Core(TM) i7-3630QM CPU @ 2.40GHz with the 3.5.1 version of PETSc.
-In Table~\ref{tab:02}, some experiments comparing the solving of the linear
-systems obtained with the previous matrices with a GMRES variant and with TSIRM
-are given. In the second column, it can be noticed that either GMRES or FGMRES
-(Flexible GMRES)~\cite{Saad:1993} is used to solve the linear system. According
+In Table~\ref{tab:02}, experiments comparing
+a GMRES variant with TSIRM in the resolution of linear systems are given.
+In the second column, it can be noticed that either GMRES or FGMRES
+(Flexible GMRES~\cite{Saad:1993}) is used to solve the linear system. Depending
to the matrices, different preconditioners are used. 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
\hline
\end{tabular}
-\caption{Comparison of (F)GMRES and TSIRM with (F)GMRES in sequential with some matrices, time is expressed in seconds.}
+\caption{Comparison between sequential standalone (F)GMRES and TSIRM with (F)GMRES (time in seconds).}
\label{tab:02}
\end{center}
\end{table}
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. Those applications are available in the \emph{ksp} part, which is
suited for scalable linear equations solvers:
\begin{itemize}
-\item ex15 is an example which solves in parallel an operator using a finite
+\item ex15 is an example that solves in parallel an operator using a finite
difference scheme. The diagonal is equal to 4 and 4 extra-diagonals
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
