\item Execution Mode: synchronous or asynchronous.
\end{itemize}
-At last, note that the two solver algorithms have been executed with the Simgrid selector -cfg=smpi/running\_power which determine the computational power (here 19GFlops) of the simulator host machine.
+At last, note that the two solver algorithms have been executed with the Simgrid selector -cfg=smpi/running\_power which determines the computational power (here 19GFlops) of the simulator host machine.
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
\label{sec:expe}
-\subsection{Setup study and Methodology}
+\subsection{Study setup and Simulation Methodology}
To conduct our study, we have put in place the following methodology
which can be reused for any grid-enabled applications.
\textbf{Step 2} : Collect the software materials needed for the
experimentation. In our case, we have two variants algorithms for the
-resolution of three 3D-Poisson problem: (1) using the classical GMRES (Algo-1)(2) and the multisplitting method (Algo-2). In addition, Simgrid simulator has been chosen to simulate the behaviors of the
+resolution of the 3D-Poisson problem: (1) using the classical GMRES (Algo-1); (2) and the multisplitting method (Algo-2). In addition, Simgrid simulator has been chosen to simulate the behaviors of the
distributed applications. Simgrid is running on the Mesocentre datacenter in Franche-Comte University but also in a virtual machine on a laptop. \\
\textbf{Step 3} : Fix the criteria which will be used for the future
and in the other hand the execution time and the number of iterations of
the application before obtaining the convergence. \\
-\textbf{Step 4 }: Setup up the different grid testbeds environment
+\textbf{Step 4 }: Set up the different grid testbed environments
which will be simulated in the simulator tool to run the program. The
following architecture has been configured in Simgrid : 2x16 - that is a
grid containing 2 clusters with 16 hosts (processors/cores) each -, 4x8,
4x16, 8x8 and 2x50. The network has been designed to operate with a
-bandwidth equals to 10Gbits (resp. 1Gbits/s) and a latency of 8E-6
-microseconds (resp. 5E-5) for the intra-clusters links (resp.
+bandwidth equals to 10Gbits (resp. 1Gbits/s) and a latency of 8.10$^{-6}$
+microseconds (resp. 5.10$^{-5}$) for the intra-clusters links (resp.
inter-clusters backbone links). \\
\textbf{Step 5}: Conduct an extensive and comprehensive testings
within these configurations in varying the key parameters, especially
the CPU power capacity, the network parameters and also the size of the
-input matrix. Note that some parameters should be fixed to be invariant to allow the
-comparison like some program input arguments. \\
+input matrix. Note that some parameters like some program input arguments should be fixed to be invariant to allow the comparison. \\
\textbf{Step 6} : Collect and analyze the output results.
receive it. Upon the network characteristics, another impacting factor
is the application dependent volume of data exchanged between the nodes
in the cluster and between distant clusters. Large volume of data can be
-transferred in transit between the clusters and nodes during the code
+transferred and transit between the clusters and nodes during the code
execution.
In a grid environment, it is common to distinguish in one hand, the
\textit{3.a Executing the algorithms on various computational grid
-architecture scaling up the input matrix size}
+architecture and scaling up the input matrix size}
\\
% environment
%\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
-The results in figure 3 show the non-variation of the number of
-iterations of classical GMRES for a given input matrix size; it is not
+In this section, we compare the algorithms performance running on various grid configuration (2x16, 4x8, 4x16 and 8x8). First, the results in figure 3 show for all grid configuration the non-variation of the number of iterations of classical GMRES for a given input matrix size; it is not
the case for the multisplitting method.
%\begin{wrapfigure}{l}{100mm}
\end{figure}
%\end{wrapfigure}
-Unless the 8x8 cluster, the time
-execution difference between the two algorithms is important when
+The execution time difference between the two algorithms is important when
comparing between different grid architectures, even with the same number of
processors (like 2x16 and 4x8 = 32 processors for example). The
experiment concludes the low sensitivity of the multisplitting method
-(compared with the classical GMRES) when scaling up to higher input
-matrix size.
+(compared with the classical GMRES) when scaling up the number of the processors in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs 40\% better (resp. 48\%) less when running from 2x16=32 to 8x8=64 processors.
-\textit{\\3.b Running on various computational grid architecture\\}
+\textit{\\3.b Running on two different speed cluster inter-networks\\}
% environment
\begin{footnotesize}
%\end{wrapfigure}
The experiments compare the behavior of the algorithms running first on
-a speed inter- cluster network (N1) and a less performant network (N2).
+a speed inter- cluster network (N1) and also on a less performant network (N2).
Figure 4 shows that end users will gain to reduce the execution time
for both algorithms in using a grid architecture like 4x16 or 8x8: the
performance was increased in a factor of 2. The results depict also that
-when the network speed drops down, the difference between the execution
+when the network speed drops down (12.5\%), the difference between the execution
times can reach more than 25\%.
\textit{\\3.c Network latency impacts on performance\\}
-The results of increasing the network bandwidth depict the improvement
-of the performance by reducing the execution time for both of the two
-algorithms (Figure 6). However, and again in this case, the multisplitting method
-presents a better performance in the considered bandwidth interval with
-a gain of 40\% which is only around 24\% for classical GMRES.
+The results of increasing the network bandwidth show the improvement
+of the performance for both of the two algorithms by reducing the execution time (Figure 6). However, and again in this case, the multisplitting method presents a better performance in the considered bandwidth interval with a gain of 40\% which is only around 24\% for classical GMRES.
\textit{\\3.e Input matrix size impacts on performance\\}
\begin{tabular}{r c }
\hline
Grid & 2x50 totaling 100 processors\\ %\hline
- Processors & 1 GFlops to 1.5 GFlops\\
+ Processors Power & 1 GFlops to 1.5 GFlops\\
Intra-Network & bw=1.25 Gbits - lat=5.10$^{-5}$ \\ %\hline
Inter-Network & bw=5 Mbits - lat=2.10$^{-2}$\\
Input matrix size & N$_{x}$ = From 62 to 150\\ %\hline
