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amr_exercise.tex
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amr_exercise.tex
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\noindent
\includegraphics[width=4.5cm]{images/meshes/AMR/amr0}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr1}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr2}\\
\includegraphics[width=4.5cm]{images/meshes/AMR/amr3}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr4}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr5}\\
\includegraphics[width=4.5cm]{images/meshes/AMR/amr6}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr7}
\includegraphics[width=4.5cm]{images/meshes/AMR/amr8}
\begin{tabular}{l|ccccccccc}
& \# l0 & \# l1 & \# l2 & \# l3 & \# l4 & \# l5 & \# l6 & \# l7 & \# l8 \\
\hline\hline
max level= 0 & 1 & \\
max level= 1 & 0 & 4 & \\
max level= 2 & 0 & 3 & 4 \\
max level= 3 & 0 & 2 & 7 & 4\\
max level= 4 & 0 & 2 & 5 & 10 & 8 \\
max level= 5 & 0 & 1 & 8 & 12 & 11 & 20 \\
max level= 6 & 0 & 1 & 8 & 11 & 13 & 20 & 32 \\
max level= 7 & 0 & 0 & 11 & 14 & 15 & 23 & 37 & 60 \\
max level= 8 & 0 & 0 & 11 & 13 & 17 & 27 & 43 & 72 & 116 \\
\hline
\end{tabular}
\includegraphics[width=7.28cm]{images/meshes/AMR/amr_data1.pdf}
\includegraphics[width=7.28cm]{images/meshes/AMR/amr_data2.pdf}
In the particular case presented here, even though the inclusion in a short
two-dimensional line, the total number of elements grows faster than the
third power of the refinement level. While of course the total number
of elements remains much smaller than the constant resolution counterpart,
this observation tells us that authorising a unit increase of the maximum
refinement level can have a substantial effect on the total number of elements.
\newpage
\noindent
\includegraphics[width=4cm]{images/meshes/AMR/amr_0}
\includegraphics[width=4cm]{images/meshes/AMR/amr_1}
\includegraphics[width=4cm]{images/meshes/AMR/amr_2}
\includegraphics[width=4cm]{images/meshes/AMR/amr_3}\\
\includegraphics[width=4cm]{images/meshes/AMR/amr_4}
\includegraphics[width=4cm]{images/meshes/AMR/amr_5}
\includegraphics[width=4cm]{images/meshes/AMR/amr_6}
\includegraphics[width=4cm]{images/meshes/AMR/amr_7}
\includegraphics[width=5cm]{images/meshes/AMR/amr_data3.pdf}
\includegraphics[width=5cm]{images/meshes/AMR/amr_data4.pdf}
\includegraphics[width=5cm]{images/meshes/AMR/amr_data5.pdf}