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Commit 8a5f44ce authored by Dominic Etienne Charrier's avatar Dominic Etienne Charrier
Browse files

Gave it a read through. Is not good yet but the information should be there.

parent b0688fd0
......@@ -397,14 +397,15 @@ subtrees that are deployed to worker processes.
Only subtrees that overlap with the computational domain are deployed.
This constraint can be used to steer work distribution.
\exahype can scale the bounding box such that \texttt{outside\_cells\_left} and/or \texttt{outside\_cells\_right} cells are placed outside of the
\exahype can scale the bounding box such that \texttt{outside\_cells\_left} and/or \\
\texttt{outside\_cells\_right} cells are placed outside of the
domain while the latter is still resolved as accurately as specified in the spec file.
Furthermore, there is an option to place exactly \texttt{ranks\_per\_dimension" on the coarse grid}.
(Note: This overrules \texttt{outside\_cells\_right} but not \texttt{outside\_cells\_left}.
Furthermore, there is an option to place exactly \texttt{ranks\_per\_dimension} on the coarse grid.
(Note: This overrules \texttt{outside\_cells\_right} but not \texttt{outside\_cells\_left}.)
This feature is particular interesting for weak scaling experiments as it can scale the number of cells per dimension
of a mesh by arbitrary integers.
An example is given in Fig. \ref{fig:weak-scaling}:
An example is given in Fig. \ref{fig:weak-scaling}.
\begin{figure}[h]
\begin{center}
......@@ -415,7 +416,8 @@ An example is given in Fig. \ref{fig:weak-scaling}:
\includegraphics[width=0.4\textwidth]{sketches/weak-scaling-4.pdf}\hspace{0.1cm}
\includegraphics[width=0.4\textwidth]{sketches/weak-scaling-8.pdf}
\end{center}
\caption{Weak scaling experiment growing the domain by factors $1$, $2^d$, $4^d$, and $8^d$. \texttt{ranks\_per\_dimension} is chosen 1,2,4,8.}
\caption{Weak scaling experiment growing the domain by factors $1$, $2^d$, $4^d$, and $8^d$. \texttt{ranks\_per\_dimension} is chosen 1,2,4,8.
The majority of cells lying outside of the domain will be erased.}
\label{fig:weak-scaling}
\end{figure}
......@@ -426,31 +428,18 @@ is interesting since it can be perfectly distributed among
$2^d$, $4^d$, and $12^d$ processes.
The same mesh refined by a factor $3^i$, $i \leq 0$ can be constructed if $3^i \times 9$ bounding box outside cells
are placed to the left of the domain.
The $36^d$ mesh requires a maximum-mesh-size of $\frac{1}{36} \approx 0.03$.
The uniformly refined variants must scale this mesh size with a factor $\frac{1}{3^i}$.
are placed to the left of the domain. The $36^d$ mesh requires a maximum-mesh-size of
$\frac{1}{36} \approx 0.03$.
The uniformly refined variants must scale this mesh size with a factor $3^{-i}$.
Another family of interesting uniform meshes are the ones with $3^i*48^d$ cells that are shifted
Another family of interesting uniform meshes are the ones with $3^i \times 48^d$ cells that are shifted
by $3^i \times 3$ cells. They can be created by choosing $\texttt{ranks\_per\_dimension}=16$
and $\texttt{outside\_cells\_left}=3$. The latter must be multiplied by a factor $3^i$ for any
additional refinement level to preserve the positioning.
The $48^d$ mesh requires a maximum-mesh-size of $\frac{1}{48} \approx 0.021$.
For further uniform refinement, the mesh size must be scaled with a factor $\frac{1}{3^i}$.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.4\textwidth]{sketches/strong-scaling-grid-223.pdf}\hspace{0.1cm}
\includegraphics[width=0.4\textwidth]{sketches/strong-scaling-grid-233.pdf}
\end{center}
\caption{Left: A grid with $36^d$ cells on the coarse grid which allows to use $1$, $2^d$, $4^d$, and $12^d$ ranks
to uniformly distribute the load.
Right: A grid with $48^d$ cells on the coarse grid which allows to use $1$, $2^d$ and $16^d$ ranks
to uniformly distribute the load. A quasi-optimal distribution can be established with $4^d$ ranks.}
\label{fig:strong-scaling}
\end{figure}
The code to draw the grids is given below:
For further uniform refinement, the mesh size must be scaled with a factor $3^{-i}$.
The code used to draw all grids is given below:
\begin{code}
\documentclass[tikz,preview,crop,11pt]{standalone}
\begin{document}
......@@ -482,6 +471,21 @@ The code to draw the grids is given below:
\end{document}
\end{code}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.4\textwidth]{sketches/strong-scaling-grid-223.pdf}\hspace{0.1cm}
\includegraphics[width=0.4\textwidth]{sketches/strong-scaling-grid-233.pdf}
\end{center}
\caption{Left: A grid with $36^d$ cells on the coarse grid which allows to use $1$, $2^d$, $4^d$, and $12^d$ ranks
to uniformly distribute the load.
Right: A grid with $48^d$ cells on the coarse grid which allows to use $1$, $2^d$ and $16^d$ ranks
to uniformly distribute the load. A quasi-optimal distribution can be established with $4^d$ ranks.
The majority of cells lying outside of the domain will be erased.}
\label{fig:strong-scaling}
\end{figure}
\section{MPI troubleshooting and inefficiency patterns}
\label{section:mpi:inefficiency-patterns}
......
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