From 764f26b4aae4eb7d00359f8a44706abaf5997369 Mon Sep 17 00:00:00 2001
From: Lucas Palazzolo <lucaspalazzolo.pro@gmail.com>
Date: Thu, 10 Aug 2023 11:14:02 +0200
Subject: [PATCH] correction of the algorithm in the implementation of the geo
 shapo

---
 docs/modules/ROOT/pages/implementation.adoc | 100 ++++++++++----------
 1 file changed, 48 insertions(+), 52 deletions(-)

diff --git a/docs/modules/ROOT/pages/implementation.adoc b/docs/modules/ROOT/pages/implementation.adoc
index 55a1912..dfe950f 100644
--- a/docs/modules/ROOT/pages/implementation.adoc
+++ b/docs/modules/ROOT/pages/implementation.adoc
@@ -158,60 +158,56 @@ Contains all the information needed to solve the optimization problem. Depending
 == Algorithm 
 Now that the data needed to solve a shape optimization problem has been described, let's present the main points of the algorithm.
 
-.Geometric shape optimisation algorithm 
-++++
-<pre id="shapeopti" style="display:hidden;">
-\begin{algorithm}
-    \caption{Geometric shape optimisation algorithm}
-    \hspace*{\algorithmicindent} \textbf{Input :} Parameters json file  \\
-    \hspace*{\algorithmicindent} \textbf{Output :} Csv and paraview files for each iteration
-    \begin{algorithmic}
-    \FUNCTION{ShapeOpti}{}
-
-
-      \STATE \textbf{Initialization:} 
-      \STATE  $n=0$.
-      \STATE  - Reading the json file containing the parameters.
-      \STATE  - Solve the primal problem. 
-      \STATE  - Solve the dual problem.
-      \STATE  - Solve the postprocessing problem.
-
-      \IF {NSGF} 
-        \STATE - Solve the postprocessing of $\xi_J$ problem.
-        \STATE - Solve the $Dg^T$ problem.
-      \ENDIF
-      
-      \STATE - Solve the expansion problem : $\theta_n$.
-
-      \WHILE{$\|\theta_n\|_{H^1}>\varepsilon_{tol}$ AND $n<N_{max}$}
-
-        \STATE  - Deforming the mesh by applying $\theta_n$.
 
-        \IF {mesh quality $< q$}
-          \STATE - Remesh.
-        \ENDIF
-
-        \STATE  - Solve the primal problem. 
-        \STATE  - Solve the dual problem.
-        \STATE  - Solve the postprocessing problem.
-
-        \IF {NSGF} 
-          \STATE - Solve the postprocessing of $\xi_J$ problem.
-          \STATE - Solve the $Dg^T$ problem.
-        \ENDIF
-      
-        \STATE - Solve the expansion problem : $\theta_n$.
-
-        \STATE $n=n+1$.
-        \STATE - Save the results.
-
-
-      \ENDWHILE
-    \ENDFUNCTION
-    \end{algorithmic}
+[.pseudocode]
+....
+\begin{algorithm}
+\caption{Geometric shape optimisation algorithm}
+\begin{algorithmic} 
+\STATE \textbf{Input:} Parameters json file
+\STATE \textbf{Output:} Csv and paraview files for each iteration\\
+
+\STATE \textbf{Initialization:} 
+  \STATE
+  \STATE
+  \STATE  $\quad$- $n=0$.
+  \STATE  $\quad$- Reading the json file containing the parameters.
+  \STATE  $\quad$- Solve the primal problem. 
+  \STATE  $\quad$- Solve the dual problem.
+  \STATE  $\quad$- Solve the postprocessing problem.
+  \STATE
+  \IF {NSGF} 
+      \STATE $\quad$- Solve the postprocessing of $\xi_J$ problem.
+      \STATE $\quad$- Solve the $Dg^T$ problem.
+  \ENDIF
+  \STATE
+  \STATE $\quad$- Solve the expansion problem : $\theta_n$.
+\STATE \textbf{Main loop:}
+\STATE
+\STATE
+  \WHILE{$\|\theta_n\|_{H^1}>\varepsilon_{tol}$ AND $n<N_{max}$}
+    \STATE  $\quad$- Deforming the mesh by applying $\theta_n$.
+    \STATE
+    \IF {mesh quality $< q$}
+      \STATE $\quad$- Remesh.
+    \ENDIF
+    \STATE
+    \STATE  $\quad$- Solve the primal problem. 
+    \STATE  $\quad$- Solve the dual problem.
+    \STATE  $\quad$- Solve the postprocessing problem.
+    \STATE
+    \IF {NSGF} 
+      \STATE $\quad$- Solve the postprocessing of $\xi_J$ problem.
+      \STATE $\quad$- Solve the $Dg^T$ problem.
+    \ENDIF
+    \STATE
+    \STATE $\quad$- Solve the expansion problem : $\theta_n$.
+    \STATE  $\quad$- $n=n+1$.
+    \STATE $\quad$- Save the results.
+  \ENDWHILE
+\end{algorithmic}
 \end{algorithm}
-</pre>
-++++
+....
 
 For reasons of visibility, certain points have been omitted, such as the calculation of the Lagrange multiplier in the case of gradient descent, or certain coefficients in the case of null space gradient flow. The various results obtained are saved after each iteration in a csv file for all cost, volume and stem:[H^1]-norm functions, etc. For fields and meshes, paraview files are also exported after each iteration.