IEEE instructions require to NOT use algorithm floating environment.

[hpcc2014.git] / hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index 99d8c3860af7fe5248aad9ab40355f87ffa6071b..7389e3e2e665b47340de7b6869da50b430a311b5 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -4,7 +4,7 @@
 \usepackage[utf8]{inputenc}
 \usepackage{amsfonts,amssymb}
 \usepackage{amsmath}
 \usepackage[utf8]{inputenc}
 \usepackage{amsfonts,amssymb}
 \usepackage{amsmath}

-\usepackage{algorithm}
+%\usepackage{algorithm}

 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}
 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}


@@ -173,8 +173,12 @@ our future work after the results.
 
 \section{SimGrid}
 
 
 \section{SimGrid}
 

-\AG{Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid} (Arnaud)}
+\AG{Décrire SimGrid~\cite{casanova+legrand+quinson.2008.simgrid,SimGrid} (Arnaud)}

 
 

+%%% brief history?
+%%% programming interfaces: MSG, SimDAG, SMPI
+%%% platforms
+%%% validation?

 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}


@@ -212,8 +216,9 @@ Y_l = B_l - \displaystyle\sum_{\substack{m=1\\ m\neq l}}^{L}A_{lm}X_m
 \end{equation}
 is solved independently by a cluster and communications are required to update the right-hand side sub-vector $Y_l$, such that the sub-vectors $X_m$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel algorithm of GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers. 
 
 \end{equation}
 is solved independently by a cluster and communications are required to update the right-hand side sub-vector $Y_l$, such that the sub-vectors $X_m$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel algorithm of GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers. 
 

-\begin{algorithm}
-\caption{A multisplitting solver with GMRES method}
+\begin{figure}
+  %%% IEEE instructions forbid to use an algorithm environment here, use figure
+  %%% instead

 \begin{algorithmic}[1]
 \Input $A_l$ (sparse sub-matrix), $B_l$ (right-hand side sub-vector)
 \Output $X_l$ (solution sub-vector)\vspace{0.2cm}
 \begin{algorithmic}[1]
 \Input $A_l$ (sparse sub-matrix), $B_l$ (right-hand side sub-vector)
 \Output $X_l$ (solution sub-vector)\vspace{0.2cm}


@@ -234,10 +239,23 @@ is solved independently by a cluster and communications are required to update t
 \State \Return $X_l^k$
 \EndFunction
 \end{algorithmic}
 \State \Return $X_l^k$
 \EndFunction
 \end{algorithmic}

+\caption{A multisplitting solver with GMRES method}

 \label{algo:01}
 \label{algo:01}

-\end{algorithm}
+\end{figure}

 
 

-Algorithm~\ref{algo:01} shows the main key points of the multisplitting method to solve a large sparse linear system. This algorithm is based on an outer-inner iteration method where the parallel synchronous GMRES method is used to solve the inner iteration. It is executed in parallel by each cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors with the subscript $l$ represent the local data for cluster $l$, while $\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and $\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with neighboring clusters. At every outer iteration $k$, asynchronous communications are performed between processors of the local cluster and those of distant clusters (lines $6$ and $7$ in Algorithm~\ref{algo:01}). The shared vector elements of the solution $x$ are exchanged by message passing using MPI non-blocking communication routines. 
+Algorithm on Figure~\ref{algo:01} shows the main key points of the
+multisplitting method to solve a large sparse linear system. This algorithm is
+based on an outer-inner iteration method where the parallel synchronous GMRES
+method is used to solve the inner iteration. It is executed in parallel by each
+cluster of processors. For all $l,m\in\{1,\ldots,L\}$, the matrices and vectors
+with the subscript $l$ represent the local data for cluster $l$, while
+$\{A_{lm}\}_{m\neq l}$ are off-diagonal matrices of sparse matrix $A$ and
+$\{X_m\}_{m\neq l}$ contain vector elements of solution $x$ shared with
+neighboring clusters. At every outer iteration $k$, asynchronous communications
+are performed between processors of the local cluster and those of distant
+clusters (lines $6$ and $7$ in Figure~\ref{algo:01}). The shared vector
+elements of the solution $x$ are exchanged by message passing using MPI
+non-blocking communication routines.

 
 \begin{figure}
 \centering
 
 \begin{figure}
 \centering