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[GMRES2stage.git] / paper.tex

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@@ -877,9 +877,10 @@ Table~\ref{tab:03} shows  the execution  times and the  number of  iterations of
 example ex15  of PETSc on the  Juqueen architecture. Differents  number of cores
 are  studied rangin  from  2,048  upto 16,383.   Two  preconditioners have  been
 tested.   For those experiments,  the number  of components  (or unknown  of the
 example ex15  of PETSc on the  Juqueen architecture. Differents  number of cores
 are  studied rangin  from  2,048  upto 16,383.   Two  preconditioners have  been
 tested.   For those experiments,  the number  of components  (or unknown  of the

-problems)  per processor is  fixed to  25,000. This  number can  seem relatively
-small. In fact, for  some applications that need a lot of  memory, the number of
-components per processor requires sometimes to be small.
+problems)  per processor  is fixed  to 25,000,  also called  weak  scaling. This
+number can seem relatively small. In fact, for some applications that need a lot
+of  memory, the  number of  components per  processor requires  sometimes  to be
+small.

 
 In this Table, we  can notice that TSIRM is always faster  than FGMRES. The last
 column shows the ratio between FGMRES and the best version of TSIRM according to
 
 In this Table, we  can notice that TSIRM is always faster  than FGMRES. The last
 column shows the ratio between FGMRES and the best version of TSIRM according to


@@ -887,7 +888,16 @@ the minimization  procedure: CGLS or  LSQR. Even if  we have computed  the worst
 case  between CGLS  and LSQR,  it is  clear that  TSIRM is  alsways  faster than
 FGMRES. For this example, the  multigrid preconditionner is faster than SOR. The
 gain  between   TSIRM  and  FGMRES  is   more  or  less  similar   for  the  two
 case  between CGLS  and LSQR,  it is  clear that  TSIRM is  alsways  faster than
 FGMRES. For this example, the  multigrid preconditionner is faster than SOR. The
 gain  between   TSIRM  and  FGMRES  is   more  or  less  similar   for  the  two

-preconditioners
+preconditioners.
+
+In  Figure~\ref{fig:01}, the number  of iterations  per second  corresponding to
+Table~\ref{tab:01} is displayed.  It should  be noticed that for TSIRM, only the
+iterations of  the Krylov solver are  taken into account. Iterations  of CGLS or
+LSQR are  not recorded but they are  time-consuming. It can be  noticed that the
+number of iterations  per second of FMGRES is constant  whereas it decrease with
+TSIRM with both preconditioner. This can  be explained by the fact that when the
+number of core  increases the time for the minimization  step also increases but
+it  is  also  more efficient  to reduce the number of iterations.

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