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fix: Ex03 - plot path in LaTeX

This commit is contained in:
Daniel Kapla 2022-05-17 18:55:25 +02:00
parent 0eaaf52c7e
commit bd3dcde4d8
2 changed files with 19 additions and 13 deletions
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6
.gitignore vendored
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@ -10,3 +10,9 @@ Exercise_02/**.txt
# vscode workspace config
.vscode/
# LaTeX compile file
*.aux
*.idx
*.log
*.out

26
Exercise_03/report.tex
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@ -220,10 +220,10 @@ for a tridiagonal matrix $A_1$ of dimensions $N_x\times N_x$
\begin{figure}[!h]
\centering
\includegraphics[width=0.48\textwidth]{task01_1_00023.png}
\includegraphics[width=0.48\textwidth]{task01_x_00023.png}
\includegraphics[width=0.48\textwidth]{task01_1_00199.png}
\includegraphics[width=0.48\textwidth]{task01_x_00199.png}
\includegraphics[width=0.48\textwidth]{plots/task01_1_00023.png}
\includegraphics[width=0.48\textwidth]{plots/task01_x_00023.png}
\includegraphics[width=0.48\textwidth]{plots/task01_1_00199.png}
\includegraphics[width=0.48\textwidth]{plots/task01_x_00199.png}
\caption{\label{fig:task01_stable}Comparison for stable (left, $d = 0.48 \leq 0.5$) vs. unstable (right, $d = 0.55 > 0.5$). At the top the simulation snapshot after 120 time steps and at the bottom after 1000 timesteps.}
\end{figure}
@ -255,8 +255,8 @@ See Figure~\ref{fig:task01_inf} for $\lim_{t\to\infty}C(x, t)$ simulation (many
\begin{figure}[!h]
\centering
\includegraphics[width=0.48\textwidth]{task01_1_Cinf.png}
\includegraphics[width=0.48\textwidth]{task01_2_Cinf.png}
\includegraphics[width=0.48\textwidth]{plots/task01_1_Cinf.png}
\includegraphics[width=0.48\textwidth]{plots/task01_2_Cinf.png}
\caption{\label{fig:task01_inf}Solution from Section~\ref{sec:task01_1} (left) and Section~\ref{sec:task01_2} (right) for $t\to\infty$ simulated by setting number of time steps to $N_t = 20000$.}
\end{figure}
@ -293,7 +293,7 @@ and the update is performed by solving for $C^{n+1}$.
\begin{figure}[!h]
\centering
\includegraphics[width = 0.8\textwidth]{task01_all.png}
\includegraphics[width = 0.8\textwidth]{plots/task01_all.png}
\caption{\label{fig:task01_all}Comparison of all four subtasks. As expected 1.1, 1.3 and 1.4 solve the same probelm and as such have (basically) identical solution while the subtask 1.2 solves for different BC (Dirichlet) which is fullfilled.}
\end{figure}
@ -431,12 +431,12 @@ with the current $C_0 = \frac{U \Delta x}{\Delta t}$. The boundary condition enf
\begin{figure}[!h]
\centering
\includegraphics[width = 0.3\textwidth]{task02_gauss_C0_0-7_00150.png}
\includegraphics[width = 0.3\textwidth]{task02_gauss_C0_1_00150.png}
\includegraphics[width = 0.3\textwidth]{task02_gauss_C0_1-1_00150.png}
\includegraphics[width = 0.3\textwidth]{task02_square_C0_0-7_00150.png}
\includegraphics[width = 0.3\textwidth]{task02_square_C0_1_00150.png}
\includegraphics[width = 0.3\textwidth]{task02_square_C0_1-1_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_gauss_C0_0-7_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_gauss_C0_1_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_gauss_C0_1-1_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_square_C0_0-7_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_square_C0_1_00150.png}
\includegraphics[width = 0.3\textwidth]{plots/task02_square_C0_1-1_00150.png}
\caption{\label{fig:task02_all}For initial Gauss wavelet (top) and Square wavelet (bottom) after 150 iterations (one leap around the boundary) with different current $C_0$. Left: $C_0 = 0.7$, Center: $C_0 = 1$ (perfect) and Right: $C_0 = 1.1$ (unstable).}
\end{figure}