v12

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 371c1ed32fed58e2fe128a54f1eb26ccb98478d7..2523d890140406bacea2fee20458bfba73eafa95 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -493,7 +493,7 @@ simulates the case of distant clusters linked with long distance network as in g
 
 
 Both codes were simulated on a two clusters based network with 50 hosts each, totaling 100 hosts. Various combinations of the above
 
 
 Both codes were simulated on a two clusters based network with 50 hosts each, totaling 100 hosts. Various combinations of the above

-factors have provided the results shown in Table~\ref{tab.cluster.2x50}. The problem size of the 3D Poisson problem  ranges from $N_x = N_y = N_z = \text{62}$ to 150 elements (that is from
+factors have provided the results shown in Table~\ref{tab.cluster.2x50}. The problem size of the 3D Poisson problem  ranges from $N=N_x = N_y = N_z = \text{62}$ to 150 elements (that is from

 $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 \text{\np{3375000}}$ entries). With the asynchronous multisplitting algorithm the simulated execution time is in average 2.5 times faster than with the synchronous GMRES one. 
 %\AG{Expliquer comment lire les tableaux.}
 $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 \text{\np{3375000}}$ entries). With the asynchronous multisplitting algorithm the simulated execution time is in average 2.5 times faster than with the synchronous GMRES one. 
 %\AG{Expliquer comment lire les tableaux.}


@@ -523,7 +523,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     power (GFlops)
     & 1         & 1         & 1         & 1.5       & 1.5       \\
     \hline
     power (GFlops)
     & 1         & 1         & 1         & 1.5       & 1.5       \\
     \hline

-    size $(n^3)$
+    size $(N)$

     & 62        & 62        & 62        & 100       & 100       \\
     \hline
     Precision
     & 62        & 62        & 62        & 100       & 100       \\
     \hline
     Precision


@@ -548,7 +548,7 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
     Power (GFlops)
     & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\
     \hline
     Power (GFlops)
     & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\
     \hline

-    size $(n^3)$
+    size $(N)$

     & 110       & 120       & 130       & 140       & 150  \\ %     & 171       & 171 \\
     \hline
     Precision
     & 110       & 120       & 130       & 140       & 150  \\ %     & 171       & 171 \\
     \hline
     Precision


@@ -650,8 +650,8 @@ Note that the program was run with the following parameters:
 \item Maximum numbers of outer and inner iterations;
 \item Outer and inner precisions on the residual error;
 \item Matrix size $N_x$, $N_y$ and $N_z$;
 \item Maximum numbers of outer and inner iterations;
 \item Outer and inner precisions on the residual error;
 \item Matrix size $N_x$, $N_y$ and $N_z$;

-\item Matrix diagonal value: $6$ (See Equation~(\ref{eq:03}));
-\item Matrix off-diagonal value: $-1$;
+\item Matrix diagonal value: $6$ (see Equation~(\ref{eq:03}));
+\item Matrix off-diagonal values: $-1$;

 \item Communication mode: asynchronous.
 \end{itemize}
 
 \item Communication mode: asynchronous.
 \end{itemize}
 


@@ -664,7 +664,7 @@ asynchronous multisplitting  compared to GMRES with two distant clusters.
 With these settings, Table~\ref{tab.cluster.2x50} shows
 that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
 of one GFlops, an efficiency of about \np[\%]{40} is
 With these settings, Table~\ref{tab.cluster.2x50} shows
 that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
 of one GFlops, an efficiency of about \np[\%]{40} is

-obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
+obtained in asynchronous mode for a matrix size of $62^3$ elements. It is noticed that the result remains

 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By
 increasing the matrix size up to 100 elements, it was necessary to increase the
 CPU power of \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency.  Maintaining such processor power but increasing network throughput inter cluster up to
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By
 increasing the matrix size up to 100 elements, it was necessary to increase the
 CPU power of \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency.  Maintaining such processor power but increasing network throughput inter cluster up to