X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/fd78ced113c137f5f83f7aea69a10961467aea3e..348f3de01d413c95e0ee5a51971ad04d01d9fec5:/paper.tex

diff --git a/paper.tex b/paper.tex
index 16b2de5..3d4826c 100644
--- a/paper.tex
+++ b/paper.tex
@@ -900,9 +900,9 @@ The  second column describes whether GMRES or FGMRES
 (Flexible GMRES~\cite{Saad:1993}) has been used for linear systems solving.  
 Different preconditioners  have been used according to the matrices.  With  TSIRM, the  same
 solver and the  same preconditionner are used.  This table  shows that TSIRM can
-drastically reduce  the number of iterations  to reach the  convergence when the
+drastically reduce  the number of iterations needed to reach the  convergence, when the
 number of iterations for  the normal GMRES is more or less  greater than 500. In
-fact this also depends on two parameters: the number of iterations to stop GMRES
+fact this also depends on two parameters: the number of iterations before stopping GMRES
 and the number of iterations to perform the minimization.
 
 
@@ -934,7 +934,7 @@ torso3             & fgmres / sor  & 37.70 & 565 & 34.97 & 510 \\
 
 
 In order to perform larger experiments, we have tested some example applications
-of  PETSc. Those  applications are  available in  the \emph{ksp}  part,  which is
+of  PETSc. These  applications are  available in  the \emph{ksp}  part,  which is
 suited for scalable linear equations solvers:
 \begin{itemize}
 \item ex15  is an example  that solves in  parallel an operator using  a finite
@@ -942,35 +942,36 @@ suited for scalable linear equations solvers:
   representing the neighbors in each directions  are equal to -1. This example is
   used  in many  physical phenomena, for  example, heat  and fluid  flow, wave
   propagation, etc.
-\item ex54 is another example based on 2D problem discretized with quadrilateral
-  finite elements. For this example, the user can define the scaling of material
+\item ex54 is another example based on a 2D problem discretized with quadrilateral
+  finite elements. In this example, the user can define the scaling of material
   coefficient in embedded circle called $\alpha$.
 \end{itemize}
 For more technical details on these applications, interested readers are invited
-to read  the codes  available in  the PETSc sources.   Those problems  have been
+to read  the codes  available in  the PETSc sources.   These problems  have been
 chosen because they are scalable with many  cores.
 
 In  the  following   larger  experiments  are  described  on   two  large  scale
-architectures: Curie  and Juqueen.   Both these architectures  are supercomputer
+architectures: Curie  and Juqueen.   Both these architectures  are supercomputers
 respectively  composed  of  80,640  cores   for  Curie  and  458,752  cores  for
 Juqueen. Those  machines are respectively hosted  by GENCI in  France and JÃ¼lich
-Supercomputing Centre in Germany.  They belongs with other similar architectures
-of the  PRACE initiative (Partnership  for Advanced Computing  in Europe) which
+Supercomputing Centre in Germany.  They belong with other similar architectures
+of the  PRACE initiative (Partnership  for Advanced Computing  in Europe), which
 aims  at  proposing  high  performance supercomputing  architecture  to  enhance
 research  in  Europe.  The  Curie  architecture is  composed  of  Intel  E5-2680
-processors  at 2.7  GHz with  2Gb memory  by core.  The Juqueen  architecture is
-composed of  IBM PowerPC  A2 at  1.6 GHz with  1Gb memory  per core.  Both those
+processors  at 2.7  GHz with  2Gb memory  by core.  The Juqueen  architecture,
+for its part, is
+composed by IBM PowerPC  A2 at  1.6 GHz with  1Gb memory  per core.  Both those
 architecture are equiped with a dedicated high speed network.
 
 
 In  many situations, using  preconditioners is  essential in  order to  find the
 solution of a linear system.  There are many preconditioners available in PETSc.
-For parallel applications all  the preconditioners based on matrix factorization
+However, for parallel applications, all  the preconditioners based on matrix factorization
 are  not  available. In  our  experiments, we  have  tested  different kinds  of
-preconditioners, however  as it is  not the subject  of this paper, we  will not
+preconditioners, but  as it is  not the subject  of this paper, we  will not
 present results with many preconditioners. In  practice, we have chosen to use a
-multigrid (mg)  and successive  over-relaxation (sor). For  more details  on the
-preconditioner in PETSc please consult~\cite{petsc-web-page}.
+multigrid (mg)  and successive  over-relaxation (sor). For  further details  on the
+preconditioner in PETSc, reader is referred to~\cite{petsc-web-page}.
 
 
 
@@ -993,7 +994,7 @@ preconditioner in PETSc please consult~\cite{petsc-web-page}.
 \hline
 
 \end{tabular}
-\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) with 25,000 components per core on Juqueen ($\epsilon_{tsirm}=1e-3$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
+\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) having 25,000 components per core on Juqueen ($\epsilon_{tsirm}=1e-3$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
 \label{tab:03}
 \end{center}
 \end{table*}
