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flowchart.tex
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flowchart.tex
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\documentclass{article}
\usepackage{geometry}
\geometry{
letterpaper,
left=1in,
right=1in,
top=1in,
bottom=1in,
}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,float}
\floatplacement{figure}{H}
\usepackage{hyperref}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.12}
\graphicspath{{./images/}}
\input{math_commands}
% used tikz libraries
\usetikzlibrary{patterns}
\usetikzlibrary{arrows}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usetikzlibrary{trees}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows}
\usetikzlibrary{chains}
\usetikzlibrary{decorations.shapes}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{shapes}
\usetikzlibrary{matrix}
\begin{document}
%=== SCHÉMA GLOBAL MÉTHODE INVERSE ===%
\begin{figure}[!ht]
\centering
\tikzset{
My Line Style/.style={smooth, ultra thick, samples=400},
punktchain/.style={
rectangle,
rounded corners,
% fill=black!10,
draw=black, very thick,
text width=20em,
minimum height=3em,
text centered,
on chain},
line/.style={draw, thick, <-},
punktchain2/.style={
rectangle,
rounded corners,
% fill=black!10,
draw=black, very thick,
text width=15em,
minimum height=3em,
text centered,
on chain},
every join/.style={->, thick,shorten >=1pt,>=stealth},
decorate sep/.style 2 args=
{decorate,decoration={shape backgrounds,shape=circle,shape size=#1,shape sep=#2}}
}
\begin{tikzpicture}
[node distance=.8cm,
start chain=going below,]
\draw (0,1.3) node{};
\draw (0,-15.5) node{};
\node[punktchain,dashed] (0) {Mesures \mbox{expérimentales} du courant de diffusion $I(t)$ et calcul du transfert de masse \vspace{-0.3cm}
\begin{align*}
K(t)=\dfrac{I(t)}{nFAC_0} \to Sh_{exp}(t^*) = \dfrac{K(t^*)l}{D}
\end{align*}
};
\node[punktchain] (1) {1. Résolution de XYZ avec $\hat{S}^*(t^*_k)$, une bonne approximation de $S^*(t^*_k)$};
% \draw[decorate sep={0.8mm}{1.2mm},fill] (0) -- (1);
\node[punktchain, join] (2) {2. Évaluation de $\hat{\Sh}(t^*_k)$ en intégrant le transfert de masse à la sonde, d'après XYZ};
\node[punktchain, join] (3) {3. Calcul de $\partial\hat{Sh}(t^*_k)/\partial{S^*}$ (c.f. sect. XYZ) et correction de $\hat{S}^*(t^*_k)$: \vspace{-0.4cm}
\begin{align*}
S^*_i(t^*_k) &= \hat{S}^*(t^*_k) + dS
\end{align*} };
\node[punktchain, join] (4) {4. Résolution de XYZ0 avec $S^*_i(t^*_k)$, puis évaluation de $Sh_i(t^*_k)$ avec XYZ};
\node[punktchain, join] (5) {5. Vérification de la convergence de $Sh_i(t^*_k)$ \vspace{-0.3cm}
\begin{align*}
|Sh_i(t^*_k) - Sh_{exp}(t^*_k)| < \epsilon \;?
\end{align*}
};
\begin{scope}[start branch]
\node[punktchain2, on chain=going right] (6) { \vspace{-0.5cm}
\begin{align*}
6. \;\; \hat{S}^*(t^*_k) &= S^*_i(t^*_k) \\
i &= i+1
\end{align*}
};
\end{scope}
\draw[->, thick,>=stealth] (5) -- node [above] {non} (6);
\draw[dashed,->, ultra thick,>=stealth] (6.north) |- (1.east);
\node[punktchain] (7) { \vspace{-0.5cm}
\begin{align*}
7.\;\; S^*_{inv}(t^*_k) = S^*_i(t^*_k) &\quad\; Sh_{inv}(t^*_k) = Sh_i(t^*_k)\\
\hat{S}^*(t^*_{k+1}) &= S^*_i(t^*_k) \\
k &= k+1
\end{align*}
};
\draw[->, thick,>=stealth] (5) -- node [left] {oui} (7);
\node[on chain=going left] (caca) {};
\draw[dashed,->, ultra thick,>=stealth] (7.west) -- (caca.center) |- (1);
\end{tikzpicture}
\end{figure}
%=== flowchart inverse method ===%
\begin{figure}[!ht]
\centering
\begin{tikzpicture}
\draw rectangle(3,0.9) node[pos=.5] {Mesures de $I_{exp}$};
\draw[thick,->,>=stealth] (1.5,0) |- +(1,-0.65) node[right] (a){$\Sh_{exp}$};%(a);
\draw[thick,->,>=stealth] (a) -- node[above=-0.05cm]{\color{blue}\footnotesize \textit{Lévêque}} +(2.5,0) node[right](b){$S_{inv}$};
\draw[thick,->,>=stealth] (b) -- node[above]{\color{blue}\footnotesize \textit{Calcul}} +(2.5,0) node[right](b1){$\Sh_{inv}$};
\draw[thick,->,>=stealth] (b1) -- +(0,-0.9) node[below](c) {$\quad\Sh_{inv} = \Sh_{exp}$?};
\draw[->,dashed,>=stealth] ($(c)-(1.2,0)$) -| node[below=0.3cm, right=0.55cm] {\footnotesize \color{red} non} node[above=0.25cm, right=0.15cm,] {\color{blue}\scriptsize \textit{Correction}} (b);
\draw[->,thick,double,>=stealth] (c) -- node[below]{\footnotesize \color{green!50!black} oui} +(3,0) node[right]{$S_{inv}=S_{exp}$};
\end{tikzpicture}
\end{figure}
\end{document}