics{part6/s6t_32x32.ps} |
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} |
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\end{center} |
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\caption{Plot of a cubed sphere topology with a 32$\times$192 domain |
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divided into six 32$\times$32 subdomains with one tile each |
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(\code{tnx=32, tny=32}). This is the default configuration. |
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} |
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\label{fig:6tile} |
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\end{figure} |
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|
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|
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Tiles can be selected from the topology to be omitted from being |
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allocated memory and processors. This tuning is useful in ocean |
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modeling for omitting tiles that fall entirely on land. The tiles |
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omitted are specified in the file |
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\filelink{blanklist.txt}{utils-exch2-matlab-topology-generator_blanklist.txt} |
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by their tile number in the topology, separated by a newline. \\ |
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|
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|
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|
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|
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\subsection{exch2, SIZE.h, and multiprocessing} |
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\label{sec:exch2mpi} |
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|
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Once the topology configuration files are created, the Fortran |
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\code{PARAMETER}s in \file{SIZE.h} must be configured to match. |
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Section \ref{sect:specifying_a_decomposition} \sectiontitle{Specifying |
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a decomposition} provides a general description of domain |
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decomposition within MITgcm and its relation to \file{SIZE.h}. The |
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current section specifies certain constraints the exch2 package |
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imposes as well as describes how to enable parallel execution with |
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MPI. \\ |
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|
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As in the general case, the parameters \varlink{sNx}{sNx} and |
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\varlink{sNy}{sNy} define the size of the individual tiles, and so |
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must be assigned the same respective values as \code{tnx} and |
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\code{tny} in \file{driver.m}.\\ |
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|
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The halo width parameters \varlink{OLx}{OLx} and \varlink{OLy}{OLy} |
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have no special bearing on exch2 and may be assigned as in the general |
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case. The same holds for \varlink{Nr}{Nr}, the number of vertical |
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levels in the model.\\ |
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|
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The parameters \varlink{nSx}{nSx}, \varlink{nSy}{nSy}, |
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\varlink{nPx}{nPx}, and \varlink{nPy}{nPy} relate to the number of |
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tiles and how they are distributed on processors. When using exch2, |
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the tiles are stored in single dimension, and so |
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\code{\varlink{nSy}{nSy}=1} in all cases. Since the tiles as |
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configured by exch2 cannot be split up accross processors without |
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regenerating the topology, \code{\varlink{nPy}{nPy}=1} as well. \\ |
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|
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The number of tiles MITgcm allocates and how they are distributed |
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between processors depends on \varlink{nPx}{nPx} and |
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\varlink{nSx}{nSx}. \varlink{nSx}{nSx} is the number of tiles per |
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processor and \varlink{nPx}{nPx} the number of processors. The total |
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number of tiles in the topology minus those listed in |
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\file{blanklist.txt} must equal \code{nSx*nPx}. \\ |
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|
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The following is an example of \file{SIZE.h} for the twelve-tile |
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configuration illustrated in figure \ref{fig:12tile} running on |
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one processor: \\ |
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|
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\begin{verbatim} |
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PARAMETER ( |
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& sNx = 16, |
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& sNy = 32, |
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& OLx = 2, |
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& OLy = 2, |
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& nSx = 12, |
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& nSy = 1, |
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& nPx = 1, |
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& nPy = 1, |
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& Nx = sNx*nSx*nPx, |
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& Ny = sNy*nSy*nPy, |
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& Nr = 5) |
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\end{verbatim} |
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|
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The following is an example for the twentyfour-tile topology in figure |
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\ref{fig:24tile} running on six processors: |
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|
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\begin{verbatim} |
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PARAMETER ( |
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& sNx = 16, |
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& sNy = 16, |
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& OLx = 2, |
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& OLy = 2, |
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& nSx = 4, |
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& nSy = 1, |
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& nPx = 6, |
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& nPy = 1, |
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& Nx = sNx*nSx*nPx, |
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& Ny = sNy*nSy*nPy, |
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& Nr = 5) |
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\end{verbatim} |
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|
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|
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|
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|
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\subsection{Key Variables} |
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|
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The descriptions of the variables are divided up into scalars, |
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one-dimensional arrays indexed to the tile number, and two and three |
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dimensional arrays indexed to tile number and neighboring tile. This |
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division reflects the functionality of these variables: The |
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scalars are common to every part of the topology, the tile-indexed |
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arrays to individual tiles, and the arrays indexed by tile and |
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neighbor to relationships between tiles and their neighbors. \\ |
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|
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\subsubsection{Scalars} |
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|
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The number of tiles in a particular topology is set with the parameter |
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\code{NTILES}, and the maximum number of neighbors of any tiles by |
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\code{MAX\_NEIGHBOURS}. These parameters are used for defining the |
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size of the various one and two dimensional arrays that store tile |
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parameters indexed to the tile number and are assigned in the files |
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generated by \file{driver.m}.\\ |
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|
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The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt} |
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and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number |
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of tiles in the $x$ and $y$ global indices. For example, the default |
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setup of six tiles (Fig. \ref{fig:6tile}) has \code{exch2\_domain\_nxt=6} and |
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\code{exch2\_domain\_nyt=1}. A topology of twenty-four square tiles, |
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four per subdomain (as in figure \ref{fig:24tile}), will have |
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\code{exch2\_domain\_nxt=12} and \code{exch2\_domain\_nyt=2}. Note |
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that these parameters express the tile layout to allow global data |
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files that are tile-layout-neutral and have no bearing on the internal |
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storage of the arrays. The tiles are internally stored in a range |
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from \code{(1:\varlink{bi}{bi})} the $x$ axis, and $y$ axis variable |
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\varlink{bj}{bj} is generally ignored within the package. \\ |
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|
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\subsubsection{Arrays Indexed to Tile Number} |
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|
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The following arrays are of length \code{NTILES}, are indexed to the |
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tile number, and the indices are omitted in their descriptions. \\ |
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|
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The arrays \varlink{exch2\_tnx}{exch2_tnx} and |
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\varlink{exch2\_tny}{exch2_tny} express the $x$ and $y$ dimensions of |
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each tile. At present for each tile \texttt{exch2\_tnx=sNx} and |
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\texttt{exch2\_tny=sNy}, as assigned in \file{SIZE.h} and described in |
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section \ref{sec:exch2mpi} \sectiontitle{exch2, SIZE.h, and |
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multiprocessing}. Future releases of MITgcm are to allow varying tile |
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sizes. \\ |
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|
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The location of the tiles' Cartesian origin within a subdomain are |
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determined by the arrays \varlink{exch2\_tbasex}{exch2_tbasex} and |
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\varlink{exch2\_tbasey}{exch2_tbasey}. These variables are used to |
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relate the location of the edges of different tiles to each other. As |
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an example, in the default six-tile topology (Fig. \ref{fig:6tile}) |
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each index in these arrays is set to \code{0} since a tile occupies |
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its entire subdomain. The twentyfour-tile case discussed above will |
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have values of \code{0} or \code{16}, depending on the quadrant the |
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tile falls within the subdomain. The elements of the arrays |
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\varlink{exch2\_txglobalo}{exch2_txglobalo} and |
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\varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to |
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\varlink{exch2\_tbasex}{exch2_tbasex} and |
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\varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the |
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global address space, similar to that used by global files. \\ |
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|
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The array \varlink{exch2\_myFace}{exch2_myFace} contains the number of |
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the subdomain of each tile, in a range \code{(1:6)} in the case of the |
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standard cube topology and indicated by \textbf{\textsf{f}}$n$ in |
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figures \ref{fig:12tile} and |
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\ref{fig:24tile}. \varlink{exch2\_nNeighbours}{exch2_nNeighbours} |
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contains a count of how many neighboring tiles each tile has, and is |
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used for setting bounds for looping over neighboring tiles. |
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\varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each |
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tile, and is used in interprocess communication. \\ |
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|
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|
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The arrays \varlink{exch2\_isWedge}{exch2_isWedge}, |
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\varlink{exch2\_isEedge}{exch2_isEedge}, |
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\varlink{exch2\_isSedge}{exch2_isSedge}, and |
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\varlink{exch2\_isNedge}{exch2_isNedge} are set to \code{1} if the |
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indexed tile lies on the edge of a subdomain, \code{0} if not. The |
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values are used within the topology generator to determine the |
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orientation of neighboring tiles, and to indicate whether a tile lies |
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on the corner of a subdomain. The latter case requires special |
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exchange and numerical handling for the singularities at the eight |
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corners of the cube. \\ |
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|
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|
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\subsubsection{Arrays Indexed to Tile Number and Neighbor} |
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|
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The following arrays are all of size |
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\code{MAX\_NEIGHBOURS}$\times$\code{NTILES} and describe the |
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orientations between the the tiles. \\ |
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|
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The array \code{exch2\_neighbourId(a,T)} holds the tile number |
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\code{Tn} for each of the tile number \code{T}'s neighboring tiles |
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\code{a}. The neighbor tiles are indexed \code{(1:MAX\_NEIGHBOURS)} |
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in the order right to left on the north then south edges, and then top |
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to bottom on the east and west edges. Maybe throw in a fig here, eh? |
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\\ |
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|
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\sloppy |
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The \code{exch2\_opposingSend\_record(a,T)} array holds the index |
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\code{b} in \texttt{exch2\_neighbourId(b,Tn)} that holds the tile |
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number \code{T}. In other words, |
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\begin{verbatim} |
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exch2_neighbourId( exch2_opposingSend_record(a,T), |
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exch2_neighbourId(a,T) ) = T |
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\end{verbatim} |
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This provides a back-reference from the neighbor tiles. \\ |
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|
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The arrays \varlink{exch2\_pi}{exch2_pi} and |
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\varlink{exch2\_pj}{exch2_pj} specify the transformations of variables |
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in exchanges between the neighboring tiles. These transformations are |
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necessary in exchanges between subdomains because a physical vector |
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component in one direction may map to one in a different direction in |
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an adjacent subdomain, and may be have its indexing reversed. This |
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swapping arises from the ``folding'' of two-dimensional arrays into a |
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three-dimensional cube. |
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|
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The dimensions of \code{exch2\_pi(t,N,T)} and \code{exch2\_pj(t,N,T)} |
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are the neighbor ID \code{N} and the tile number \code{T} as explained |
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above, plus a vector of length 2 containing transformation factors |
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\code{t}. The first element of the transformation vector indicates |
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the factor \code{t} by which variables representing the same |
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\emph{physical} vector component of a tile \code{T} will be multiplied |
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in exchanges with neighbor \code{N}, and the second element indicates |
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the transform to the physical vector in the other direction. To |
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clarify (hopefully), \code{exch2\_pi(1,N,T)} holds the transform of |
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the $i$ component of a vector variable in tile \code{T} to the $i$ |
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component of tile \code{T}'s neighbor \code{N}, and |
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\code{exch2\_pi(2,N,T)} holds the transform of \code{T}'s $i$ |
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components to the neighbor \code{N}'s $j$ component. \\ |
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|
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Under the current cube topology, one of the two elements of |
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\code{exch2\_pi} or \code{exch2\_pj} for a given tile \code{T} and |
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neighbor \code{N} will be \code{0}, reflecting the fact that the two |
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vector components are orthogonal. The other element will be \code{1} |
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or \code{-1}, depending on whether the components are indexed in the |
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same or opposite directions. For example, the transform vector of the |
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arrays for all tile neighbors on the same subdomain will be |
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\code{(1,0)}, since all tiles on the same subdomain are oriented |
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identically. A vector direction that corresponds to the orthogonal |
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dimension with the same index direction in a particular tile-neighbor |
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orientation will have \code{(0,1)}, whereas those in the opposite |
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index direction will have \code{(0,-1)}. \\ |
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|
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|
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\varlink{exch2\_oi}{exch2_oi}, |
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\varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and |
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\varlink{exch2\_oj\_f}{exch2_oj_f} |
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|
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|
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|
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This needs some diagrams. \\ |
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{\footnotesize |
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\begin{verbatim} |
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C exch2_pi :: X index row of target to source permutation |
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C :: matrix for each neighbour entry. |
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C exch2_pj :: Y index row of target to source permutation |
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C :: matrix for each neighbour entry. |
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C exch2_oi :: X index element of target to source |
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C :: offset vector for cell-centered quantities |
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C :: of each neighbor entry. |
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C exch2_oj :: Y index element of target to source |
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C :: offset vector for cell-centered quantities |
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C :: of each neighbor entry. |
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C exch2_oi_f :: X index element of target to source |
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C :: offset vector for face quantities |
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C :: of each neighbor entry. |
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C exch2_oj_f :: Y index element of target to source |
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C :: offset vector for face quantities |
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C :: of each neighbor entry. |
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\end{verbatim} |
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} |
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\subsection{Key Routines} |
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\subsection{References} |
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