X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/671864fc27e3f1eaeff1a01d2a0a99d047e43247..3357d4486bff13d056f39c12f3852ef9c3dbe45b:/hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 29eca38..d376194 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -72,6 +72,7 @@
 
 \RC{Ordre des auteurs pas définitif.}
 \begin{abstract}
+\AG{L'abstract est AMHA incompréhensible et ne donne pas envie de lire la suite.}
 In recent years, the scalability of large-scale implementation in a 
 distributed environment of algorithms becoming more and more complex has 
 always been hampered by the limits of physical computing resources 
@@ -151,11 +152,11 @@ approach of the simulation of AIAC algorithms using a simulation tool (i.e. the
 SimGrid toolkit~\cite{SimGrid}). Second, we confirm the effectiveness of
 asynchronous mode algorithms by comparing their performance with the synchronous
 mode. More precisely, we had implemented a program for solving large
-non-symmetric linear system of equations by numerical method GMRES (Generalized
-Minimal Residual) []\AG[]{[]?}\LZK[]{\cite{ref1}}.\LZK{Problème traité dans le papier est symétrique ou asymétrique? (Poisson 3D symétrique?)} We show, that with minor modifications of the
+linear system of equations by numerical method GMRES (Generalized
+Minimal Residual) \cite{ref1}. We show, that with minor modifications of the
 initial MPI code, the SimGrid toolkit allows us to perform a test campaign of a
 real AIAC application on different computing architectures. The simulated
-results we obtained are in line with real results exposed in ??\AG[]{??}.
+results we obtained are in line with real results exposed in ??\AG[]{ref?}.
 SimGrid had allowed us to launch the application from a modest computing
 infrastructure by simulating different distributed architectures composed by
 clusters nodes interconnected by variable speed networks.  With selected
@@ -165,6 +166,9 @@ in the simulated environment, the experimental results have demonstrated not
 only the algorithm convergence within a reasonable time compared with the
 physical environment performance, but also a time saving of up to \np[\%]{40} in
 asynchronous mode.
+\AG{Il faudrait revoir la phrase précédente (couper en deux?).  Là, on peut
+  avoir l'impression que le gain de \np[\%]{40} est entre une exécution réelle
+  et une exécution simulée!}
 
 This article is structured as follows: after this introduction, the next  section will give a brief description of
 iterative asynchronous model.  Then, the simulation framework SimGrid is presented with the settings to create various
@@ -187,7 +191,9 @@ times generated by synchronizations are very penalizing. One way to overcome thi
 \textit{Asynchronous Iterations~-- Asynchronous Communications (AIAC)} model. Here, local computations do not need to
 wait for required data. Processors can then perform their iterations with the data present at that time. Figure~\ref{fig:aiac}
 illustrates this model where the gray blocks represent the computation phases, the white spaces the idle
-times and the arrows the communications. With this algorithmic model, the number of iterations required before the
+times and the arrows the communications.
+\AG{There are no ``white spaces'' on the figure.}
+With this algorithmic model, the number of iterations required before the
 convergence is generally greater than for the two former classes. But, and as detailed in~\cite{bcvc06:ij}, AIAC
 algorithms can significantly reduce overall execution times by suppressing idle times due to synchronizations especially
 in a grid computing context.
@@ -252,8 +258,11 @@ with their computing power, the interconnection links with their bandwidth and
 latency, and the routing strategy.  The simulated running time of the
 application is computed according to these properties.
 
+%%% TODO: add some words+refs about SimGrid's accuracy and scalability.}
+
 \AG{Faut-il ajouter quelque-chose ?} 
-\CER{Comme tu as décrit la plateforme d'exécution, on peut ajouter éventuellement le fichier XML contenant des hosts dans les clusters formant la grille} 
+\CER{Comme tu as décrit la plateforme d'exécution, on peut ajouter éventuellement le fichier XML contenant des hosts dans les clusters formant la grille
+  \AG{Bof.}}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
@@ -331,17 +340,31 @@ Algorithm on Figure~\ref{algo:01} shows the main key points of the multisplittin
 \label{fig:4.1}
 \end{figure}
 
-The global convergence of the asynchronous multisplitting solver is detected when the clusters of processors have all converged locally. We implemented the global convergence detection process as follows. On each cluster a master 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 $i$ sets the token to {\it True} if the local convergence is achieved or to {\it False} otherwise, and sends it to master processor $i+1$. Finally, the global convergence is detected when the master of cluster 1 receives from the master of cluster $L$ a token set to {\it True}. In this case, the master of cluster 1 broadcasts a stop message to masters of other clusters. In this work, the local convergence on each cluster $l$ is detected when the following condition is satisfied
+The global convergence of the asynchronous multisplitting solver is detected
+when the clusters of processors have all converged locally. We implemented the
+global convergence detection process as follows. On each cluster a master
+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 $i$
+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
+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,
+the local convergence on each cluster $l$ is detected when the following
+condition is satisfied
 \begin{equation*}
   (k\leq \MI) \text{ or } (\|X_l^k - X_l^{k+1}\|_{\infty}\leq\epsilon)
 \end{equation*}
-where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the tolerance threshold of the error computed between two successive local solution $X_l^k$ and $X_l^{k+1}$. 
+where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the
+tolerance threshold of the error computed between two successive local solution
+$X_l^k$ and $X_l^{k+1}$.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 We did not encounter major blocking problems when adapting the multisplitting algorithm previously described to a simulation environment like SimGrid unless some code 
-debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between the six neighbors of each point (left,right,front,behind,top,down) in a cubic partitionned submatrix within a cluster or between clusters, \CER{J'ai rajouté quelques précisions mais serait-il nécessaire de décrire a ce niveau la discrétisation 3D ?}
-\LZK{Non ce n'est pas nécessaire. A ce niveau, on décrit l'algorithme général de multisplitting. Donc, je pense qu'il est préférable de ne pas préciser le schéma de communication qui peut changer selon le type de problème. \\ {\bf Par exemple: Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters}}
-the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. In synchronous 
+debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters, the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. In synchronous 
 mode, the execution of the program raised no particular issue but in asynchronous mode, the review of the sequence of MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions
 and with the addition of the primitive MPI\_Test was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm.
 \CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async}
@@ -405,7 +428,7 @@ u^{k+1}(x,y,z)= & u^k(x,y,z) - \frac{1}{6}\times\\
 \end{equation} 
 where the iteration matrix $A$ of size $N_x\times N_y\times N_z$ of the discretized linear system is sparse, symmetric and positive definite. 
 
-The parallel solving of the 3D Poisson problem with our multisplitting method requires a data partitioning of the problem between clusters and between processors within a cluster. We have chosen the 3D partitioning instead of the row-by-row partitioning in order to reduce the data exchanges at sub-domain boundaries. Figure~\ref{fig:4.2} shows an example of the data partitioning of the 3D Poisson problem between two clusters of processors, where each sub-problem is assigned to a processor. In this context, a processor has at most six neighbors within a cluster of in distant clusters with which it shares data at sub-domain boundaries. 
+The parallel solving of the 3D Poisson problem with our multisplitting method requires a data partitioning of the problem between clusters and between processors within a cluster. We have chosen the 3D partitioning instead of the row-by-row partitioning in order to reduce the data exchanges at sub-domain boundaries. Figure~\ref{fig:4.2} shows an example of the data partitioning of the 3D Poisson problem between two clusters of processors, where each sub-problem is assigned to a processor. In this context, a processor has at most six neighbors within a cluster or in distant clusters with which it shares data at sub-domain boundaries. 
 
 \begin{figure}[!t]
 \centering