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3. Traditional parallel implementation
The traditional distribution of data in electronic structure
calculations is shown schematically in Fig. 1 for the case
of a
grid and 4 nodes. When applying the
potential to a trial eigenvector, the data is initially represented in
momentumspace (on the lefthand side of Fig. 1) and each
node deals with a number of ``rods'' of data in the direction. In
the first stage of the 3DFFT, each node performs a 1DFFT in the
direction on each of its rods. The nodes then communicate to
effect a transpose in which the data is redistributed from
``rods'' to ``rods'' (middle of Fig. 1). Each node
then performs a second 1DFFT in the direction on these rods. A
second communication stage transposes the data to ``rods'' (right
of Fig. 1), and the final stage is to perform a 1DFFT on
these rods. The DFT from real to momentumspace is performed
similarly by reversing these operations.
Figure 1:
Distribution of data for traditional implementation.

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Peter Haynes