X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/f99a638c921635746c3df9d45c46fe345f57a074..fd6a9d41eaf24ef22ee658eb5da80ca4ea0df577:/paper.tex

diff --git a/paper.tex b/paper.tex
index e60e242..42f4b5d 100644
--- a/paper.tex
+++ b/paper.tex
@@ -465,19 +465,19 @@ and  between distant  clusters.  This parameter is application dependent.
 
 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.
+method. With a synchronous  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.\\
 
 
-\subsubsection{Execution of the the algorithms on various computational grid
-architecture and scaling up the input matrix size}
+\subsubsection{Execution of the algorithms on various computational grid
+architectures and scaling up the input matrix size}
 \ \\
 % environment
 
@@ -501,9 +501,9 @@ architecture and scaling up the input matrix size}
 
 
 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
+grid configurations  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}
+show for all grid configurations 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 vÃ©rifie...}
@@ -524,9 +524,9 @@ grid architectures, even  with the same number of processors  (for example, 2x16
 and  4x8). We  can  observ  the low  sensitivity  of  the Krylov multisplitting  method
 (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.
+$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.
 
-\subsubsection{Running on two different speed cluster inter-networks}
+\subsubsection{Running on two different inter-clusters network speed}
 \ \\
 
 \begin{figure} [ht!]
@@ -536,7 +536,7 @@ in the  grid: in  average, the GMRES  (resp. Multisplitting)  algorithm performs
  Grid & 2x16, 4x8\\ %\hline
  Network & N1 : bw=10Gbs-lat=8.10$^{-6}$ \\ %\hline
  - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\
- Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline 
+ Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}
 \caption{Clusters x Nodes - Networks N1 x N2}
 \end{center}
@@ -557,9 +557,10 @@ These experiments  compare the  behavior of  the algorithms  running first  on a
 speed inter-cluster  network (N1) and  also on  a less performant  network (N2).
 Figure~\ref{fig:02} 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
+performance was increased  by a factor of  $2$. The results depict  also that when
 the  network speed  drops down  (12.5\%), the  difference between  the execution
 times can reach more than 25\%. \RC{c'est pas clair : la diffÃ©rence entre quoi et quoi?}
+\DL{pas clair}
 
 \subsubsection{Network latency impacts on performance}
 \ \\
@@ -571,7 +572,7 @@ times can reach more than 25\%. \RC{c'est pas clair : la diffÃ©rence entre quoi
  Network & N1 : bw=1Gbs \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}
-\caption{Network latency impact}
+\caption{Network latency impacts}
 \end{figure}
 
 
@@ -579,20 +580,20 @@ times can reach more than 25\%. \RC{c'est pas clair : la diffÃ©rence entre quoi
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
-\caption{Network latency impact on execution time}
+\caption{Network latency impacts on execution time}
 \label{fig:03}
 \end{figure}
 
 
-According  the results  in  Figure~\ref{fig:03}, a  degradation  of the  network
-latency from 8.10$^{-6}$  to 6.10$^{-5}$ implies an absolute  time increase more
-than 75\%  (resp. 82\%) of the  execution for the classical  GMRES (resp. Krylov
+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.   In   addition,   it  appears   that  the   Krylov
 multisplitting method tolerates  more the network latency variation  with a less
 rate  increase  of  the  execution   time.   Consequently,  in  the  worst  case
-(lat=6.10$^{-5 }$), the  execution time for GMRES is almost  the double than the
+($lat=6.10^{-5 }$), the  execution time for GMRES is almost  the double than the
 time of the Krylov multisplitting, even  though, the performance was on the same
-order of magnitude with a latency of 8.10$^{-6}$.
+order of magnitude with a latency of $8.10^{-6}$.
 
 \subsubsection{Network bandwidth impacts on performance}
 \ \\
@@ -604,19 +605,17 @@ order of magnitude with a latency of 8.10$^{-6}$.
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
  \end{tabular}
-\caption{Network bandwidth impact}
+\caption{Network bandwidth impacts}
 \end{figure}
 
 
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}
-\caption{Network bandwith impact on execution time}
+\caption{Network bandwith impacts on execution time}
 \label{fig:04}
 \end{figure}
 
-
-
 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
@@ -630,7 +629,7 @@ of 40\% which is only around 24\% for classical GMRES.
 \begin{tabular}{r c }
  \hline
  Grid & 4x8\\ %\hline
- Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ 
+ 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}
