sec 5.4

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 4b06bd77ffd87d86d67ea86124070688b459169b..f67fa56ed6ec33da28d5efb5f8050c7dbbe391f0 100644 (file)
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -895,7 +895,9 @@ cores to more than 16 with 8,192 cores.
 \r
 %%NEW\r
 \subsection{Influence of parameters for TSIRM}\r
 \r
 %%NEW\r
 \subsection{Influence of parameters for TSIRM}\r

+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.\r

 \r
 \r

+%time mpirun ../ex48 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -snes_rtol 1.e-8 -snes_monitor -ksp_type tsirm -ksp_pc_type bjacobi -pc_type ksp -ksp_tsirm_tol 1e-8 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_restarts 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 15 -ksp_tsirm_size_ls 10 \r

 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_cgls_iter_total}\r
 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_cgls_iter_total}\r


@@ -910,6 +912,7 @@ cores to more than 16 with 8,192 cores.
 \label{fig:cgls-time} \r
 \end{figure}\r
 \r
 \label{fig:cgls-time} \r
 \end{figure}\r
 \r

+%time mpirun ../ex35 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -snes_rtol 1.e-8 -snes_monitor -ksp_type tsirm -ksp_pc_type bjacobi -pc_type ksp -ksp_tsirm_tol 1e-8 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_restarts 38 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 15 -ksp_tsirm_size_ls 10\r

 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_inner_restarts_iter_total}\r
 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_inner_restarts_iter_total}\r


@@ -924,6 +927,7 @@ cores to more than 16 with 8,192 cores.
 \label{fig:inner_restarts_time} \r
 \end{figure}\r
 \r
 \label{fig:inner_restarts_time} \r
 \end{figure}\r
 \r

+%time mpirun ../ex14 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -snes_rtol 1.e-8 -snes_monitor -ksp_type tsirm -ksp_pc_type bjacobi -pc_type ksp -ksp_tsirm_tol 1e-8 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 1000 -ksp_tsirm_inner_restarts 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 15 -ksp_tsirm_size_ls 10\r

 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_max_inner_iter}\r
 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_max_inner_iter}\r


@@ -938,6 +942,7 @@ cores to more than 16 with 8,192 cores.
 \label{fig:max_inner_time} \r
 \end{figure}\r
 \r
 \label{fig:max_inner_time} \r
 \end{figure}\r
 \r

+%time mpirun ../ex14 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -snes_rtol 1.e-8 -snes_monitor -ksp_type tsirm -ksp_pc_type bjacobi -pc_type ksp -ksp_tsirm_tol 1e-8 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_restarts 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 5 -ksp_tsirm_size_ls 10\r

 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_maxiter_ls_iter}\r
 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_maxiter_ls_iter}\r


@@ -952,6 +957,7 @@ cores to more than 16 with 8,192 cores.
 \label{fig:maxiter_ls_time} \r
 \end{figure}\r
 \r
 \label{fig:maxiter_ls_time} \r
 \end{figure}\r
 \r

+%time mpirun ../ex14 -da_grid_x 147 -da_grid_y 147 -da_grid_z 147 -snes_rtol 1.e-8 -snes_monitor -ksp_type tsirm -ksp_pc_type bjacobi -pc_type ksp -ksp_tsirm_tol 1e-8 -ksp_tsirm_maxiter 10000 -ksp_ksp_type fgmres -ksp_tsirm_max_inner_iter 30 -ksp_tsirm_inner_restarts 30 -ksp_tsirm_inner_tol 1e-10 -ksp_tsirm_cgls 0 -ksp_tsirm_tol_ls 1.e-40 -ksp_tsirm_maxiter_ls 15 -ksp_tsirm_size_ls 2\r

 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_size_ls_iter}\r
 \begin{figure}[htbp]\r
 \centering\r
   \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_size_ls_iter}\r