\subsection{\bf NI.4:\ \ Parallel Computing}
\subsection{\bf and Integration}

\begin{slide}

\centerline{\psfig{figure=ni.fig3.ps,clip=true,width=6.0in}}

\begin{itemize}
\item If have $n+1$ point integration ($n=15$ above) divide into
$N_{\rm proc}$ ($N_{\rm proc}=4$ above) equal parts.

\item $M=(n+1)/N_{\rm proc}$ ($=4$ above) integration points in each
processor.  Each processor does an internal sum.
\begin{eqnarray*}
I_l & = & \sum^{F_l}_{i=B_l} w_i\,f(x_i) \qquad l=0 \ldots N_{{\rm proc} -1} \\
\mbox{index}\ B_l & = & Ml \\
F_l & = & B_l + M-1 \\
\end{eqnarray*}

\item Then total integral is
$$
I=I_0 + I_1 \ldots + I_{N_{\rm proc} -1}
$$
\item There is ONLY communication in one place---a global COMBINE
(reduction).
\end{itemize}
\end{slide}

