première version de la conclusion

[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index d114bdd53ae94f8c783ed289ed9747e70f167d62..6a83f5221e0d087a74df1fc7b2502da6cbc1f965 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -381,7 +381,7 @@
 % affiliations
 
 \author{\IEEEauthorblockN{Rapha\"el Couturier\IEEEauthorrefmark{1}, Lilia Ziane Khodja\IEEEauthorrefmark{2}, and Christophe Guyeux\IEEEauthorrefmark{1}}
 % affiliations
 
 \author{\IEEEauthorblockN{Rapha\"el Couturier\IEEEauthorrefmark{1}, Lilia Ziane Khodja\IEEEauthorrefmark{2}, and Christophe Guyeux\IEEEauthorrefmark{1}}

-\IEEEauthorblockA{\IEEEauthorrefmark{1} Femto-ST Institute, University of Franche Comte, France\\
+\IEEEauthorblockA{\IEEEauthorrefmark{1} Femto-ST Institute, University of Franche-Comt\'e, France\\

 Email: \{raphael.couturier,christophe.guyeux\}@univ-fcomte.fr}
 \IEEEauthorblockA{\IEEEauthorrefmark{2} INRIA Bordeaux Sud-Ouest, France\\
 Email: lilia.ziane@inria.fr}
 Email: \{raphael.couturier,christophe.guyeux\}@univ-fcomte.fr}
 \IEEEauthorblockA{\IEEEauthorrefmark{2} INRIA Bordeaux Sud-Ouest, France\\
 Email: lilia.ziane@inria.fr}


@@ -564,7 +564,7 @@ gradient and GMRES ones (Generalized Minimal RESidual).
 
 However,  iterative  methods suffer  from scalability  problems  on parallel
 computing  platforms  with many  processors, due  to  their need  of  reduction
 
 However,  iterative  methods suffer  from scalability  problems  on parallel
 computing  platforms  with many  processors, due  to  their need  of  reduction

-operations, and to  collective    communications   to  achive   matrix-vector
+operations, and to  collective    communications   to  achieve   matrix-vector

 multiplications. The  communications on large  clusters with thousands  of cores
 and  large  sizes of  messages  can  significantly  affect the  performances  of these
 iterative methods. As a consequence, Krylov subspace iteration methods are often used
 multiplications. The  communications on large  clusters with thousands  of cores
 and  large  sizes of  messages  can  significantly  affect the  performances  of these
 iterative methods. As a consequence, Krylov subspace iteration methods are often used


@@ -1029,13 +1029,22 @@ In Table~\ref{tab:04}, some experiments with example ex54 on the Curie architect
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-
-future plan : \\
-- study other kinds of matrices, problems, inner solvers\\
-- test the influence of all parameters\\
-- adaptative number of outer iterations to minimize\\
-- other methods to minimize the residuals?\\
-- implement our solver inside PETSc
+A novel two-stage iterative  algorithm has been proposed in this article,
+in order to accelerate the convergence Krylov iterative  methods.
+Our TSIRM proposal acts as a merger between Krylov based solvers and
+a least-squares minimization step.
+The convergence of the method has been proven in some situations, while 
+experiments up to 16,394 cores have been led to verify that TSIRM runs
+5 or  7 times  faster than GMRES.
+
+
+For future work, the authors' intention is to investigate 
+other kinds of matrices, problems, and inner solvers. The 
+influence of all parameters must be tested too, while 
+other methods to minimize the residuals must be regarded.
+The number of outer iterations to minimize should become 
+adaptative to improve the overall performances of the proposal.
+Finally, this solver will be implemented inside PETSc.

 
 
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 % conference papers do not normally have an appendix