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works as follows: |
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\begin{enumerate} |
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\item Each processor computes the convex hull for its own atomic sites |
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(dashed lines in Fig. \ref{fig:parallel}). |
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(left panel in Fig. \ref{fig:parallel}). |
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\item The Hull vertices from each processor are passed out to all of |
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the processors, and each processor assembles a complete list of hull |
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sites (this is much smaller than the original number of points in |
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the point cloud). |
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\item Each processor computes the global convex hull (solid line in |
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\item Each processor computes the global convex hull (right panel in |
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Fig. \ref{fig:parallel}) using only those points that are the union |
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of sites gathered from all of the subset hulls. Delaunay |
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triangulation is then done to obtain the facets of the global hull. |
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|
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\begin{figure} |
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\begin{centering} |
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\includegraphics[width=3in]{parallel} |
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\includegraphics[width=\linewidth]{parallel} |
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\caption{When the sites are distributed among many nodes for parallel |
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computation, the processors first compute the convex hulls for their |
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own sites (dashed lines in upper panel). The positions of the sites |
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own sites (dashed lines in left panel). The positions of the sites |
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that make up the convex hulls are then communicated to all |
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processors. The convex hull of the system (solid line in lower |
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panel) is the convex hull of the points on the hulls for all |
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processors. } |
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processors (middle panel). The convex hull of the system (solid line in right panel) is the convex hull of the points on the hulls for all |
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processors.} |
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\label{fig:parallel} |
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\end{centering} |
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\label{fig:parallel} |
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\end{figure} |