détail

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index e4c77d374f9709dcde3a325c65566c6df4ab4bee..edba67f7c0fb5f612852e6fd6fe8e9c3e03d1c28 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -1,3 +1,4 @@
+
 \documentclass[conference]{IEEEtran}
 
 \usepackage[T1]{fontenc}
@@ -422,7 +423,7 @@ u =0 \text{~on~} \Gamma =\partial\Omega
 where $\nabla^2$ is the Laplace operator, $f$ and $u$ are real-valued functions, and $\Omega=[0,1]^3$. The spatial discretization with a finite difference scheme reduces problem~(\ref{eq:02}) to a system of sparse linear equations. Our multisplitting method solves the 3D Poisson problem using a seven point stencil whose the general expression could be written as
 \begin{equation}
 \begin{array}{l}
-u(x-1,y,z) + u(x,y-1,z) + u(x,y,z-1)\\+u(x+1,y,z)+u(x,y+1,z)+u(x,y,z+1) \\ -6u(x,y,z)=h^2f(x,y,z)
+u(x-1,y,z) + u(x,y-1,z) + u(x,y,z-1)\\+u(x+1,y,z)+u(x,y+1,z)+u(x,y,z+1) \\ -6u(x,y,z)=h^2f(x,y,z),
 %u(x,y,z)= & \frac{1}{6}\times [u(x-1,y,z) + u(x+1,y,z) + \\
  %         & u(x,y-1,z) + u(x,y+1,z) + \\
   %        & u(x,y,z-1) + u(x,y,z+1) - \\ & h^2f(x,y,z)],
@@ -646,8 +647,8 @@ Note that the program was run with the following parameters:
 \item Maximum number of iterations;
 \item Precisions on the residual error;
 \item Matrix size $N_x$, $N_y$ and $N_z$;
-\item Matrix diagonal value: \np{1.0} (See~(\ref{eq:03}));
-\item Matrix off-diagonal value: \np{-1}/\np{6} (See~(\ref{eq:03}));
+\item Matrix diagonal value: $6$ (See~(\ref{eq:03}));
+\item Matrix off-diagonal value: $-1$;
 \item Communication mode: asynchronous.
 \end{itemize}