From: lilia <lilia@amazigh.bordeaux.inria.fr>
Date: Mon, 28 Apr 2014 12:02:58 +0000 (+0200)
Subject: 28-04-2014b
X-Git-Tag: hpcc2014_submission~46
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/commitdiff_plain/6eddf32c46080635350a6e56b38746b941029d9d?ds=sidebyside;hp=--cc

28-04-2014b
---

6eddf32c46080635350a6e56b38746b941029d9d
diff --git a/hpcc.tex b/hpcc.tex
index e4c77d3..9313c4d 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -422,7 +422,7 @@ 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)],