X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/4f3f422c55e11ca375bf5f17203c5d82ed9928aa..7598268ddab4631d2d0bbb07f6e4f7cbf8cfc2f3:/paper.tex

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@@ -90,7 +90,7 @@ analysis of simulated grid-enabled numerical iterative algorithms}
 
 %% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be
 
-\begin{abstract}   The behavior of multicore applications is always a challenge
+\begin{abstract}   The behavior of multi-core applications is always a challenge
 to predict, especially with a new architecture for which no experiment has been
 performed. With some applications, it is difficult, if not impossible, to build
 accurate performance models. That is why another solution is to use a simulation
@@ -101,7 +101,7 @@ applications.
 
 In this paper, we focus our attention on two parallel iterative algorithms based
 on the  Multisplitting algorithm  and we  compare them  to the  GMRES algorithm.
-These algorithms  are used to  solve libear  systems. Two different  variantsof
+These algorithms  are used to  solve libear  systems. Two different  variants of
 the Multisplitting are studied: one  using synchronoous  iterations and  another
 one  with asynchronous iterations. For each algorithm we have  tested different
 parameters to see their influence.  We strongly  recommend people  interested
@@ -119,8 +119,8 @@ their  applications  using  a simulation tool before.
 
 \maketitle
 
-\section{Introduction}  The use of multi-core architectures for solving large
-scientific problems seems to  become imperative  in  a  lot  of  cases.
+\section{Introduction}  The use of multi-core architectures to solve large
+scientific problems seems to  become imperative  in  many situations.
 Whatever the scale of these architectures (distributed clusters, computational
 grids, embedded multi-core,~\ldots) they  are generally  well adapted to execute
 complex parallel applications operating on a large amount of data.
@@ -131,8 +131,7 @@ are often very important. So, in this context it is difficult to optimize a
 given application for a given  architecture. In this way and in order to reduce
 the access cost to these computing resources it seems very interesting to use a
 simulation environment.  The advantages are numerous: development life cycle,
-code debugging, ability to obtain results quickly,~\ldots at the condition that
-the simulation results are in education with the real ones.
+code debugging, ability to obtain results quickly,~\ldots. In counterpart, the simulation results need to be consistent with the real ones.
 
 In this paper we focus on a class of highly efficient parallel algorithms called
 \emph{iterative algorithms}. The parallel scheme of iterative methods is quite
@@ -147,7 +146,7 @@ from its neighbors. We say that the iteration computation follows a synchronous
 scheme. In the asynchronous scheme a task can compute a new iteration without
 having to wait for the data dependencies coming from its neighbors. Both
 communication and computations are asynchronous inducing that there is no more
-idle times, due to synchronizations, between two iterations~\cite{bcvc06:ij}.
+idle time, due to synchronizations, between two iterations~\cite{bcvc06:ij}.
 This model presents some advantages and drawbacks that we detail in
 section~\ref{sec:asynchro} but even if the number of iterations required to
 converge is generally  greater  than for the synchronous  case, it appears that
@@ -155,15 +154,15 @@ the asynchronous  iterative scheme  can significantly  reduce  overall execution
 times by  suppressing idle  times due to  synchronizations~(see~\cite{bahi07}
 for more details).
 
-Nevertheless, in both cases (synchronous or asynchronous) it is very time
-consuming to find optimal configuration and deployment requirements  for a given
-application on a given multi-core architecture. Finding good resource
-allocations policies under varying CPU power, network speeds and  loads is very
-challenging and labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
-problematic is even more difficult for the asynchronous scheme  where variations
-of the parameters of the execution platform can lead to very different number of
-iterations required to converge and so to very different execution times. In
-this challenging context we think that the use of a simulation tool can greatly
+Nevertheless,  in both  cases  (synchronous  or asynchronous)  it  is very  time
+consuming to find optimal configuration  and deployment requirements for a given
+application  on   a  given   multi-core  architecture.  Finding   good  resource
+allocations policies under  varying CPU power, network speeds and  loads is very
+challenging and  labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
+problematic is  even more difficult  for the  asynchronous scheme where  a small
+parameter variation of the execution platform can lead to very different numbers
+of iterations to reach the converge and so to very different execution times. In
+this challenging context we think that the  use of a simulation tool can greatly
 leverage the possibility of testing various platform scenarios.
 
 The main contribution of this paper is to show that the use of a simulation tool
@@ -175,7 +174,7 @@ algorithm  with  the  GMRES   (Generalized   Minimal  Residual)
 solver~\cite{saad86} in synchronous mode. The obtained results on different
 simulated multi-core architectures confirm the real results previously obtained
 on non simulated architectures.  We also confirm  the efficiency  of the
-asynchronous  multisplitting algorithm  comparing to the synchronous  GMRES. In
+asynchronous  multisplitting algorithm  compared to the synchronous  GMRES. In
 this way and with a simple computing architecture (a laptop) SimGrid allows us
 to run a test campaign  of  a  real parallel iterative  applications on
 different simulated multi-core architectures.  To our knowledge, there is no
@@ -193,6 +192,25 @@ concluding remarks and perspectives.
 \section{The asynchronous iteration model}
 \label{sec:asynchro}
 
+Asynchronous iterative methods have been  studied for many years theorecally and
+practically. Many methods have been considered and convergence results have been
+proved. These  methods can  be used  to solve in  parallel fixed  point problems
+(i.e. problems  for which  the solution is  $x^\star =f(x^\star)$.  In practice,
+asynchronous iterations  methods can be used  to solve, for example,  linear and
+non-linear systems of equations or optimization problems, interested readers are
+invited to read~\cite{BT89,bahi07}.
+
+Before  using  an  asynchronous  iterative   method,  the  convergence  must  be
+studied. Otherwise, the  application is not ensure to reach  the convergence. An
+algorithm that supports both the synchronous or the asynchronous iteration model
+requires very few modifications  to be able to be executed  in both variants. In
+practice, only  the communications and  convergence detection are  different. In
+the  synchronous   mode,  the  iterations   are  synchronized  whereas   in  the
+asynchronous  one,  they are  not.   It  should  be  noticed that  non  blocking
+communications can be used in  both modes. Concerning the convergence detection,
+synchronous variants  can use  a global  convergence procedure  which acts  as a
+global synchronization point. In the asynchronous model, the convergence dectection is more tricky as it must not synchronize all the processors. Interested readers can consult~\cite{myBCCV05c,bahi07,ccl09:ij}. 
+
 \section{SimGrid}
  \label{sec:simgrid}
 
