Merge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/rce2015

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 81265832b8f3ef293ab021a567b2c5379ed20e04..8a5553037a33766770df3f15fd337bb0583042c7 100644 (file)
--- 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}
 
 \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
 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$50. The first number
 represents the number  of clusters in the grid and  the second number represents
 simulated in the  simulator tool to run the program.  The following architectures
 have been configured in SimGrid : 2$\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 réseaux varient dans les expés d'une simu à l'autre. On vire la dernière 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
 
 \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.
 
  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 dernière 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}
 \subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}

-\ \\
+\  \\

 % environment
 
 % 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 différence? Dans la figure 3 de la section 5.4.1 pourquoi il n'y a pas N1 et N2?}
 
 \begin{table} [ht!]
 \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 différence? Dans la figure 3 de la section 5.4.1 pourquoi il n'y a pas N1 et N2?}
 
 \begin{table} [ht!]