From: ziane <ziane@spirou.ltas.ulg.ac.be>
Date: Tue, 5 May 2015 16:54:51 +0000 (+0200)
Subject: 3D Poisson problem
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/commitdiff_plain/dad13e36a03a1d7b58cfff7721b3b81d7537968b?ds=inline;hp=--cc

3D Poisson problem
---

dad13e36a03a1d7b58cfff7721b3b81d7537968b
diff --git a/paper.tex b/paper.tex
index ca1c7e7..827e7e6 100644
--- a/paper.tex
+++ b/paper.tex
@@ -358,7 +358,12 @@ It should also be noticed that both solvers have been executed with the Simgrid
 
 In this section, experiments for both Multisplitting algorithms are reported. First the problem sued in our experiments is described.
 
-\RC{Lilia a toi de jouer}
+We use our two-stage algorithms to solve the well-known 3D Poisson problem $\nabla^2\phi=f$, where $\nabla^2$ is the Laplace operator. 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~}\Omega
+\label{eq:07}
+\end{equation}
+where the real-valued function $\phi(x,y,z)=0\mbox{~on~}\partial\Omega$ is the solution sought, $f(x,y,z)$ is a known function and the domain $\Omega=[0,1]^3$. 
 
 \subsection{Study setup and Simulation Methodology}