From 72e7fac8be6a0c49a876bb60d0e1f9eb243d7a25 Mon Sep 17 00:00:00 2001
From: Adrian Kummerlaender
Date: Mon, 17 Dec 2018 20:34:31 +0100
Subject: Start tracking bachelor thesis source

Some scaffolding as well as the initial port of usable parts from my seminar talk on grid refinement criterions.
---
 img/cavity2D.pdf                       | Bin 0 -> 153410 bytes
 img/cavity2d.png                       | Bin 0 -> 28162 bytes
 img/cavity2d.tikz                      |  16 +++++++++
 img/d2q9.tikz                          |  29 +++++++++++++++++
 img/grid_factors.tikz                  |  57 +++++++++++++++++++++++++++++++++
 img/grid_refinement_overlap_zone_1.png | Bin 0 -> 50027 bytes
 img/grid_refinement_overlap_zone_2.png | Bin 0 -> 52852 bytes
 img/kit-logo.jpg                       | Bin 0 -> 671621 bytes
 img/linear_convergence.pdf             | Bin 0 -> 35633 bytes
 img/multi_domain.tikz                  |  38 ++++++++++++++++++++++
 img/multi_grid.tikz                    |  25 +++++++++++++++
 img/overlap_zone.tikz                  |  24 ++++++++++++++
 12 files changed, 189 insertions(+)
 create mode 100644 img/cavity2D.pdf
 create mode 100644 img/cavity2d.png
 create mode 100644 img/cavity2d.tikz
 create mode 100644 img/d2q9.tikz
 create mode 100644 img/grid_factors.tikz
 create mode 100644 img/grid_refinement_overlap_zone_1.png
 create mode 100644 img/grid_refinement_overlap_zone_2.png
 create mode 100644 img/kit-logo.jpg
 create mode 100644 img/linear_convergence.pdf
 create mode 100644 img/multi_domain.tikz
 create mode 100644 img/multi_grid.tikz
 create mode 100644 img/overlap_zone.tikz

(limited to 'img')

diff --git a/img/cavity2D.pdf b/img/cavity2D.pdf
new file mode 100644
index 0000000..a326a98
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diff --git a/img/cavity2d.png b/img/cavity2d.png
new file mode 100644
index 0000000..8409ec5
Binary files /dev/null and b/img/cavity2d.png differ
diff --git a/img/cavity2d.tikz b/img/cavity2d.tikz
new file mode 100644
index 0000000..cb99dba
--- /dev/null
+++ b/img/cavity2d.tikz
@@ -0,0 +1,16 @@
+\begin{tikzpicture}
+\node[anchor=south west,inner sep=0] at (0,0) {\includegraphics[width=5cm]{img/cavity2d.png}};
+\foreach \x in {0,...,4}
+	\foreach \y in {0,...,4}
+		\draw[white] (\x,\y) rectangle (\x+1,\y+1);
+
+\draw[black,thick] (0,0) rectangle (5,5);
+
+\draw[->] (0,5.2) -- node[above,midway] {\footnotesize\(u=(1,0)\)} (5,5.2);
+\draw (0,0) -- node[below] {\footnotesize\(u=(0,0)\)} (5,0);
+\draw (0,0) -- node[rotate=90,yshift=10pt] {\footnotesize\(u=(0,0)\)} (0,5);
+\draw (5,0) -- node[rotate=90,yshift=-10pt] {\footnotesize\(u=(0,0)\)} (5,5);
+
+\draw[<->] (-0.7,0) -- node[rotate=90,yshift=10pt] {\scriptsize \(L=1\), diskretisiert in \(N\) Knoten} (-0.7,5);
+\draw[<->] (0,-0.7) -- node[below] {\scriptsize \(L=1\), diskretisiert in \(N\) Knoten} (5,-0.7);
+\end{tikzpicture}
diff --git a/img/d2q9.tikz b/img/d2q9.tikz
new file mode 100644
index 0000000..bd44101
--- /dev/null
+++ b/img/d2q9.tikz
@@ -0,0 +1,29 @@
+\begin{tikzpicture}[
+	scale=1.5,
+	dot/.style={circle,fill=black,inner sep=2pt},
+	center/.style={circle,fill=red,inner sep=3pt},
+	arrow/.style={thick,->,>=stealth}
+]
+
+\node[dot,label=below left:\(\xi_3\)] at (0,0){ };
+\node[dot,label=below:\(\xi_4\)] at (1,0){ };
+\node[dot,label=below right:\(\xi_5\)] at (2,0){ };
+
+\node[dot,label=left:\(\xi_2\)] at (0,1){ };
+\node[center] at (1,1){ };
+\node[dot,label=right:\(\xi_6\)] at (2,1){ };
+
+\node[dot,label=above left:\(\xi_1\)] at (0,2){ };
+\node[dot,label=above:\(\xi_8\)] at (1,2){ };
+\node[dot,label=above right:\(\xi_7\)] at (2,2){ };
+
+\draw[arrow] (1.0,1.2) -- (1.0,1.8);
+\draw[arrow] (1.2,1.0) -- (1.8,1.0);
+\draw[arrow] (1.0,0.8) -- (1.0,0.2);
+\draw[arrow] (0.8,1.0) -- (0.2,1.0);
+
+\draw[arrow] (1.2,1.2) -- (1.8,1.8);
+\draw[arrow] (1.2,0.8) -- (1.8,0.2);
+\draw[arrow] (0.8,0.8) -- (0.2,0.2);
+\draw[arrow] (0.8,1.2) -- (0.2,1.8);
+\end{tikzpicture}
diff --git a/img/grid_factors.tikz b/img/grid_factors.tikz
new file mode 100644
index 0000000..edb80ae
--- /dev/null
+++ b/img/grid_factors.tikz
@@ -0,0 +1,57 @@
+\begin{tikzpicture}[
+	cavity/.style = {
+		matrix of nodes,
+		nodes in empty cells,
+		column sep = -\pgflinewidth,
+		row sep    = -\pgflinewidth,
+		nodes={
+			inner sep=0mm,
+			outer sep=0pt,
+			minimum size=5mm,
+			text height=\ht\strutbox,
+			text depth=\dp\strutbox,
+			draw
+		}
+	}
+]
+
+\matrix[cavity,label=below:{\(N=15\)}] {
+	5 & 4 & 4 & 4 & 5 \\
+	3 & 3 & 2 & 3 & 4 \\
+	2 & 2 & 2 & 2 & 3 \\
+	1 & 1 & 1 & 1 & 1 \\
+	0 & 1 & 1 & 1 & 0 \\
+};
+
+\matrix[cavity,label=below:{\(N=30\)}] at (3, 0) {
+	4 & 3 & 3 & 3 & 4 \\
+	1 & 1 & 1 & 1 & 2 \\
+	1 & 0 & 0 & 1 & 2 \\
+	0 & 0 & 0 & 1 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+};
+
+\matrix[cavity,label=below:{\(N=60\)}] at (6, 0) {
+	3 & 2 & 2 & 2 & 3 \\
+	0 & 0 & 0 & 0 & 1 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+};
+
+\matrix[cavity,label=below:{\(N=120\)}] at (9, 0) {
+	2 & 1 & 1 & 1 & 2 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+};
+
+\matrix[cavity,label=below:{\(N=240\)}] at (12, 0) {
+	1 & 0 & 0 & 0 & 1 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+	0 & 0 & 0 & 0 & 0 \\
+};
+\end{tikzpicture}
diff --git a/img/grid_refinement_overlap_zone_1.png b/img/grid_refinement_overlap_zone_1.png
new file mode 100644
index 0000000..34e7c5b
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diff --git a/img/grid_refinement_overlap_zone_2.png b/img/grid_refinement_overlap_zone_2.png
new file mode 100644
index 0000000..4210a50
Binary files /dev/null and b/img/grid_refinement_overlap_zone_2.png differ
diff --git a/img/kit-logo.jpg b/img/kit-logo.jpg
new file mode 100644
index 0000000..5da07af
Binary files /dev/null and b/img/kit-logo.jpg differ
diff --git a/img/linear_convergence.pdf b/img/linear_convergence.pdf
new file mode 100644
index 0000000..a1176fe
Binary files /dev/null and b/img/linear_convergence.pdf differ
diff --git a/img/multi_domain.tikz b/img/multi_domain.tikz
new file mode 100644
index 0000000..8b9a02c
--- /dev/null
+++ b/img/multi_domain.tikz
@@ -0,0 +1,38 @@
+\begin{tikzpicture}[
+	scale=0.4,
+	coarse/.style={circle,draw=black,inner sep=2pt},
+	fine/.style={circle,draw=black,inner sep=1pt}
+]
+
+\foreach \x in {0,...,3}
+	\foreach \y in {0,...,7}
+		\node[coarse] at (\x,\y){ };
+\foreach \x in {4,...,7}
+	\foreach \y in {0,...,2}
+		\node[coarse] at (\x,\y){ };
+\foreach \x in {4,...,7}
+	\foreach \y in {5,...,7}
+		\node[coarse] at (\x,\y){ };
+
+\draw (9,3.5) node[cross out,draw=black,line width=0.5mm,rotate=45]{};
+
+\foreach \x in {0,...,10}
+	\foreach \y in {0,...,10}
+		\node[fine] at (11+0.5*\x,1+0.5*\y){ };
+
+\draw[->,line width=0.5mm] (18,3.5) -- (20,3.5);
+
+\foreach \x in {22,...,25}
+	\foreach \y in {0,...,7}
+		\node[coarse] at (\x,\y){ };
+\foreach \x in {26,...,29}
+	\foreach \y in {0,...,2}
+		\node[coarse] at (\x,\y){ };
+\foreach \x in {26,...,29}
+	\foreach \y in {5,...,7}
+		\node[coarse] at (\x,\y){ };
+
+\foreach \x in {0,...,10}
+	\foreach \y in {0,...,10}
+		\node[fine] at (24+0.5*\x,1+0.5*\y){ };
+\end{tikzpicture}
diff --git a/img/multi_grid.tikz b/img/multi_grid.tikz
new file mode 100644
index 0000000..28661c5
--- /dev/null
+++ b/img/multi_grid.tikz
@@ -0,0 +1,25 @@
+\begin{tikzpicture}[
+	scale=0.4,
+	coarse/.style={circle,draw=black,inner sep=2pt},
+	fine/.style={circle,draw=black,inner sep=1pt}
+]
+
+\foreach \x in {0,...,7}
+	\foreach \y in {0,...,7}
+		\node[coarse] at (\x,\y){ };
+
+\draw (9,3.5) node[cross out,draw=black,line width=0.5mm,rotate=45]{};
+
+\foreach \x in {0,...,8}
+	\foreach \y in {0,...,8}
+		\node[fine] at (11+0.5*\x,1+0.5*\y){ };
+
+\draw[->,line width=0.5mm] (18,3.5) -- (20,3.5);
+
+\foreach \x in {0,...,7}
+	\foreach \y in {0,...,7}
+		\node[coarse] at (22+\x,\y){ };
+\foreach \x in {0,...,8}
+	\foreach \y in {0,...,8}
+		\node[fine] at (24+0.5*\x,1+0.5*\y){ };
+\end{tikzpicture}
diff --git a/img/overlap_zone.tikz b/img/overlap_zone.tikz
new file mode 100644
index 0000000..a491292
--- /dev/null
+++ b/img/overlap_zone.tikz
@@ -0,0 +1,24 @@
+\begin{tikzpicture}[
+	scale=1.5,
+	coarse/.style={circle,draw=black,thick,inner sep=4pt},
+	fine/.style={cross out,draw=black,thick,minimum size=8pt},
+	arrow/.style={-{Latex[length=2mm]},thick}
+]
+
+\foreach \x in {-1,...,3}
+	\foreach \y in {0,...,2}
+		\node[coarse] at (\x,\y){ };
+
+\foreach \x in {0,...,8}
+	\foreach \y in {0,...,4}
+		\node[fine] at (2+\x*0.5,\y*0.5){ };
+
+\draw[dashed,thick] (1.8,-0.2) rectangle (2.2,2.2);
+\draw[dashed,thick] (2.8,-0.2) rectangle (3.2,2.2);
+
+\draw[arrow] (2,3.3) node[right] {Übertragung von grob nach fein} -- (2,2.3);
+\draw[arrow] (3,2.8) node[right] {Übertragung von fein nach grob} -- (3,2.3);
+
+\draw[decorate,decoration={brace,amplitude=10pt,mirror},line width=1pt]
+(1.8,-0.4) -- (3.2,-0.4) node[midway,below,yshift=-6pt] {Übergangsbereich};
+\end{tikzpicture}
-- 
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