X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/cb07dd536bdfe2ca24b31fdd3d95195cde19513b..18a590b4593843d38f5012c20a06f000388301cf:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index c198158..b9d11d4 100644
--- a/paper.tex
+++ b/paper.tex
@@ -45,6 +45,8 @@
   \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
 \newcommand{\RCE}[2][inline]{%
   \todo[color=yellow!10,#1]{\sffamily\textbf{RCE:} #2}\xspace}
+\newcommand{\DL}[2][inline]{%
+    \todo[color=pink!10,#1]{\sffamily\textbf{DL:} #2}\xspace}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
@@ -344,18 +346,16 @@ nodes/processors for each cluster).
 In addition, the following arguments are given to the programs at runtime:
 
 \begin{itemize}
-	\item maximum number of inner and outer iterations;
-	\item inner and outer precisions;
-	\item maximum number of the GMRES restarts in the Arnorldi process;
-	\item maximum number of iterations and the tolerance threshold in classical GMRES;
-	\item tolerance threshold for outer and inner-iterations;
-	\item matrix size (N$_{x}$, N$_{y}$ and N$_{z}$) respectively on $x, y, z$ axis;
-	\item matrix diagonal value is fixed to $6.0$ for synchronous Krylov multisplitting experiments and $6.2$ for asynchronous block Jacobi experiments; \RC{CE tu vÃ©rifies, je dis ca de tÃªte}
-	\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} \RC{Vu que tu n'as pas fait varier ce paramÃ¨tre, on peut ne pas en parler}
-	\item Size of matrix S;
-	\item Maximum number of iterations and tolerance threshold for CGLS.
+	\item maximum number of inner iterations $\MIG$ and outer iterations $\MIM$,
+	\item inner precision $\TOLG$ and outer precision $\TOLM$,
+	\item matrix sizes of the 3D Poisson problem: N$_{x}$, N$_{y}$ and N$_{z}$ on axis $x$, $y$ and $z$ respectively,
+	\item matrix diagonal value is fixed to $6.0$ for synchronous Krylov multisplitting experiments and $6.2$ for asynchronous block Jacobi experiments, \RC{CE tu vÃ©rifies, je dis ca de tÃªte}
+	\item matrix off-diagonal value is fixed to $-1.0$,
+	\item number of vectors in matrix $S$ (i.e. value of $s$),
+	\item maximum number of iterations $\MIC$ and precision $\TOLC$ for CGLS method,
+        \item maximum number of iterations and precision for the classical GMRES method,
+        \item maximum number of restarts for the Arnorldi process in GMRES method,
+      	\item execution mode: synchronous or asynchronous,
 \end{itemize}
 
 It should also be noticed that both solvers have been executed with the Simgrid selector \texttt{-cfg=smpi/running\_power} which determines the computational power (here 19GFlops) of the simulator host machine.
@@ -620,7 +620,7 @@ The results  of increasing  the network  bandwidth show  the improvement  of the
 performance  for   both  algorithms   by  reducing   the  execution   time  (see
 Figure~\ref{fig:04}). However,  in this  case, the Krylov  multisplitting method
 presents a better  performance in the considered bandwidth interval  with a gain
-of 40\% which is only around 24\% for classical GMRES.
+of $40\%$ which is only around $24\%$ for the classical GMRES.
 
 \subsubsection{Input matrix size impacts on performance}
 \ \\
@@ -632,27 +632,27 @@ of 40\% which is only around 24\% for classical GMRES.
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\
  Input matrix size & N$_{x}$ = From 40 to 200\\ \hline
  \end{tabular}
-\caption{Input matrix size impact}
+\caption{Input matrix size impacts}
 \end{figure}
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{pb_size_impact_on_execution_time.pdf}
-\caption{Problem size impact on execution time}
+\caption{Problem size impacts on execution time}
 \label{fig:05}
 \end{figure}
 
-In these experiments, the input matrix size  has been set from N$_{x}$ = N$_{y}$
-= N$_{z}$ = 40 to 200 side elements  that is from 40$^{3}$ = 64.000 to 200$^{3}$
-= 8,000,000  points. Obviously, as  shown in Figure~\ref{fig:05},  the execution
+In these experiments, the input matrix size  has been set from $N_{x} = N_{y}
+= N_{z} = 40$ to $200$ side elements  that is from $40^{3} = 64.000$ to $200^{3}
+= 8,000,000$  points. Obviously, as  shown in Figure~\ref{fig:05},  the execution
 time for  both algorithms increases when  the input matrix size  also increases.
 But the interesting results are:
 \begin{enumerate}
-  \item the drastic increase (300 times) \RC{Je ne vois pas cela sur la figure}
+  \item the drastic increase ($300$ times) \RC{Je ne vois pas cela sur la figure}
 of the  number of  iterations needed  to reach the  convergence for  the classical
-GMRES algorithm when  the matrix size go beyond N$_{x}$=150;
-\item the  classical GMRES execution time  is almost the double  for N$_{x}$=140
+GMRES algorithm when  the matrix size go beyond $N_{x}=150$;
+\item the  classical GMRES execution time  is almost the double  for $N_{x}=140$
   compared with the Krylov multisplitting method.
 \end{enumerate}
 
@@ -661,7 +661,7 @@ targeted environment for the application deployment when focusing on the problem
 size scale up.  It  should be noticed that the same test has  been done with the
 grid 2x16 leading to the same conclusion.
 
-\subsubsection{CPU Power impact on performance}
+\subsubsection{CPU Power impacts on performance}
 
 \begin{figure} [ht!]
 \centering
@@ -671,22 +671,26 @@ grid 2x16 leading to the same conclusion.
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ = 150 x 150 x 150\\ \hline
  \end{tabular}
-\caption{CPU Power impact}
+\caption{CPU Power impacts}
 \end{figure}
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cpu_power_impact_on_execution_time.pdf}
-\caption{CPU Power impact on execution time}
+\caption{CPU Power impacts on execution time}
 \label{fig:06}
 \end{figure}
 
 Using the Simgrid  simulator flexibility, we have tried to  determine the impact
 on the  algorithms performance in  varying the CPU  power of the  clusters nodes
-from 1  to 19 GFlops.  The outputs  depicted in Figure~\ref{fig:06}  confirm the
-performance gain,  around 95\% for  both of the  two methods, after  adding more
+from $1$ to $19$ GFlops.  The outputs  depicted in Figure~\ref{fig:06}  confirm the
+performance gain,  around $95\%$ for  both of the  two methods, after  adding more
 powerful CPU.
 
+\DL{il faut une conclusion sur ces tests : ils confirment les rÃ©sultats dÃ©jÃ 
+obtenus en grandeur rÃ©elle. Donc c'est une aide prÃ©cieuse pour les dev. Pas
+besoin de dÃ©ployer sur une archi rÃ©elle}
+
 \subsection{Comparing GMRES in native synchronous mode and the multisplitting algorithm in asynchronous mode}
 
 The previous paragraphs  put in evidence the interests to  simulate the behavior
