X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/96e726f9524ffdb8eaead14a943d80870ea1da65..3b175ad474db1b6208b1115e91d0b5bfde6f0288:/paper.tex

diff --git a/paper.tex b/paper.tex
index c3cfdbb..60fcffc 100644
--- a/paper.tex
+++ b/paper.tex
@@ -442,8 +442,6 @@ In this section, experiments for both multisplitting algorithms are reported. Fi
 
 \subsection{The 3D Poisson problem}
 \label{3dpoisson}
-
-
 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}
 \frac{\partial^2}{\partial x^2}\phi(x,y,z)+\frac{\partial^2}{\partial y^2}\phi(x,y,z)+\frac{\partial^2}{\partial z^2}\phi(x,y,z)=f(x,y,z)\mbox{~in the domain~}\Omega
@@ -489,13 +487,7 @@ and on the other hand the execution time and the number of iterations to reach t
 simulated in the  simulator tool to run the program.  The following architectures
 have been configured in SimGrid : 2$\times$16, 4$\times$8, 4$\times$16, 8$\times$8 and 2$\times$50. The first number
 represents the number  of clusters in the grid and  the second number represents
-the number  of hosts (processors/cores)  in each  cluster. The network has been
-designed to  operate with a bandwidth  equals to 10Gbits (resp.  1Gbits/s) and a
-latency of 8.10$^{-6}$ seconds (resp.  5.10$^{-5}$) for the intra-clusters links
-(resp.  inter-clusters backbone links).  \\
-
-\LZK{Il me semble que le bw et lat des deux rÃ©seaux varient dans les expÃ©s d'une simu Ã  l'autre. On vire la derniÃ¨re phrase?}
-\RC{il me semble qu'on peut laisser ca}
+the number  of hosts (processors/cores)  in each  cluster. \\
 
 \textbf{Step 5}: Conduct an extensive and comprehensive testings
 within these configurations by varying the key parameters, especially
@@ -536,26 +528,17 @@ and  between distant  clusters.  This parameter is application dependent.
  a lower speed.  The network  between distant  clusters might  be a  bottleneck
  for  the global performance of the application.
 
-\subsection{Comparison of GMRES and Krylov two-stage algorithms in synchronous mode}
-
-In the scope  of this paper, our  first objective is to analyze  when the 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 convergence.
-In what follows, we will present the test conditions, the output results and our comments.
-
-%%RAPH : on vire ca, c'est pas clair et pas important
-%For a systematic study,  the experiments  should figure  out  that, for  various
-%grid  parameters values, the simulator will confirm Multisplitting method  better performance compared to classical GMRES, particularly on poor and slow networks.
-%\LZK{Pas du tout claire la derniÃ¨re phrase (For a systematic...)!!}
-%\RCE { Reformule autrement}
 
+\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 convergence. In what follows, we will present the test conditions, the output results and our comments. For all simulations, we fix the network parameters of the intra-cluster links: the bandwidth $bw$=10Gbs and the latency $lat$=8$\times$10$^{-6}$.
 
-
-%\subsubsection{Execution of the algorithms on various computational grid architectures and scaling up the input matrix size}
 \subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
-\ \\
+\  \\
 % environment
 
+ The network of intra-clusters links has been
+designed to  operate with a bandwidth  equals to 10Gbits and a latency of 8$\times$10$^{-6}$ seconds. \\
+
 \RC{Je ne comprends plus rien CE : pourquoi dans 5.4.1 il y a 2 network et aussi dans 5.4.2. Quelle est la diffÃ©rence? Dans la figure 3 de la section 5.4.1 pourquoi il n'y a pas N1 et N2?}
 
 \begin{table} [ht!]
@@ -644,9 +627,9 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 \begin{figure} [htbp]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
-\caption{Various grid configurations with networks N1 vs N2
-\AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}
-\RCE{Corrige}
+\caption{Various grid configurations with networks N1 vs N2}
+%\AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}
+%\RCE{Corrige}
 \label{fig:02}
 \end{figure}
 %\end{wrapfigure}
@@ -670,18 +653,19 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 \begin{figure} [htbp]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
-\caption{Network latency impacts on execution time
-\AG{\np{E-6}}}
+\caption{Network latency impacts on execution time}
+%\AG{\np{E-6}}}
 \label{fig:03}
 \end{figure}
 
-According to  the results of  Figure~\ref{fig:03}, a degradation of  the network
-latency from  $8.10^{-6}$ to  $6.10^{-5}$ implies an  absolute time  increase of
-more  than $75\%$  (resp.  $82\%$)  of the  execution  for  the classical  GMRES
-(resp.  Krylov multisplitting)  algorithm which means that the GMRES seems tolerate more the network latency variation with a less  rate increase  of  the  execution time. However, the execution time factor between the two algorithms varies from 2.2 to 1.5 times with a network latency decreasing from $8.10^{-6}$ to  $6.10^{-5}$.
+In Table~\ref{tab:03}, parameters  for the influence of the  network latency are
+reported.  According to the results of Figure~\ref{fig:03}, a degradation of the
+network  latency  from  $8.10^{-6}$  to $6.10^{-5}$  implies  an  absolute  time
+increase of more than $75\%$ (resp.   $82\%$) of the execution for the classical
+GMRES  (resp.   Krylov  multisplitting)  algorithm. The  execution  time  factor
+between the two algorithms  varies from 2.2 to 1.5 times  with a network latency
+decreasing from $8.10^{-6}$ to $6.10^{-5}$.
 
-\RC{Les  2  prÃ©cÃ©dentes phrases  me  semblent en contradiction....}  
-\RCE{Reformule}
 
 \subsubsection{Network bandwidth impacts on performance}
 \ \\
@@ -694,8 +678,9 @@ more  than $75\%$  (resp.  $82\%$)  of the  execution  for  the classical  GMRES
                           & $lat$= 5.10$^{-5}$ second \\
  Input matrix size & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline \\
  \end{tabular}
-\caption{Test conditions: Network bandwidth impacts\RC{Qu'est ce qui varie ici? Il n'y a pas de variation dans le tableau}}
-\RCE{C est le bw}
+\caption{Test conditions: Network bandwidth impacts}
+%  \RC{Qu'est ce qui varie ici? Il n'y a pas de variation dans le tableau}
+%\RCE{C est le bw}
 \label{tab:04}
 \end{table}
 
