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<h2 class="chapter">6 Distributed-memory FFTW with MPI</h2>
<p><a name="index-MPI-344"></a>
<a name="index-parallel-transform-345"></a>In this chapter we document the parallel FFTW routines for parallel
systems supporting the MPI message-passing interface. Unlike the
shared-memory threads described in the previous chapter, MPI allows
you to use <em>distributed-memory</em> parallelism, where each CPU has
its own separate memory, and which can scale up to clusters of many
thousands of processors. This capability comes at a price, however:
each process only stores a <em>portion</em> of the data to be
transformed, which means that the data structures and
programming-interface are quite different from the serial or threads
versions of FFTW.
<a name="index-data-distribution-346"></a>
<p>Distributed-memory parallelism is especially useful when you are
transforming arrays so large that they do not fit into the memory of a
single processor. The storage per-process required by FFTW's MPI
routines is proportional to the total array size divided by the number
of processes. Conversely, distributed-memory parallelism can easily
pose an unacceptably high communications overhead for small problems;
the threshold problem size for which parallelism becomes advantageous
will depend on the precise problem you are interested in, your
hardware, and your MPI implementation.
<p>A note on terminology: in MPI, you divide the data among a set of
“processes” which each run in their own memory address space.
Generally, each process runs on a different physical processor, but
this is not required. A set of processes in MPI is described by an
opaque data structure called a “communicator,” the most common of
which is the predefined communicator <code>MPI_COMM_WORLD</code> which
refers to <em>all</em> processes. For more information on these and
other concepts common to all MPI programs, we refer the reader to the
documentation at <a href="http://www.mcs.anl.gov/research/projects/mpi/">the MPI home page</a>.
<a name="index-MPI-communicator-347"></a><a name="index-MPI_005fCOMM_005fWORLD-348"></a>
<p>We assume in this chapter that the reader is familiar with the usage
of the serial (uniprocessor) FFTW, and focus only on the concepts new
to the MPI interface.
<ul class="menu">
<li><a accesskey="1" href="FFTW-MPI-Installation.html#FFTW-MPI-Installation">FFTW MPI Installation</a>
<li><a accesskey="2" href="Linking-and-Initializing-MPI-FFTW.html#Linking-and-Initializing-MPI-FFTW">Linking and Initializing MPI FFTW</a>
<li><a accesskey="3" href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>
<li><a accesskey="4" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>
<li><a accesskey="5" href="Multi_002ddimensional-MPI-DFTs-of-Real-Data.html#Multi_002ddimensional-MPI-DFTs-of-Real-Data">Multi-dimensional MPI DFTs of Real Data</a>
<li><a accesskey="6" href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms">Other Multi-dimensional Real-data MPI Transforms</a>
<li><a accesskey="7" href="FFTW-MPI-Transposes.html#FFTW-MPI-Transposes">FFTW MPI Transposes</a>
<li><a accesskey="8" href="FFTW-MPI-Wisdom.html#FFTW-MPI-Wisdom">FFTW MPI Wisdom</a>
<li><a accesskey="9" href="Avoiding-MPI-Deadlocks.html#Avoiding-MPI-Deadlocks">Avoiding MPI Deadlocks</a>
<li><a href="FFTW-MPI-Performance-Tips.html#FFTW-MPI-Performance-Tips">FFTW MPI Performance Tips</a>
<li><a href="Combining-MPI-and-Threads.html#Combining-MPI-and-Threads">Combining MPI and Threads</a>
<li><a href="FFTW-MPI-Reference.html#FFTW-MPI-Reference">FFTW MPI Reference</a>
<li><a href="FFTW-MPI-Fortran-Interface.html#FFTW-MPI-Fortran-Interface">FFTW MPI Fortran Interface</a>
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