commenter fig 2

[kahina_paper2.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 34d2fb498361becb357ac0e2ce5f2515c3fb13f3..414bd83fcbf18342ebfe9806d3d4ca6c8fe7cddc 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -784,6 +784,14 @@ to $10^{-7}$.
 %CPUs versus on GPUs.
 The initialization values of the vector solution
 of the methods are given in %Section~\ref{sec:vec_initialization}.
 %CPUs versus on GPUs.
 The initialization values of the vector solution
 of the methods are given in %Section~\ref{sec:vec_initialization}.

+
+\subsection{Test with Multi-GPU (CUDA OpenMP) approach}
+
+In this part we performed  a set of experiments on Multi-GPU (CUDA OpenMP) approach for full and sparse polynomials of different degrees, compare it with Single GPU (CUDA).
+ \subsubsection{Execution times in seconds of the Ehrlich-Aberth method for solving sparse polynomials on GPUs using shared memory paradigm with OpenMP}
+ 
+ In this experiments we report the execution time of the EA algorithm, on single GPU and Multi-GPU with (2,3,4) GPUs, for different sparse polynomial degrees ranging from 100,000 to 1,400,000
+

 \begin{figure}[htbp]
 \centering
   \includegraphics[angle=-90,width=0.5\textwidth]{Sparse_omp}
 \begin{figure}[htbp]
 \centering
   \includegraphics[angle=-90,width=0.5\textwidth]{Sparse_omp}


@@ -791,12 +799,11 @@ of the methods are given in %Section~\ref{sec:vec_initialization}.
 \label{fig:01}
 \end{figure}
 
 \label{fig:01}
 \end{figure}
 

-\begin{figure}[htbp]
-\centering
-  \includegraphics[angle=-90,width=0.5\textwidth]{Sparse_mpi}
-\caption{Execution times in seconds of the Ehrlich-Aberth method for solving sparse polynomials on GPUs using distributed memory paradigm with MPI}
-\label{fig:02}
-\end{figure}
+This figure~\ref{fig:01} shows that (CUDA OpenMP) Multi-GPU approach reduce the execution time up to the scale 100 whereas single GPU is of scale 1000 for polynomial who exceed 1,000,000. It shows the advantage to use OpenMP parallel paradigm  to connect the performances of several GPUs and solve a  polynomial of high degrees.   
+
+\subsubsection{Execution times in seconds of the Ehrlich-Aberth method for solving full polynomials on GPUs using shared memory paradigm with OpenMP}
+
+This experiments shows the execution time of the EA algorithm, on single GPU (CUDA) and Multi-GPU (CUDA OpenMP)approach for full polynomials of degrees ranging from 100,000 to 1,400,000

 
 \begin{figure}[htbp]
 \centering
 
 \begin{figure}[htbp]
 \centering


@@ -805,6 +812,16 @@ of the methods are given in %Section~\ref{sec:vec_initialization}.
 \label{fig:03}
 \end{figure}
 
 \label{fig:03}
 \end{figure}
 

+The second test with full polynomial shows a very important saving of time, for a polynomial of degrees 1,4M (CUDA OpenMP) approach with 4 GPUs compute and solve it 4 times as fast as single GPU. We notice that curves are positioned one below the other one, more the number of used GPUs increases more the execution time decreases.
+
+\begin{figure}[htbp]
+\centering
+  \includegraphics[angle=-90,width=0.5\textwidth]{Sparse_mpi}
+\caption{Execution times in seconds of the Ehrlich-Aberth method for solving sparse polynomials on GPUs using distributed memory paradigm with MPI}
+\label{fig:02}
+\end{figure}
+
+

 \begin{figure}[htbp]
 \centering
   \includegraphics[angle=-90,width=0.5\textwidth]{Full_mpi}
 \begin{figure}[htbp]
 \centering
   \includegraphics[angle=-90,width=0.5\textwidth]{Full_mpi}