X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/549b5689e29828e7d7a2ea9dc3af2da5fa46555e..47cd097a55beb36dbcbbdce56442ca355531d1a8:/hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index cb85b00..8a1dfe8 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -395,9 +395,9 @@ processor is designated (for example the processor with rank 1) and masters of
 all clusters are interconnected by a virtual unidirectional ring network (see
 Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
 the virtual ring from a master processor to another until the global convergence
-is achieved. So starting from the cluster with rank 1, each master processor $i$
+is achieved. So starting from the cluster with rank 1, each master processor $\ell$
 sets the token to \textit{True} if the local convergence is achieved or to
-\textit{False} otherwise, and sends it to master processor $i+1$. Finally, the
+\textit{False} otherwise, and sends it to master processor $\ell+1$. Finally, the
 global convergence is detected when the master of cluster 1 receives from the
 master of cluster $L$ a token set to \textit{True}. In this case, the master of
 cluster 1 broadcasts a stop message to masters of other clusters. In this work,
@@ -483,7 +483,7 @@ The ratio between the simulated execution time of synchronous GMRES algorithm
 compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
 our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.
 A priori, obtaining a relative gain greater than 1 would be difficult in a local
-area network configuration where the synchronous mode will take advantage on the
+area network configuration where the synchronous GMRES method will take advantage on the
 rapid exchange of information on such high-speed links. Thus, the methodology
 adopted was to launch the application on a clustered network. In this
 configuration, degrading the inter-cluster network performance will penalize the
@@ -657,10 +657,10 @@ Note that the program was run with the following parameters:
 
 After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
 the results have given a relative gain more than 2.5, showing the effectiveness of the
-asynchronous multiplsitting  compared to GMRES with two distant clusters.
+asynchronous multisplitting  compared to GMRES with two distant clusters.
 
 With these settings, Table~\ref{tab.cluster.2x50} shows
-that after a deterioration of inter cluster network with a bandwidth of \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
+that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5} and a latency in order of one hundredth of millisecond and a processor power
 of one GFlops, an efficiency of about \np[\%]{40} is
 obtained in asynchronous mode for a matrix size of 62 elements. It is noticed that the result remains
 stable even we vary the residual error precision from \np{E-5} to \np{E-9}. By