X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/8a9c44cff1e89fecee221a84aa00ac7be4d7b827..757a3d8174e2736033052c4acc64de277cd66e11:/hpcc.tex?ds=sidebyside

diff --git a/hpcc.tex b/hpcc.tex
index dc76042..da2ec91 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -1,4 +1,3 @@
-
 \documentclass[conference]{IEEEtran}
 
 \usepackage[T1]{fontenc}
@@ -664,12 +663,12 @@ asynchronous multisplitting  compared to GMRES with two distant clusters.
 With these settings, Table~\ref{tab.cluster.2x50} shows
 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
+obtained in asynchronous mode for a matrix size of $62^3$ 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
-increasing the matrix size up to 100 elements, it was necessary to increase the
+increasing the matrix size up to $100^3$ elements, it was necessary to increase the
 CPU power of \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency.  Maintaining such processor power but increasing network throughput inter cluster up to
 \np[Mbit/s]{50}, the result of efficiency with a relative gain of 2.5 is obtained with
-high external precision of \np{E-11} for a matrix size from 110 to 150 side
+high external precision of \np{E-11} for a matrix size from $110^3$ to $150^3$ side
 elements.
 
 %For the 3 clusters architecture including a total of 100 hosts,
@@ -704,7 +703,7 @@ reach the following two objectives:
 
 \item To test the combination of the cluster and network specifications permitting to execute an asynchronous algorithm faster than a synchronous one.
 \end{enumerate}
-Our results have shown that with two distant clusters, the asynchronous multisplitting is faster to \np[\%]{40} compared to the synchronous GMRES method
+Our results have shown that with two distant clusters, the asynchronous multisplitting method is faster to \np[\%]{40} compared to the synchronous GMRES method
 which is not negligible for solving complex practical problems with more 
 and more increasing size.
 
@@ -715,7 +714,7 @@ tool to run efficiently an iterative parallel algorithm in asynchronous
 mode in a grid architecture. 
 
 In future works, we plan to extend our experimentations to larger scale platforms by increasing the number of computing cores and the number of clusters. 
-We will also have to increase the size of the input problem which will require the use of a more powerful simulation platform. At last, we expect to compare our simulation results to real execution results on real architectures in order to experimentally validate our study.
+We will also have to increase the size of the input problem which will require the use of a more powerful simulation platform. At last, we expect to compare our simulation results to real execution results on real architectures in order to experimentally validate our study. Finally, we also plan to study other problems with the multisplitting method and other asynchronous iterative methods.
 
 \section*{Acknowledgment}