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[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
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--- a/hpcc.tex
+++ b/hpcc.tex
@@ -476,15 +476,14 @@ study that the results depend on the following parameters:
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the
 \item Hosts processors power (GFlops) can also influence on the results.
 \item Finally, when submitting job batches for execution, the arguments values
   passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the

-  algorithm but also to get the main objective in getting an execution time in asynchronous communication less than in
-  synchronous mode. The ratio between the simulated execution time of synchronous GMRES algorithm
-  compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
-  our objective running the algorithm in SimGrid is to obtain a relative gain
-  greater than 1.
-\end{itemize}
+  algorithm but also to get the main objective in getting an execution time with the asynchronous multisplitting  less than with synchronous GMRES. 
+  \end{itemize}

 
 

+The ratio between the simulated execution time of synchronous GMRES algorithm
+compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
+our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.

 A priori, obtaining a relative gain greater than 1 would be difficult in a local
 A priori, obtaining a relative gain greater than 1 would be difficult in a local

-area network configuration where the synchronous mode will take advantage on the
+area network configuration where the synchronous GMRES method will take advantage on the

 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the
 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the


@@ -509,7 +508,8 @@ $\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
 
 \begin{table}[!t]
   \centering
 
 \begin{table}[!t]
   \centering

-  \caption{2 clusters, each with 50 nodes}
+  \caption{Relative gain  of the multisplitting algorithm compared  to GMRES for
+    different configurations with 2 clusters, each one composed of 50 nodes.}

   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}
   \label{tab.cluster.2x50}
 
   \begin{mytable}{5}


@@ -657,10 +657,10 @@ Note that the program was run with the following parameters:
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the

-asynchronous performance compared to the synchronous mode.
+asynchronous multisplitting  compared to GMRES with two distant clusters.

 
 With these settings, Table~\ref{tab.cluster.2x50} shows
 
 With these settings, Table~\ref{tab.cluster.2x50} shows

-that after a deterioration of inter cluster network with a bandwidth of \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
+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
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By
 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
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By