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	{\bf Domain Decomposition}
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{\underline {\it Aim}} : Minimize communications cost by distributing 
the cells in the domain in some optimal way.
$$
\textrm {time} = \textrm {latency} + \frac{\textrm {message size}}{\textrm {communications bandwidth}}
$$
{\underline {\it Approach \#1}}
\begin{itemize}
\item Ideal for large problems, slow networks or whenever many small messages
are passed.
\item Neglects latency.
\item Total length of inter-domain boundaries is minimized (which is length
of all shared data)..in other words minimizes shared part of 
perimeter/surface area of the domain.
\item Requires a-priori knowledge of number of domains (compute nodes)
and hence has to be done online every time the problem is run on
a different number of nodes.
\item Popular techniques need eigenvalue of the connectivity matrix
and thus can be expensive for large problems.
\item However, produces best grids for large problems. \\
\end{itemize}

{\underline {\it Approach \#2}}
\begin{itemize}
\item Ideal for small problems, fast networks or whenever few big messages
are passed.
\item Neglects second term as communication bandwidth is assumed large.
\item The total number of messages exchanged is minimized.
\item Since the above minimization corresponds to minimization of
bandwidth of the cell connectivity matrix, this approach is independent
of the number of domains (compute nodes).
\item A large knowledge base exists in this area and is readily accessible
so implementation is sound and easy.
\end{itemize}

These domain decomposition techniques are absolutely essential since
we are dealing with unstructured grids in which the ordering
of grid cells is generally arbitrary (especially, if say, Advancing
Front Method was used to create the 2D/3D grids or Delaunay Triangulation
for the 2D grids).

Approach \#$2$ is used in PUMA as it is aimed at machines with
high communications bandwidth.


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