suite

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 397decc12af88aba0e11d0f4c954cde9f731e27d..f1f47bfdab19a0b0a5386607d55dd3b16c737738 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -317,10 +317,12 @@ suppress all global variables by replacing  them with local variables or using a
 Simgrid      selector       called      "runtime       automatic      switching"
 (smpi/privatize\_global\_variables). Indeed, global  variables can generate side
 effects on runtime between the threads running in the same process, generated by
 Simgrid      selector       called      "runtime       automatic      switching"
 (smpi/privatize\_global\_variables). Indeed, global  variables can generate side
 effects on runtime between the threads running in the same process, generated by

-Simgrid  to simulate the  grid environment.  \RC{On vire cette  phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
-last modification on the  MPI program pointed out for some  cases, the review of
-the sequence of  the MPI\_Isend, MPI\_Irecv and  MPI\_Waitall instructions which
-might cause an infinite loop.
+Simgrid  to simulate the  grid environment.
+
+%\RC{On vire cette  phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
+%last modification on the  MPI program pointed out for some  cases, the review of
+%the sequence of  the MPI\_Isend, MPI\_Irecv and  MPI\_Waitall instructions which
+%might cause an infinite loop.

 
 
 \paragraph{Simgrid Simulator parameters}
 
 
 \paragraph{Simgrid Simulator parameters}


@@ -350,7 +352,7 @@ In addition, the following arguments are given to the programs at runtime:
        \item matrix diagonal value = 6.0 for synchronous Krylov multisplitting experiments and 6.2 for asynchronous block Jacobi experiments; \RC{CE tu vérifies, je dis ca de tête}
        \item matrix off-diagonal value;
        \item execution mode: synchronous or asynchronous;
        \item matrix diagonal value = 6.0 for synchronous Krylov multisplitting experiments and 6.2 for asynchronous block Jacobi experiments; \RC{CE tu vérifies, je dis ca de tête}
        \item matrix off-diagonal value;
        \item execution mode: synchronous or asynchronous;

-       \RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les  arguments pour CGLS ci dessous}
+       \RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les  arguments pour CGLS ci dessous} \RC{Vu que tu n'as pas fait varier ce paramètre, on peut ne pas en parler}

        \item Size of matrix S;
        \item Maximum number of iterations and tolerance threshold for CGLS. 
 \end{itemize}
        \item Size of matrix S;
        \item Maximum number of iterations and tolerance threshold for CGLS. 
 \end{itemize}


@@ -363,7 +365,10 @@ It should also be noticed that both solvers have been executed with the Simgrid
 \section{Experimental Results}
 \label{sec:expe}
 
 \section{Experimental Results}
 \label{sec:expe}
 

-In this section, experiments for both Multisplitting algorithms are reported. First the problem used in our experiments is described.
+In this section, experiments for both Multisplitting algorithms are reported. First the 3D Poisson problem used in our experiments is described.
+
+\subsection{3D Poisson}
+

 
 We use our two-stage algorithms to solve the well-known Poisson problem $\nabla^2\phi=f$~\cite{Polyanin01}. In three-dimensional Cartesian coordinates in $\mathbb{R}^3$, the problem takes the following form
 \begin{equation}
 
 We use our two-stage algorithms to solve the well-known Poisson problem $\nabla^2\phi=f$~\cite{Polyanin01}. In three-dimensional Cartesian coordinates in $\mathbb{R}^3$, the problem takes the following form
 \begin{equation}


@@ -377,16 +382,13 @@ such that
 where the real-valued function $\phi(x,y,z)$ is the solution sought, $f(x,y,z)$ is a known function and $\Omega=[0,1]^3$. The 3D discretization of the Laplace operator $\nabla^2$ with the finite difference scheme includes 7 points stencil on the computational grid. The numerical approximation of the Poisson problem on three-dimensional grid is repeatedly computed as $\phi=\phi^\star$ such that      
 \begin{equation}
 \begin{array}{ll}
 where the real-valued function $\phi(x,y,z)$ is the solution sought, $f(x,y,z)$ is a known function and $\Omega=[0,1]^3$. The 3D discretization of the Laplace operator $\nabla^2$ with the finite difference scheme includes 7 points stencil on the computational grid. The numerical approximation of the Poisson problem on three-dimensional grid is repeatedly computed as $\phi=\phi^\star$ such that      
 \begin{equation}
 \begin{array}{ll}

-\phi^\star(x,y,z)= & \frac{1}{6}(\phi(x-h,y,z)+\phi(x+h,y,z) \\
-                  & +\phi(x,y-h,z)+\phi(x,y+h,z) \\
-                  & +\phi(x,y,z-h)+\phi(x,y,z+h)\\
-                  & -h^2f(x,y,z))
+\phi^\star(x,y,z)=&\frac{1}{6}(\phi(x-h,y,z)+\phi(x,y-h,z)+\phi(x,y,z-h)\\&+\phi(x+h,y,z)+\phi(x,y+h,z)+\phi(x,y,z+h)\\&-h^2f(x,y,z))

 \end{array}
 \label{eq:08}
 \end{equation}
 until convergence where $h$ is the grid spacing between two adjacent elements in the 3D computational grid. 
 
 \end{array}
 \label{eq:08}
 \end{equation}
 until convergence where $h$ is the grid spacing between two adjacent elements in the 3D computational grid. 
 

-In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic sub-problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 
+In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic block of the problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 

 
 \subsection{Study setup and Simulation Methodology}
 
 
 \subsection{Study setup and Simulation Methodology}
 


@@ -459,30 +461,28 @@ transit between the clusters and nodes during the code execution.
  speed.  The network  between distant  clusters might  be a  bottleneck for  the
  global performance of the application.
 
  speed.  The network  between distant  clusters might  be a  bottleneck for  the
  global performance of the application.
 

-\subsection{Comparing GMRES and Multisplitting algorithms in
-synchronous mode}
+\subsection{Comparison of GMRES and Krylov Multisplitting algorithms in synchronous mode}

 
 

-In the scope of this paper, our first objective is to demonstrate the
-Algo-2 (Multisplitting method) shows a better performance in grid
-architecture compared with Algo-1 (Classical GMRES) both running in
-\textit{synchronous mode}. Better algorithm performance
-should means a less number of iterations output and a less execution time
-before reaching the convergence. For a systematic study, the experiments
-should figure out that, for various grid parameters values, the
-simulator will confirm the targeted outcomes, particularly for poor and
-slow networks, focusing on the impact on the communication performance
-on the chosen class of algorithm.
+In the scope  of this paper, our  first objective is to analyze  when the Krylov
+Multisplitting  method   has  better  performances  than   the  classical  GMRES
+method. With an  iterative method, better performances mean a  smaller number of
+iterations and execution time before reaching the convergence.  For a systematic
+study,  the experiments  should figure  out  that, for  various grid  parameters
+values, the simulator will confirm  the targeted outcomes, particularly for poor
+and slow  networks, focusing on the  impact on the communication  performance on
+the chosen class of algorithm.

 
 The following paragraphs present the test conditions, the output results
 and our comments.\\
 
 
 
 The following paragraphs present the test conditions, the output results
 and our comments.\\
 
 

-\textit{3.a Executing the algorithms on various computational grid
+\subsubsection{Execution of the the algorithms on various computational grid

 architecture and scaling up the input matrix size}
 architecture and scaling up the input matrix size}

-\\
-
+\ \\

 % environment
 % environment

-\begin{footnotesize}
+
+\begin{figure} [ht!]
+\begin{center}

 \begin{tabular}{r c }
  \hline
  Grid & 2x16, 4x8, 4x16 and 8x8\\ %\hline
 \begin{tabular}{r c }
  \hline
  Grid & 2x16, 4x8, 4x16 and 8x8\\ %\hline


@@ -490,26 +490,34 @@ architecture and scaling up the input matrix size}
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
  - &  N$_{x}$ x N$_{y}$ x N$_{z}$  =170 x 170 x 170    \\ \hline
  \end{tabular}
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
  - &  N$_{x}$ x N$_{y}$ x N$_{z}$  =170 x 170 x 170    \\ \hline
  \end{tabular}

-Table 1 : Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \\
+\caption{Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \RC{je ne comprends pas la légende... Ca ne serait pas plutot Characteristics of cluster (mais il faudrait lui donner un nom)}}
+\end{center}
+\end{figure}

 
 

-\end{footnotesize}

 
 
 
 %\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
 
 
 
 
 
 %\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
 
 

-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.
+In this  section, we analyze the  performences of algorithms running  on various
+grid configuration  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}
+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.
+
+\RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
+\RC{Les légendes ne sont pas explicites...}
+

 
 

-%\begin{wrapfigure}{l}{100mm}

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

-\centering
-\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
-\caption{Cluster x Nodes N$_{x}$=150 and N$_{x}$=170}
-%\label{overflow}}
+  \begin{center}
+    \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
+  \end{center}
+  \caption{Cluster x Nodes N$_{x}$=150 and N$_{x}$=170}
+  \label{fig:01}

 \end{figure}
 \end{figure}

-%\end{wrapfigure}
+

 
 The execution time difference between the two algorithms is important when
 comparing between different grid architectures, even with the same number of
 
 The execution time difference between the two algorithms is important when
 comparing between different grid architectures, even with the same number of