\usepackage[utf8]{inputenc} %Eingabekodierung
\usepackage{fixltx2e} %Deutschsprach Bugs
-\definecolor{gray}{gray}{.95}
+\definecolor{gray}{gray}{.8}
+\definecolor{dred}{rgb}{.8,0,0}
+\definecolor{dgreen}{rgb}{0,.8,.4}
+\definecolor{dblue}{rgb}{0,.4,.4}
-\def\todo#1{\textcolor{red}{#1}}
+\def\todo#1{\textcolor{dred}{#1}}
\def\why#1{\textcolor{blue}{#1}}
\def\Matlab{{\sc Matlab}}
\def\q{\Q}
\section{Analytische Berechnung der Integrale}
Es seien $T_j,T_k \subseteq\R^3$ zwei beschränkte, achsenorientierte Rechtecke in $\R^3$.
Die Berechnung der Matrix für das Galerkin-Verfahren benötigt die Auswertung von
-\begin{eqnarray*}
+\begin{eqnarray}\label{math:V}
\frac{1}{4\pi} \int_{T_j} \int_{T_k} \frac{1}{|\bs x- \bs y|} ds_{\bs y} ds_{\bs x} \in \R^3.
-\end{eqnarray*}
-Wir betrachten zunächst die Berechnung von zwei Integralen, die im Zuge der Berechnungen auftreten werden.
+\end{eqnarray}
+Wir betrachten zunächst die Berechnung von zwei Integralen, die dabei auftreten werden.
\subsection{einfach Integral}
Wir bezeichnen
\begin{eqnarray*}
\end{align*}
\subsection{Integral über zwei Elemente}
-Bei der Integration über zwei Seitenelemente \Ta, \Tb $\in \T_{\ell}$ haben wir geometrisch zischen zwei Fällen unterschieden. Entweder die beiden Elemente liegen in parallelen Ebenen oder in orthogonalen Ebenen.
+Bei der Berechnung von \ref{math:V} haben wir geometrisch zwischen zwei Fällen zu unterschei den. Entweder die beiden Elemente liegen in parallelen Ebenen oder in orthogonalen Ebenen.
\subsubsection{Parallele Elemente}
Liegen die beiden Elemente parallel zueinander lassen sie sich Folgendermaßen darstellen:
\subsection{Datenstruktur}
Für die Implementierung in \Matlab~und C++ wollen wollen wir eine einheitliche Datenstruktur einführen.
-Die für die Partition $\mathcal{T}_{\ell} = \{T_1\ldots T_M\}$ benötigen Knoten $\mathcal{K}_{\ell} = \{C_1\ldots C_N\}$ stellen wir in einer $ N \times 3$ Matrix dar. Dabei enthält die $j$-te Zeile die Koordinaten des Knoten $C_j$ im $\R^3$.
+Die für die Partition $\mathcal{T}_{\ell} = \{T_1\ldots T_N\}$ benötigten Knoten $\mathcal{K}_{\ell} = \{C_1\ldots C_M\}$ stellen wir in einer $M \times 3$ Matrix $COO$ dar. Dabei enthält die $j$-te Zeile die Koordinaten des Knoten $C_j$, d.h. :
\begin{displaymath}
- COO[j,1:3] = C_j := (x_j,y_j,z_j)^{T} \text{ wobei } x,y,z \in \R
+ COO[j,1:3] = C_j := (x_j,y_j,z_j)^{T} \text{ wobei } x_j,y_j,z_j \in \R.
\end{displaymath}
-Die Elemente $\mathcal{E}_{\ell}$ werden wir ebenfalls Zeilenweise in einer $M \times 4$ Matrix abspeichern. Dabei soll die $i$-te Zeile den Indizes der Knoten $\{C_j,C_k,C_{\ell},C_m\}$ des Elements $T_j$ entsprechen.
+Die Elemente $\mathcal{T}_{\ell}$ werden wir ebenfalls Zeilenweise in einer $N \times 4$ Matrix $ELE$ abspeichern. Dabei soll die $i$-te Zeile den Indizes der Knoten $\{C_j,C_k,C_{\ell},C_m\}$ des Elements $T_i$ entsprechen, also:
\begin{displaymath}
- ELE[i,1:4] = T_i := (j,k,l,m)
+ ELE[i,1:4] = T_i := (j,k,l,m).
\end{displaymath}
-Die Knoten wollen wir gegen den Uhrzeigersinn anordnen und der Knoten $C_j$ soll der kleinste bezüglich der Koordinaten sein.
+Die Knoten wollen wir gegen den Uhrzeigersinn anordnen \todo{und der Knoten $C_j$ soll der kleinste bezüglich der Koordinaten sein}.
\noindent
Für die bessere Handhabung der Elemente beim Verfeinern der Partition, wollen wir auch die Nachbarschaftsrelationen geeignet abspeichern. Dazu überlegen wir uns, dass wir Aufgrund der Netzstabilität maximal zwei Nachbarn pro Kante eines Elements zulassen wollen.
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/exmpl11_ref.eps
-%%CreationDate: 08/31/2012 13:37:03
+%%CreationDate: 08/31/2012 20:24:57
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
(1) s
gs 624 269 3721 2937 MR c np
8.33333 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 1224 -1550 0 0 -1224 1550 0 934 1738 5 MP stroke
0 1224 -1550 0 0 -1224 1550 0 2484 1738 5 MP stroke
2 & 12 & 16 & 17 & 13\\
3 & 9 & 14 & 15 & 11\\
4 & 2 & 10 & 11 & 3\\
- 5 & 3 & 6 & 7 & 4\\
- 6 & 11 & 15 & 16 & 12\\
- 7 & 1 & 9 & 10 & 2\\
- 8 & 7 & 12 & 13 & 8\\
- 9 & 6 & 11 & 12 & 7
+ 5 & 7 & 12 & 13 & 8\\
+ 6 & 6 & 11 & 12 & 7\\
+ 7 & 3 & 6 & 7 & 4\\
+ 8 & 11 & 15 & 16 & 12\\
+ 9 & 1 & 9 & 10 & 2
\end{tabular}
\label{exmpl12:ele}
\ No newline at end of file
\begin{tabular}{>{\columncolor{gray}}rcccc}
\rowcolor{gray}
Index & e1 & e2 & e3 & e4\\
- 1 & 5 & 9 & 8 & 1\\
- 2 & 6 & 6 & 2 & 2\\
+ 1 & 7 & 6 & 5 & 1\\
+ 2 & 8 & 8 & 2 & 2\\
3 & 3 & 3 & 3 & 3\\
- 4 & 7 & 7 & 4 & 4
+ 4 & 9 & 9 & 4 & 4
\end{tabular}
\label{exmpl12:f2s}
\ No newline at end of file
\begin{tabular}{>{\columncolor{gray}}rcccccccc}
\rowcolor{gray}
Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\
- 1 & 5 & 8 & 0 & 0 & 0 & 0 & 0 & 0\\
- 2 & 6 & 0 & 0 & 8 & 0 & 0 & 0 & 0\\
- 3 & 0 & 0 & 6 & 7 & 0 & 0 & 0 & 4\\
- 4 & 7 & 3 & 5 & 0 & 0 & 0 & 9 & 0\\
- 5 & 4 & 9 & 1 & 0 & 0 & 0 & 0 & 0\\
- 6 & 3 & 0 & 2 & 9 & 0 & 0 & 0 & 0\\
- 7 & 0 & 3 & 4 & 0 & 0 & 0 & 0 & 0\\
- 8 & 9 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\
- 9 & 4 & 6 & 8 & 5 & 0 & 0 & 0 & 0
+ 1 & 7 & 5 & 0 & 0 & 0 & 0 & 0 & 0\\
+ 2 & 8 & 0 & 0 & 5 & 0 & 0 & 0 & 0\\
+ 3 & 0 & 0 & 8 & 9 & 0 & 0 & 0 & 4\\
+ 4 & 9 & 3 & 7 & 0 & 0 & 0 & 6 & 0\\
+ 5 & 6 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\
+ 6 & 4 & 8 & 5 & 7 & 0 & 0 & 0 & 0\\
+ 7 & 4 & 6 & 1 & 0 & 0 & 0 & 0 & 0\\
+ 8 & 3 & 0 & 2 & 6 & 0 & 0 & 0 & 0\\
+ 9 & 0 & 3 & 4 & 0 & 0 & 0 & 0 & 0
\end{tabular}
\label{exmpl12:nei}
\ No newline at end of file
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/exmpl12_ref.eps
-%%CreationDate: 08/31/2012 13:37:03
+%%CreationDate: 08/31/2012 20:24:57
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
(1) s
gs 624 269 3721 2937 MR c np
8.33333 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 612 -775 0 0 -612 775 0 934 1126 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1126 5 MP stroke
0 1223 -1550 0 0 -1223 1550 0 2484 2961 5 MP stroke
0 611 -1550 0 0 -611 1550 0 934 2349 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
0 612 -775 0 0 -612 775 0 934 1738 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1738 5 MP stroke
0 612 -1550 0 0 -612 1550 0 934 2961 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
gr
8.33333 w
(\(3\)) s
1709 2073 mt
(\(4\)) s
-1321 1462 mt
+2096 850 mt
(\(5\)) s
-3259 1462 mt
+2096 1462 mt
(\(6\)) s
-1709 2685 mt
+1321 1462 mt
(\(7\)) s
-2096 850 mt
+3259 1462 mt
(\(8\)) s
-2096 1462 mt
+1709 2685 mt
(\(9\)) s
/c9 { 1.000000 0.000000 0.000000 sr} bdef
c9
2 & 18 & 22 & 23 & 19\\
3 & 15 & 20 & 21 & 17\\
4 & 2 & 10 & 11 & 3\\
- 5 & 4 & 8 & 9 & 5\\
- 6 & 17 & 21 & 22 & 18\\
- 7 & 1 & 15 & 16 & 2\\
- 8 & 13 & 18 & 19 & 14\\
- 9 & 11 & 17 & 18 & 13\\
- 10 & 3 & 7 & 8 & 4\\
+ 5 & 13 & 18 & 19 & 14\\
+ 6 & 11 & 17 & 18 & 13\\
+ 7 & 4 & 8 & 9 & 5\\
+ 8 & 17 & 21 & 22 & 18\\
+ 9 & 1 & 15 & 16 & 2\\
+ 10 & 10 & 16 & 17 & 11\\
11 & 8 & 12 & 13 & 9\\
- 12 & 10 & 16 & 17 & 11\\
- 13 & 7 & 11 & 12 & 8
+ 12 & 7 & 11 & 12 & 8\\
+ 13 & 3 & 7 & 8 & 4
\end{tabular}
\label{exmpl13:ele}
\ No newline at end of file
1 & 1 & 1 & 1 & 1\\
2 & 2 & 2 & 2 & 2\\
3 & 3 & 3 & 3 & 3\\
- 4 & 4 & 12 & 12 & 4\\
- 5 & 10 & 13 & 11 & 5\\
+ 4 & 4 & 10 & 10 & 4\\
+ 5 & 5 & 5 & 5 & 5\\
6 & 6 & 6 & 6 & 6\\
- 7 & 7 & 7 & 7 & 7\\
+ 7 & 13 & 12 & 11 & 7\\
8 & 8 & 8 & 8 & 8\\
9 & 9 & 9 & 9 & 9
\end{tabular}
\begin{tabular}{>{\columncolor{gray}}rcccccccc}
\rowcolor{gray}
Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\
- 1 & 11 & 8 & 0 & 0 & 5 & 0 & 0 & 0\\
- 2 & 6 & 0 & 0 & 8 & 0 & 0 & 0 & 0\\
- 3 & 0 & 0 & 6 & 7 & 0 & 0 & 0 & 12\\
- 4 & 7 & 12 & 10 & 0 & 0 & 0 & 13 & 0\\
- 5 & 10 & 11 & 1 & 0 & 0 & 0 & 0 & 0\\
- 6 & 3 & 0 & 2 & 9 & 0 & 0 & 0 & 0\\
- 7 & 0 & 3 & 4 & 0 & 0 & 0 & 12 & 0\\
- 8 & 9 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\
- 9 & 12 & 6 & 8 & 13 & 0 & 0 & 0 & 11\\
- 10 & 4 & 13 & 5 & 0 & 0 & 0 & 0 & 0\\
- 11 & 13 & 9 & 1 & 5 & 0 & 0 & 0 & 0\\
- 12 & 7 & 3 & 9 & 4 & 0 & 0 & 0 & 0\\
- 13 & 4 & 9 & 11 & 10 & 0 & 0 & 0 & 0
+ 1 & 11 & 5 & 0 & 0 & 7 & 0 & 0 & 0\\
+ 2 & 8 & 0 & 0 & 5 & 0 & 0 & 0 & 0\\
+ 3 & 0 & 0 & 8 & 9 & 0 & 0 & 0 & 10\\
+ 4 & 9 & 10 & 13 & 0 & 0 & 0 & 12 & 0\\
+ 5 & 6 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\
+ 6 & 10 & 8 & 5 & 12 & 0 & 0 & 0 & 11\\
+ 7 & 13 & 11 & 1 & 0 & 0 & 0 & 0 & 0\\
+ 8 & 3 & 0 & 2 & 6 & 0 & 0 & 0 & 0\\
+ 9 & 0 & 3 & 4 & 0 & 0 & 0 & 10 & 0\\
+ 10 & 9 & 3 & 6 & 4 & 0 & 0 & 0 & 0\\
+ 11 & 12 & 6 & 1 & 7 & 0 & 0 & 0 & 0\\
+ 12 & 4 & 6 & 11 & 13 & 0 & 0 & 0 & 0\\
+ 13 & 4 & 12 & 7 & 0 & 0 & 0 & 0 & 0
\end{tabular}
\label{exmpl13:nei}
\ No newline at end of file
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/exmpl13_ref.eps
-%%CreationDate: 08/31/2012 13:37:04
+%%CreationDate: 08/31/2012 20:24:58
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
(1) s
gs 624 269 3721 2937 MR c np
8.33333 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 612 -775 0 0 -612 775 0 934 1126 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1126 5 MP stroke
0 1223 -1550 0 0 -1223 1550 0 2484 2961 5 MP stroke
0 611 -775 0 0 -611 775 0 934 2349 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
0 306 -387 0 0 -306 387 0 934 1432 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1738 5 MP stroke
0 612 -1550 0 0 -612 1550 0 934 2961 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
-0 306 -387 0 0 -306 387 0 934 1738 5 MP stroke
-0 306 -388 0 0 -306 388 0 1321 1432 5 MP stroke
0 611 -775 0 0 -611 775 0 1709 2349 5 MP stroke
+0 306 -388 0 0 -306 388 0 1321 1432 5 MP stroke
0 306 -388 0 0 -306 388 0 1321 1738 5 MP stroke
+0 306 -387 0 0 -306 387 0 934 1738 5 MP stroke
gr
8.33333 w
(\(3\)) s
1321 2073 mt
(\(4\)) s
-1127 1309 mt
+2096 850 mt
(\(5\)) s
-3259 1462 mt
+2096 1462 mt
(\(6\)) s
-1709 2685 mt
+1127 1309 mt
(\(7\)) s
-2096 850 mt
+3259 1462 mt
(\(8\)) s
-2096 1462 mt
+1709 2685 mt
(\(9\)) s
-1127 1615 mt
+2096 2073 mt
(\(10\)) s
1515 1309 mt
(\(11\)) s
-2096 2073 mt
-(\(12\)) s
1515 1615 mt
+(\(12\)) s
+1127 1615 mt
(\(13\)) s
/c9 { 1.000000 0.000000 0.000000 sr} bdef
c9
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/net1.eps
-%%CreationDate: 08/31/2012 13:37:04
+%%CreationDate: 08/31/2012 20:24:58
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 612 -775 0 0 -612 775 0 934 1126 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1126 5 MP stroke
0 1223 -1550 0 0 -1223 1550 0 2484 2961 5 MP stroke
0 611 -775 0 0 -611 775 0 934 2349 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
+0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
0 306 -387 0 0 -306 387 0 934 1432 5 MP stroke
0 612 -1550 0 0 -612 1550 0 2484 1738 5 MP stroke
0 612 -1550 0 0 -612 1550 0 934 2961 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1126 5 MP stroke
-0 612 -775 0 0 -612 775 0 1709 1738 5 MP stroke
-0 306 -387 0 0 -306 387 0 934 1738 5 MP stroke
-0 306 -388 0 0 -306 388 0 1321 1432 5 MP stroke
0 611 -775 0 0 -611 775 0 1709 2349 5 MP stroke
+0 306 -388 0 0 -306 388 0 1321 1432 5 MP stroke
0 306 -388 0 0 -306 388 0 1321 1738 5 MP stroke
+0 306 -387 0 0 -306 387 0 934 1738 5 MP stroke
4.16667 w
gr
5 0 obj
<</Length 6 0 R/Filter /FlateDecode>>
stream
-x\9cuRIn\ 4!\f¼ó
-¿\80\98¥ixAÎ\19\ ey@\94\8c\145\91&9äû\ 1Mc÷Øiq@\14Ta\97ë\ 6h\1dàXûþÖÌÓe\85ë\8f¹\99b])ÞC\84\90\11m\86\80.Á÷;¼Â\97qp5\83\10Óê¬\87°dìWæÃx\84ß~û9nm(\1e\ví\97g\13º\ eb\ 6ï}î\8aÍ\944\107\81\8d\81\92B\17Þ\98¢\80I©Æå2
-$Õ°.\87óFç)1ß˳VL÷¿Xr\aHÓÅ\12md\ryfB¥Ê×Ô=Ãph\7f"Ü?éL\92\ 2\98ÃÊ.w0uáX\961¾ l\ 4°'ÒF¡qpaÿº©\9e¥ÏÒGé \17ÊÆ*\9fv`´7
-~lø\119\9a+\92ÔÎ\8a¡¡«¤©,V9\8dv:e\15_ üã\ 1\89Ò°æ\e5=5\e\95\8a*I\1c."©âT(ÔÇUE´\1d\atÏ\9f4Eõ¬c^eÓí\9c¥2¬\ 1v᥯?Q6ò}endstream
+x\9cuSËnÄ \f¼û+ü\ 5Ô<Bà\vzîrè\aTíJURiÛC\7f\7fA\e0kï\8aCÂ\80'ã\19ç\82d,R[Çóc\87\97Ó\8aç?¸@66gç0 OD&¡'\eñ÷\13ßñ\a,\9e¡\15\84¸ZãÐ/\89ê\11|\81#ü¯§ßíÔø\9c39~9½\82¯LD \9ds©rî\90cCl\a6\ 6rô\95zã\12\ 5ô\92\ 26å&q°úu\99öÛØw\8a~_î5c¼}\8b)\ f`pÚ\90\83 Ì!÷\P\86ò5V×ÈOíw\84û\1f<½H\ 1\S¤\8d»êHv¬lVA\14)e\7fÚ¢ÊN\ 2£\82=°©Ê\8f\954ä¥\8dZ\a¶\ 1pz2pÁ1å5¤ÊtäD<ñç\81P\1e\ 1\95è\ 1´ \9aàûhî\91y\fdèûLtKTÊQFêÁ)ÒI\9e®á\93
+HyÒ\98h»·OŨ\b5ð`\10:º£XTîêß(ðV×\15k&òïendstream
endobj
6 0 obj
-310
+311
endobj
4 0 obj
<</Type/Page/MediaBox [0 0 381 302]
<?adobe-xap-filters esc="CRLF"?>
<x:xmpmeta xmlns:x='adobe:ns:meta/' x:xmptk='XMP toolkit 2.9.1-13, framework 1.6'>
<rdf:RDF xmlns:rdf='http://www.w3.org/1999/02/22-rdf-syntax-ns#' xmlns:iX='http://ns.adobe.com/iX/1.0/'>
-<rdf:Description rdf:about='uuid:bc4d2242-2b7c-11ed-0000-5b20b665609a' xmlns:pdf='http://ns.adobe.com/pdf/1.3/' pdf:Producer='GPL Ghostscript 9.05'/>
-<rdf:Description rdf:about='uuid:bc4d2242-2b7c-11ed-0000-5b20b665609a' xmlns:xmp='http://ns.adobe.com/xap/1.0/'><xmp:ModifyDate>2012-08-31T13:37:04+02:00</xmp:ModifyDate>
-<xmp:CreateDate>2012-08-31T13:37:04+02:00</xmp:CreateDate>
+<rdf:Description rdf:about='uuid:b7f12c36-2bb5-11ed-0000-ecf77e1e55fe' xmlns:pdf='http://ns.adobe.com/pdf/1.3/' pdf:Producer='GPL Ghostscript 9.05'/>
+<rdf:Description rdf:about='uuid:b7f12c36-2bb5-11ed-0000-ecf77e1e55fe' xmlns:xmp='http://ns.adobe.com/xap/1.0/'><xmp:ModifyDate>2012-08-31T20:24:58+02:00</xmp:ModifyDate>
+<xmp:CreateDate>2012-08-31T20:24:58+02:00</xmp:CreateDate>
<xmp:CreatorTool>MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.</xmp:CreatorTool></rdf:Description>
-<rdf:Description rdf:about='uuid:bc4d2242-2b7c-11ed-0000-5b20b665609a' xmlns:xapMM='http://ns.adobe.com/xap/1.0/mm/' xapMM:DocumentID='uuid:bc4d2242-2b7c-11ed-0000-5b20b665609a'/>
-<rdf:Description rdf:about='uuid:bc4d2242-2b7c-11ed-0000-5b20b665609a' xmlns:dc='http://purl.org/dc/elements/1.1/' dc:format='application/pdf'><dc:title><rdf:Alt><rdf:li xml:lang='x-default'>../doc/fig/net1.eps</rdf:li></rdf:Alt></dc:title></rdf:Description>
+<rdf:Description rdf:about='uuid:b7f12c36-2bb5-11ed-0000-ecf77e1e55fe' xmlns:xapMM='http://ns.adobe.com/xap/1.0/mm/' xapMM:DocumentID='uuid:b7f12c36-2bb5-11ed-0000-ecf77e1e55fe'/>
+<rdf:Description rdf:about='uuid:b7f12c36-2bb5-11ed-0000-ecf77e1e55fe' xmlns:dc='http://purl.org/dc/elements/1.1/' dc:format='application/pdf'><dc:title><rdf:Alt><rdf:li xml:lang='x-default'>../doc/fig/net1.eps</rdf:li></rdf:Alt></dc:title></rdf:Description>
</rdf:RDF>
</x:xmpmeta>
endobj
2 0 obj
<</Producer(GPL Ghostscript 9.05)
-/CreationDate(D:20120831133704+02'00')
-/ModDate(D:20120831133704+02'00')
+/CreationDate(D:20120831202458+02'00')
+/ModDate(D:20120831202458+02'00')
/Creator(MATLAB, The MathWorks, Inc. Version 7.14.0.739 \(R2012a\). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.)
/Title(../doc/fig/net1.eps)>>endobj
xref
0 10
0000000000 65535 f
-0000000604 00000 n
-0000002300 00000 n
-0000000545 00000 n
-0000000414 00000 n
+0000000605 00000 n
+0000002301 00000 n
+0000000546 00000 n
+0000000415 00000 n
0000000015 00000 n
-0000000395 00000 n
-0000000668 00000 n
-0000000709 00000 n
-0000000738 00000 n
+0000000396 00000 n
+0000000669 00000 n
+0000000710 00000 n
+0000000739 00000 n
trailer
<< /Size 10 /Root 1 0 R /Info 2 0 R
-/ID [<EC37CA9391FA1424ECBE3089B317DE73><EC37CA9391FA1424ECBE3089B317DE73>]
+/ID [<2D7D7384BA0E4985F5907B3D11BE82C6><2D7D7384BA0E4985F5907B3D11BE82C6>]
>>
startxref
-2613
+2614
%%EOF
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/net_wrong.eps
-%%CreationDate: 08/31/2012 13:37:04
+%%CreationDate: 08/31/2012 20:24:58
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 612 -1550 0 0 -612 1550 0 2484 1126 5 MP stroke
0 611 -1550 0 0 -611 1550 0 2484 2349 5 MP stroke
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/refType_1.eps
-%%CreationDate: 08/31/2012 16:03:30
+%%CreationDate: 08/31/2012 20:13:46
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 2447 -3100 0 0 -2447 3100 0 934 2961 5 MP stroke
gr
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/refType_2.eps
-%%CreationDate: 08/31/2012 16:03:31
+%%CreationDate: 08/31/2012 20:13:46
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 1224 -1550 0 0 -1224 1550 0 934 1738 5 MP stroke
0 1224 -1550 0 0 -1224 1550 0 2484 1738 5 MP stroke
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/refType_3.eps
-%%CreationDate: 08/31/2012 16:03:31
+%%CreationDate: 08/31/2012 20:13:46
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 1224 -3100 0 0 -1224 3100 0 934 1738 5 MP stroke
0 1223 -3100 0 0 -1223 3100 0 934 2961 5 MP stroke
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/refType_4.eps
-%%CreationDate: 08/31/2012 16:03:32
+%%CreationDate: 08/31/2012 20:13:47
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 2447 -1550 0 0 -2447 1550 0 934 2961 5 MP stroke
0 2447 -1550 0 0 -2447 1550 0 2484 2961 5 MP stroke
%!PS-Adobe-2.0 EPSF-1.2
%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-29-generic #46-Ubuntu SMP Fri Jul 27 17:03:23 UTC 2012 x86_64.
%%Title: ../doc/fig/refType_full.eps
-%%CreationDate: 08/31/2012 16:03:30
+%%CreationDate: 08/31/2012 20:13:45
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
4.16667 w
gs 624 269 3721 2937 MR c np
16.6667 w
-/c8 { 0.000000 0.392157 0.392157 sr} bdef
+/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
0 2447 -3100 0 0 -2447 3100 0 934 2961 5 MP stroke
gr
export_mesh(coordinates,elements,neigh,f2s,'exmpl12')
marked = ones(1,9);
-marked(5) = 2;
+marked(7) = 2;
% marked([4,7]) = 3;
[coordinates elements neigh f2s sites] =...
refineQuad(coordinates,elements,neigh,sites,marked);
for idx = eles
current = coordinates(elements(idx,[1:4,1])',:);
% current(3,:) = current(3,:)-current(1,:)+current(2,:);
- fill3(current(:,1),current(:,2),current(:,3),[0,200,100]/255); % Zeichnet Oberflaeche
+ fill3(current(:,1),current(:,2),current(:,3),[0,204,102]/255); % Zeichnet Oberflaeche
hold on
end
elseif(e==2)
for idx = eles
current = coordinates(elements(idx,[1:4,1])',:);
% current(3,:) = current(3,:)-current(1,:)+current(2,:);
- plot3(current(:,1),current(:,2),current(:,3),'LineWidth',line,'color',[0,100,100]/255); % Zeichnet nur Kanten
+ plot3(current(:,1),current(:,2),current(:,3),'LineWidth',line,'color',[0,102,102]/255); % Zeichnet nur Kanten
hold on
end
end