X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/a45b1d7df54f09b78efd3333be8d8cc4a89dccdf..8192f9fb8a826474106f2a576ca55c7a2a2fab1a:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 2d0bd55..ff3c605 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -1033,7 +1033,7 @@ cores to more than 16 with 8,192 cores.
 
 %%NEW
 \subsection{Influence of parameters for TSIRM}
-In this section we present some experimental results in order to study the influence of some parameters on the TSIRM algorithm. We conducted experiments on $16$ cores to solve 3D problems of size $200,000$ components per core. We solved nonlinear problems token from examples of PETSc. We fixed some parameters of the TSIRM algorithm as follows: the nonlinear systems are solved with a precision of $10^{-8}$, block Jacobi preconditioner is used, the tolerance threshold $\epsilon_{tsirm}$ is $10^{-8}$ , the maximum number of iterations $max\_iter_{tsirm}$ is set to $10,000$ iterations, the FGMRES method is used as the inner solver with a tolerance threshold $\epsilon_{kryl}=10^{-10}$ and the least-squares problem is solved with a precision $\epsilon_{ls}=10^{-40}$ in the minimization process.
+In this section we present some experimental results in order to study the influence of some parameters on the TSIRM algorithm which are: the method to solve the linear least-squares problem in the minimization process, the number of inner iterations $max\_iter_{kryl}$, and the size $s$ of matrix $AS$ (i.e. matrix $S$) of the least-squares problem. We conducted experiments on $16$ cores to solve linear and nonlinear problems of size $200,000$ components per core. We solved problems token from examples {\it ksp} and {\it snes} of PETSc~\cite{ksp,snes}. We fixed some parameters of the TSIRM algorithm as follows: the nonlinear systems are solved with a precision of $10^{-8}$, the tolerance threshold and the maximum number of iterations of TSIRM algorithm are $\epsilon_{tsirm}=10^{-10}$ and $max\_iter_{tsirm}=10,000$, the FGMRES method is used as the inner solver with a tolerance threshold $\epsilon_{kryl}=10^{-10}$, the additive Schwarz method (ASM) is used as a preconditioner, and the least-squares problem is solved with a precision $\epsilon_{ls}=10^{-40}$ in the minimization process.
 
 %time mpirun ../ex34 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -ksp_type tsirm -ksp_pc_type asm -pc_type ksp -ksp_tsirm_tol 1e-10 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 20 -ksp_tsirm_size_ls 10
 \begin{figure}[htbp]
@@ -1043,6 +1043,20 @@ In this section we present some experimental results in order to study the influ
 \label{fig:cgls} 
 \end{figure}
 
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.5\textwidth]{ksp_ex12}
+\caption{Total number of iterations in example {\it ksp ex12} of PETSc by varyin the number of inner iterations and the size of the least-squares problem.}
+\label{fig:ksp_ex12} 
+\end{figure}
+
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.5\textwidth]{ksp_ex34}
+\caption{Total number of iterations in example {\it ksp ex34} of PETSc by varyin the number of inner iterations and the size of the least-squares problem.}
+\label{fig:ksp_ex34} 
+\end{figure}
+
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.5\textwidth]{snes_ex14}
@@ -1050,6 +1064,14 @@ In this section we present some experimental results in order to study the influ
 \label{fig:snes_ex14} 
 \end{figure}
 
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.5\textwidth]{snes_ex20}
+\caption{Total number of iterations in example {\it snes ex20} of PETSc by varyin the number of inner iterations and the size of the least-squares problem.}
+\label{fig:snes_ex20} 
+\end{figure}
+
+
 
 
 
