suite

diff --git a/paper.tex b/paper.tex
index 67599b9a912632d8b41122c3b57fa6a06fb8da34..43093696c090919f90204b9fc3cc29323e6bc448 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -488,7 +488,7 @@ SimGrid  to simulate the  grid environment.
 \paragraph{Simulation parameters for SimGrid}
 \  \\ \noindent  Before running  a SimGrid  benchmark, many  parameters for  the
 computation platform must be defined. For our experiments, we consider platforms
 \paragraph{Simulation parameters for SimGrid}
 \  \\ \noindent  Before running  a SimGrid  benchmark, many  parameters for  the
 computation platform must be defined. For our experiments, we consider platforms

-in which  several clusters are  geographically distant,  so there are  intra and
+in which  several clusters are  geographically distant,  so that there are  intra and

 inter-cluster communications. In the following, these parameters are described:
 
 \begin{itemize}
 inter-cluster communications. In the following, these parameters are described:
 
 \begin{itemize}


@@ -563,8 +563,8 @@ the application to be tested. Numerical parallel iterative algorithms
 have been chosen for the study in this paper. \\
 
 \textbf{Step 2}: Collect the software materials needed for the experimentation.
 have been chosen for the study in this paper. \\
 
 \textbf{Step 2}: Collect the software materials needed for the experimentation.

-In our case, we have two variants algorithms for the resolution of the
-3D-Poisson problem: (1) using the classical GMRES; (2) and the multisplitting
+In our case, we have two variants for the resolution of the
+3D-Poisson problem: (1) using the classical GMRES; (2) using the multisplitting

 method. In addition, the SimGrid simulator has been chosen to simulate the
 behaviors of the distributed applications. SimGrid is running in a virtual
 machine on a simple laptop. \\
 method. In addition, the SimGrid simulator has been chosen to simulate the
 behaviors of the distributed applications. SimGrid is running in a virtual
 machine on a simple laptop. \\


@@ -580,7 +580,7 @@ have been configured in SimGrid : 2$\times$16, 4$\times$8, 4$\times$16, 8$\times
 represents the number  of clusters in the grid and  the second number represents
 the number  of hosts (processors/cores)  in each  cluster. \\
 
 represents the number  of clusters in the grid and  the second number represents
 the number  of hosts (processors/cores)  in each  cluster. \\
 

-\textbf{Step 5}: Conduct an extensive and comprehensive testings
+\textbf{Step 5}: Conduct  extensive and comprehensive testings

 within these configurations by varying the key parameters, especially
 the CPU power capacity, the network parameters and also the size of the
 input data.  \\
 within these configurations by varying the key parameters, especially
 the CPU power capacity, the network parameters and also the size of the
 input data.  \\


@@ -600,39 +600,38 @@ Another important factor  impacting the overall performance  of the application
 is the network configuration. Two main network parameters can modify drastically
 the program output results:
 \begin{enumerate}
 is the network configuration. Two main network parameters can modify drastically
 the program output results:
 \begin{enumerate}

-\item  the network  bandwidth  ($bw$ in bits/s) also  known  as "the  data-carrying
-    capacity" of the network is defined as  the maximum of data that can transit
+\item  the network  bandwidth  ($bw$ in Gbits/s) also  known  as "the  data-carrying
+    capacity" of the network is defined as  the maximum amount of data that can transit

     from one point to another in a unit of time.
 \item the  network latency  ($lat$ in microseconds) defined as  the delay  from the
     from one point to another in a unit of time.
 \item the  network latency  ($lat$ in microseconds) defined as  the delay  from the

-  start time to send  a simple data from a source to a destination.
+  starting time to send  a simple data from a source to a destination.

 \end{enumerate}
 \end{enumerate}

-Upon  the   network  characteristics,  another  impacting   factor  is  the volume of data exchanged  between the nodes in the cluster
+Among  the   network  characteristics,  another  impacting   factor  is  the volume of data exchanged  between the nodes in the cluster

 and  between distant  clusters.  This parameter is application dependent.
 
 and  between distant  clusters.  This parameter is application dependent.
 

- In  a grid  environment, it  is common  to distinguish,  on one hand,  the
+ In  a grid  environment, it  is common  to distinguish,  on the one hand,  the

  \textit{intra-network} which refers  to the links between nodes within  a
  cluster and on  the other  hand, the  \textit{inter-network} which  is the
  backbone link  between clusters.  In   practice,  these  two   networks  have
  different   speeds. The intra-network  generally works  like a  high speed
  \textit{intra-network} which refers  to the links between nodes within  a
  cluster and on  the other  hand, the  \textit{inter-network} which  is the
  backbone link  between clusters.  In   practice,  these  two   networks  have
  different   speeds. The intra-network  generally works  like a  high speed

- local network  with a high bandwidth and very low latency. In opposite, the
- inter-network connects clusters sometime via  heterogeneous networks components
- through internet with a lower speed.  The network  between distant  clusters
+ local network  with a high bandwidth and very low latency. On the contrary, the
+ inter-network connects clusters sometimes via  heterogeneous networks components the through internet with a lower speed.  The network  between distant  clusters

  might  be a  bottleneck for  the global performance of the application.
 
 
 \subsection{Comparison between GMRES and two-stage multisplitting algorithms in
 synchronous mode}
 In the scope of this paper, our first objective is to analyze
  might  be a  bottleneck for  the global performance of the application.
 
 
 \subsection{Comparison between GMRES and two-stage multisplitting algorithms in
 synchronous mode}
 In the scope of this paper, our first objective is to analyze

-when the synchronous Krylov two-stage method has better performance than the
-classical GMRES method. With a synchronous iterative method, better performance
-means a smaller number of iterations and execution time before reaching the
+when the synchronous Krylov two-stage method has better performances than the
+classical GMRES method. With a synchronous iterative method, better performances
+mean a smaller number of iterations and execution time before reaching the

 convergence.
 
 Table~\ref{tab:01} summarizes the parameters used in the different simulations:
 the grid architectures (i.e. the number of clusters and the number of nodes per
 cluster), the network of inter-clusters backbone links and the matrix sizes of
 the 3D Poisson problem. However, for all simulations we fix the network
 convergence.
 
 Table~\ref{tab:01} summarizes the parameters used in the different simulations:
 the grid architectures (i.e. the number of clusters and the number of nodes per
 cluster), the network of inter-clusters backbone links and the matrix sizes of
 the 3D Poisson problem. However, for all simulations we fix the network

-parameters of the intra-clusters links: the bandwidth $bw$=10Gbs and the latency
+parameters of the intra-clusters links: the bandwidth $bw$=10Gbit/s and the latency

 $lat=8\mu$s. In what follows, we will present the test conditions, the output
 results and our comments.
 
 $lat=8\mu$s. In what follows, we will present the test conditions, the output
 results and our comments.
 


@@ -641,8 +640,8 @@ results and our comments.
 \begin{tabular}{ll}
 \hline
 Grid architecture                       & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\
 \begin{tabular}{ll}
 \hline
 Grid architecture                       & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\

-\multirow{2}{*}{Network inter-clusters} & $N1$: $bw$=10Gbs, $lat=8\mu$s \\
-                                        & $N2$: $bw$=1Gbs, $lat=50\mu$s \\
+\multirow{2}{*}{Network inter-clusters} & $N1$: $bw$=10Gbit/s, $lat=8\mu$s \\
+                                        & $N2$: $bw$=1Gbit/s, $lat=50\mu$s \\

 \multirow{2}{*}{Matrix size}            & $Mat1$: N$_{x}\times$N$_{y}\times$N$_{z}$=150$\times$150$\times$150\\
                                         & $Mat2$: N$_{x}\times$N$_{y}\times$N$_{z}$=170$\times$170$\times$170 \\ \hline
 \end{tabular}
 \multirow{2}{*}{Matrix size}            & $Mat1$: N$_{x}\times$N$_{y}\times$N$_{z}$=150$\times$150$\times$150\\
                                         & $Mat2$: N$_{x}\times$N$_{y}\times$N$_{z}$=170$\times$170$\times$170 \\ \hline
 \end{tabular}


@@ -705,7 +704,7 @@ efficient for distributed systems with high latency networks.
 \end{figure}
 
 \subsubsection{Network latency impacts on performances\\}
 \end{figure}
 
 \subsubsection{Network latency impacts on performances\\}

-Figure~\ref{fig:03} shows the impact of the network latency on the performances of both algorithms. The simulation is conducted on a computational grid of 2 clusters of 16 processors each (i.e. configuration 2$\times$16) interconnected by a network of bandwidth $bw$=1Gbs to solve a 3D Poisson problem of size $150^3$. According to the results, a degradation of the network latency from $8\mu$s to $60\mu$s implies an absolute execution time increase for both algorithms, but not with the same rate of degradation. The GMRES algorithm is more sensitive to the latency degradation than the Krylov two-stage algorithm.
+Figure~\ref{fig:03} shows the impact of the network latency on the performances of both algorithms. The simulation is conducted on a computational grid of 2 clusters of 16 processors each (i.e. configuration 2$\times$16) interconnected by a network of bandwidth $bw$=1Gbit/s to solve a 3D Poisson problem of size $150^3$. According to the results, a degradation of the network latency from $8\mu$s to $60\mu$s implies an absolute execution time increase for both algorithms, but not with the same rate of degradation. The GMRES algorithm is more sensitive to the latency degradation than the Krylov two-stage algorithm.

 
 \begin{figure}[ht]
 \centering
 
 \begin{figure}[ht]
 \centering


@@ -719,7 +718,7 @@ Figure~\ref{fig:03} shows the impact of the network latency on the performances
 Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of
 $2\times16$ processors interconnected by a network of latency $lat=50\mu$s to
 solve a 3D Poisson problem of size $150^3$. The results of increasing the
 Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of
 $2\times16$ processors interconnected by a network of latency $lat=50\mu$s to
 solve a 3D Poisson problem of size $150^3$. The results of increasing the

-network bandwidth from $1$Gbs to $10$Gbs show the performances improvement for
+network bandwidth from $1$Gbit/s to $10$Gbit/s show the performances improvement for

 both algorithms by reducing the execution times. However, the Krylov two-stage
 algorithm presents a better performance gain in the considered bandwidth
 interval with a gain of $40\%$ compared to only about $24\%$ for the classical
 both algorithms by reducing the execution times. However, the Krylov two-stage
 algorithm presents a better performance gain in the considered bandwidth
 interval with a gain of $40\%$ compared to only about $24\%$ for the classical