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}.
\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*}
