From 8192f9fb8a826474106f2a576ca55c7a2a2fab1a Mon Sep 17 00:00:00 2001 From: ziane Date: Wed, 23 Sep 2015 16:31:42 +0200 Subject: [PATCH] section 5.4 --- IJHPCN/biblio.bib | 14 +++++++++++++- IJHPCN/paper.tex | 24 +++++++++++++++++++++++- 2 files changed, 36 insertions(+), 2 deletions(-) diff --git a/IJHPCN/biblio.bib b/IJHPCN/biblio.bib index 0b3b1ec..be24b60 100644 --- a/IJHPCN/biblio.bib +++ b/IJHPCN/biblio.bib @@ -265,4 +265,16 @@ year = 2015, year = "2006", keywords = "parallel software tools,", note = "ch 8,", -} \ No newline at end of file +} + +@misc{ksp, + title = {{K}rylov {M}ethods - {KSP}: {E}xamples}, + howpublished = {\url{http://www.mcs.anl.gov/petsc/petsc-dev/src/ksp/ksp/examples/tutorials/}}, + note = {Accessed: 2015-09-23} +} + +@misc{snes, + title = {{N}onlinear solvers - {SNES}: {E}xamples}, + howpublished = {\url{http://www.mcs.anl.gov/petsc/petsc-current/src/snes/examples/tutorials/index.html}}, + note = {Accessed: 2015-09-23} +} 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} + + -- 2.39.5