Petites corrections: partie poisson problem

diff --git a/biblio.bib b/biblio.bib
index 97de9709bfc56ae0178e583c53b3e48cb434853f..30be1066a8b2b6640f3c6351d11b0c0a525cf2a7 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -144,11 +144,10 @@ year = {2006},
 }
 
 @Article{myBCCV05c,
 }
 
 @Article{myBCCV05c,

-        author =                         {J. M. Bahi and S. Contassot-Vivier and R. Co
-uturier  and F. Vernier},
-        title =                          {A decentralized convergence detection algorithm for asynchronous parallel iterative algorithms},
-        journal =                {IEEE Transactions on Parallel and Distributed Systems},
-        year =                           {2005},
+        author = {Bahi, J.M. and Contassot-Vivier, S. and Couturier, R.  and  Vernier, F.},
+        title =  {A decentralized convergence detection algorithm for asynchronous parallel iterative algorithms},
+        journal ={IEEE Transactions on Parallel and Distributed Systems},
+        year =   {2005},

   volume = {16},
   number = {1},
   pages = {4--13},
   volume = {16},
   number = {1},
   pages = {4--13},

diff --git a/paper.tex b/paper.tex
index 397decc12af88aba0e11d0f4c954cde9f731e27d..a1c18890e2f7d30143a2fd06068c3cb6a43eddd3 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -377,16 +377,13 @@ such that
 where the real-valued function $\phi(x,y,z)$ is the solution sought, $f(x,y,z)$ is a known function and $\Omega=[0,1]^3$. The 3D discretization of the Laplace operator $\nabla^2$ with the finite difference scheme includes 7 points stencil on the computational grid. The numerical approximation of the Poisson problem on three-dimensional grid is repeatedly computed as $\phi=\phi^\star$ such that      
 \begin{equation}
 \begin{array}{ll}
 where the real-valued function $\phi(x,y,z)$ is the solution sought, $f(x,y,z)$ is a known function and $\Omega=[0,1]^3$. The 3D discretization of the Laplace operator $\nabla^2$ with the finite difference scheme includes 7 points stencil on the computational grid. The numerical approximation of the Poisson problem on three-dimensional grid is repeatedly computed as $\phi=\phi^\star$ such that      
 \begin{equation}
 \begin{array}{ll}

-\phi^\star(x,y,z)= & \frac{1}{6}(\phi(x-h,y,z)+\phi(x+h,y,z) \\
-                  & +\phi(x,y-h,z)+\phi(x,y+h,z) \\
-                  & +\phi(x,y,z-h)+\phi(x,y,z+h)\\
-                  & -h^2f(x,y,z))
+\phi^\star(x,y,z)=&\frac{1}{6}(\phi(x-h,y,z)+\phi(x,y-h,z)+\phi(x,y,z-h)\\&+\phi(x+h,y,z)+\phi(x,y+h,z)+\phi(x,y,z+h)\\&-h^2f(x,y,z))

 \end{array}
 \label{eq:08}
 \end{equation}
 until convergence where $h$ is the grid spacing between two adjacent elements in the 3D computational grid. 
 
 \end{array}
 \label{eq:08}
 \end{equation}
 until convergence where $h$ is the grid spacing between two adjacent elements in the 3D computational grid. 
 

-In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic sub-problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 
+In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic block of the problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 

 
 \subsection{Study setup and Simulation Methodology}
 
 
 \subsection{Study setup and Simulation Methodology}