X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/2e6154ec59cf3bf10609cc7de399aa809e9b44ea..f906225644f3d763193e909f019cce9455984280:/paper.tex

diff --git a/paper.tex b/paper.tex
index 8ffd387..e7e7e0d 100644
--- a/paper.tex
+++ b/paper.tex
@@ -354,6 +354,7 @@
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{multirow}
+\usepackage{graphicx}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
@@ -583,8 +584,7 @@ performances.
 The present paper is organized  as follows. In Section~\ref{sec:02} some related
 works are presented. Section~\ref{sec:03} presents our two-stage algorithm using
 a  least-square  residual  minimization.   Section~\ref{sec:04}  describes  some
-convergence  results  on this  method.   In Section~\ref{sec:05},  parallization
-details  of  TSARM  are  given.  Section~\ref{sec:06}  shows  some  experimental
+convergence  results  on this  method.   Section~\ref{sec:05}  shows  some  experimental
 results  obtained on large  clusters of  our algorithm  using routines  of PETSc
 toolkit.  Finally Section~\ref{sec:06} concludes and gives some perspectives.
 %%%*********************************************************
@@ -615,7 +615,7 @@ points of our solver are given in Algorithm~\ref{algo:01}.
 
 In order to accelerate the convergence, the outer iteration periodically applies
 a least-square minimization  on the residuals computed by  the inner solver. The
-inner solver is a Krylov based solver which does not required to be changed.
+inner solver is based on a Krylov method which does not require to be changed.
 
 At each outer iteration, the sparse linear system $Ax=b$ is solved, only for $m$
 iterations, using an iterative method restarting with the previous solution. For
@@ -680,18 +680,6 @@ To summarize, the important parameters of TSARM are:
 \item $\epsilon_{ls}$ the threshold to stop the least-square method
 \end{itemize}
 
-%%%*********************************************************
-%%%*********************************************************
-
-\section{Convergence results}
-\label{sec:04}
-
-
-
-%%%*********************************************************
-%%%*********************************************************
-\section{Parallelization}
-\label{sec:05}
 
 The  parallelisation  of  TSARM  relies   on  the  parallelization  of  all  its
 parts. More  precisely, except  the least-square step,  all the other  parts are
@@ -733,10 +721,21 @@ In each iteration  of CGLS, there is two  matrix-vector multiplications and some
 classical operations:  dots, norm, multiplication  and addition on  vectors. All
 these operations are easy to implement in PETSc or similar environment.
 
+
+
+%%%*********************************************************
+%%%*********************************************************
+
+\section{Convergence results}
+\label{sec:04}
+
+
+
+
 %%%*********************************************************
 %%%*********************************************************
 \section{Experiments using petsc}
-\label{sec:06}
+\label{sec:05}
 
 
 In order to see the influence of our algorithm with only one processor, we first
@@ -856,6 +855,17 @@ but they are not scalable with many cores.
 \end{table*}
 
 
+\begin{figure}
+\centering
+  \includegraphics[width=0.45\textwidth]{nb_iter_sec_ex15_juqueen}
+\caption{Number of iterations per second with ex15 and the same parameters than in Table~\ref{tab:03}}
+\label{fig:01}
+\end{figure}
+
+
+
+
+
 \begin{table*}
 \begin{center}
 \begin{tabular}{|r|r|r|r|r|r|r|r|r|} 
@@ -913,7 +923,7 @@ but they are not scalable with many cores.
 %%%*********************************************************
 %%%*********************************************************
 \section{Conclusion}
-\label{sec:07}
+\label{sec:06}
 %The conclusion goes here. this is more of the conclusion
 %%%*********************************************************
 %%%*********************************************************