\end{itemize}
}
+\noindent
+An dieser Stelle betrachten wir die homogene Laplace-Gleichung mit Dirichlet-\-Rand\-bedingungen
+\begin{align*} \label{math:num:lapGLS}
+- \varDelta u &= 0 \quad\text{ in } \Omega \subset \R^3, \\
+u &= g \quad \text{ auf }\Gamma,
+\end{align*}
+wobei $\varDelta u := \partial_x^2u+\partial_y^2u+\partial_z^2u$ den Laplace-Operator bezeichnet und $\Omega \subset \R^3$ eine beschränkte Teilmenge von $\R^3$ mit Lipschitz-Rand $\Gamma := \partial \Omega$ ist.\\
+
+\begin{align}
+ V \phi := - \frac 1 {4\pi} \int_{T_j} \int_{T_k} \frac {1}{\abs{\bs x - \bs y}} \phi(\bs y) ds_{\bs y} ds_{\bs x}
+\end{align}
+
+
+
% \noindent
% Wir wissen, dass die Laplace-Gleichung erfüllt wird durch:
\end{itemize}
}
-
-
\subsection{Fehlerschätzer}
-In diesem Abschnitt definieren wir die a-posteriori Fehlerschätzer, die wir im Folgenden zur Steuerung des adaptiven Algorithmus einsetzen werden. Wir verwenden dazu die $h-h/2$ Strategie aus Ferraz-Leite, wo die folgende Aussage bewiesen wird.
-
-\begin{defi}Es bezeichne $\phi$ die Lösung von Formel , $\phi_{\ell}$ die Galerkinlösung auf dem Gitter $\T_{\ell}$ und $\hat \phi_{\ell}$ die Galerkinlösung auf dem uniform verfeinerten Gitter $\hat \T_{\ell}$. Dann gilt, der Schätzer
+In diesem Abschnitt definieren wir die a-posteriori Fehlerschätzer, die wir zur Steuerung des adaptiven Algorithmus einsetzen werden.
+Wir verwenden dazu die $h-h/2$ Strategie aus \cite{fer:errbem}.
+Im Folgenden bezeichnen wir mit $\hat \T_{\ell}$ das Gitter welches entsteht, wenn das Gitter $\T_{\ell}$ uniform, also entlang aller Kanten geteilt wird. Weiterhin bezeichne $\phi$ die exakte Lösung des Galerkin-Verfahrens und $\phi_{\ell}$ die Lösung zum Gitter $\T_{\ell}$, sowie $\hat \phi_{\ell}$ die Lösung zum uniformen Gitter $\hat \T_{\ell}$.
+\begin{defi}Es bezeichne $\phi$ die Lösung von Formel \todo{ref}, $\phi_{\ell}$ die Galerkin-Lösung auf dem Gitter $\T_{\ell}$ und $\hat \phi_{\ell}$ die Lösung auf dem uniform verfeinerten Gitter $\hat \T_{\ell}$. Dann gilt, der Schätzer
\begin{align}
\eta_{\ell} &:= \enorm{\hat \phi_{\ell} - \phi_{\ell}}
\end{align}
ist effizient
\begin{align}
-\eta_{ell} &\leq \enorm{\phi - \phi_{\ell}}
+\eta_{\ell} &\leq \enorm{\phi - \phi_{\ell}}
\end{align}
und unter der Saturationsannahme
\begin{align}
\end{itemize}
-Siehe S.F. Paper $\mapsto$ THM 3.2 \& 3.4
+Siehe \cite[Theorem 3.2 \& 3.4]{fer:errbem}.
+
\subsection{Adaptiver Algorithmus}
Mithilfe der oben Definierten Funktionen ist es uns nun möglich den Ablauf der Berechnungen zusammen zu fassen.
+\begin{alg}[Adaptives Verfahren]
$\theta \in (0,1),i =0$
\begin{enumerate}
\renewcommand{\theenumi}{(\roman{enumi})}
\item Verfeinere die Markierten Elemente $M_{\ell}$ um $\T_{\ell}^{(i+1)}$ zu erhalten
\item $i \mapsto i+1$, gehe zu $(i)$
\end{enumerate}
+\end{alg}
Zum Plotten (Abb.\ref{fig:exmplAA_2DQuad})werden noch folgende Schritte ausgeführt
\begin{itemize}
\showMesh[Beispiel 1.2]{exmpl12}
\showMesh[Beispiel 1.3]{exmpl13}
-
\begin{figure}[ht]
\caption{Objekt Beispiele}
\centering
%!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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl11_ref.eps
-%%CreationDate: 09/01/2012 16:57:04
+%%CreationDate: 03/21/2013 23:08:01
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
%!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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl12_ref.eps
-%%CreationDate: 09/01/2012 16:57:04
+%%CreationDate: 03/21/2013 23:08:01
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
%!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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl13_ref.eps
-%%CreationDate: 09/01/2012 16:57:05
+%%CreationDate: 03/21/2013 23:08:02
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
%!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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl_2DLShape_ref.eps
-%%CreationDate: 09/01/2012 16:57:05
+%%CreationDate: 03/21/2013 23:08:02
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
%!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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl_2DQuad_ref.eps
-%%CreationDate: 09/01/2012 16:57:05
+%%CreationDate: 03/21/2013 23:08:03
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
\rowcolor{gray}
Index & x1 & x2 & x3\\
1 & 0 & 0 & 0\\
- 2 & 1 & 0 & 0\\
- 3 & 0 & 1 & 0\\
- 4 & 1 & 1 & 0\\
- 5 & 0 & 0 & 1\\
- 6 & 1 & 0 & 1\\
- 7 & 0 & 1 & 1\\
- 8 & 1 & 1 & 1
+ 2 & 0 & 0 & 0.5\\
+ 3 & 0 & 0 & 1\\
+ 4 & 0 & 0.5 & 0\\
+ 5 & 0 & 0.5 & 0.5\\
+ 6 & 0 & 0.5 & 1\\
+ 7 & 0 & 1 & 0\\
+ 8 & 0 & 1 & 0.5\\
+ 9 & 0 & 1 & 1\\
+ 10 & 0.5 & 0 & 0\\
+ 11 & 0.5 & 0 & 0.5\\
+ 12 & 0.5 & 0 & 1\\
+ 13 & 0.5 & 0.5 & 0\\
+ 14 & 0.5 & 0.5 & 1\\
+ 15 & 0.5 & 1 & 0\\
+ 16 & 0.5 & 1 & 0.5\\
+ 17 & 0.5 & 1 & 1\\
+ 18 & 1 & 0 & 0\\
+ 19 & 1 & 0 & 0.5\\
+ 20 & 1 & 0 & 1\\
+ 21 & 1 & 0.5 & 0\\
+ 22 & 1 & 0.5 & 0.5\\
+ 23 & 1 & 0.5 & 1\\
+ 24 & 1 & 1 & 0\\
+ 25 & 1 & 1 & 0.5\\
+ 26 & 1 & 1 & 1
\end{tabular}
\begin{tabular}{>{\columncolor{gray}}rcccc}
\rowcolor{gray}
Index & c1 & c2 & c3 & c4\\
- 1 & 1 & 3 & 4 & 2\\
- 2 & 1 & 2 & 6 & 5\\
- 3 & 1 & 5 & 7 & 3\\
- 4 & 2 & 4 & 8 & 6\\
- 5 & 3 & 7 & 8 & 4\\
- 6 & 5 & 6 & 8 & 7
+ 1 & 10 & 13 & 21 & 18\\
+ 2 & 2 & 11 & 12 & 3\\
+ 3 & 4 & 5 & 8 & 7\\
+ 4 & 19 & 22 & 23 & 20\\
+ 5 & 15 & 16 & 25 & 24\\
+ 6 & 6 & 14 & 17 & 9\\
+ 7 & 13 & 15 & 24 & 21\\
+ 8 & 4 & 7 & 15 & 13\\
+ 9 & 1 & 4 & 13 & 10\\
+ 10 & 1 & 10 & 11 & 2\\
+ 11 & 5 & 6 & 9 & 8\\
+ 12 & 2 & 3 & 6 & 5\\
+ 13 & 1 & 2 & 5 & 4\\
+ 14 & 22 & 25 & 26 & 23\\
+ 15 & 21 & 24 & 25 & 22\\
+ 16 & 18 & 21 & 22 & 19\\
+ 17 & 16 & 17 & 26 & 25\\
+ 18 & 8 & 9 & 17 & 16\\
+ 19 & 7 & 8 & 16 & 15\\
+ 20 & 3 & 12 & 14 & 6\\
+ 21 & 11 & 19 & 20 & 12\\
+ 22 & 14 & 23 & 26 & 17\\
+ 23 & 10 & 18 & 19 & 11\\
+ 24 & 12 & 20 & 23 & 14
\end{tabular}
\label{exmpl_3DCube:ele}
\ No newline at end of file
\begin{tabular}{>{\columncolor{gray}}rcccccccc}
\rowcolor{gray}
Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\
- 1 & 3 & 5 & 3 & 2 & 0 & 0 & 0 & 0\\
- 2 & 1 & 4 & 6 & 3 & 0 & 0 & 0 & 0\\
- 3 & 2 & 6 & 5 & 1 & 0 & 0 & 0 & 0\\
- 4 & 1 & 5 & 6 & 2 & 0 & 0 & 0 & 0\\
- 5 & 3 & 6 & 4 & 1 & 0 & 0 & 0 & 0\\
- 6 & 2 & 4 & 5 & 3 & 0 & 0 & 0 & 0
+ 1 & 9 & 7 & 16 & 23 & 0 & 0 & 0 & 0\\
+ 2 & 10 & 21 & 20 & 12 & 0 & 0 & 0 & 0\\
+ 3 & 13 & 11 & 19 & 8 & 0 & 0 & 0 & 0\\
+ 4 & 16 & 14 & 24 & 21 & 0 & 0 & 0 & 0\\
+ 5 & 19 & 17 & 15 & 7 & 0 & 0 & 0 & 0\\
+ 6 & 20 & 22 & 18 & 11 & 0 & 0 & 0 & 0\\
+ 7 & 8 & 5 & 15 & 1 & 0 & 0 & 0 & 0\\
+ 8 & 3 & 19 & 7 & 9 & 0 & 0 & 0 & 0\\
+ 9 & 13 & 8 & 1 & 10 & 0 & 0 & 0 & 0\\
+ 10 & 9 & 23 & 2 & 13 & 0 & 0 & 0 & 0\\
+ 11 & 12 & 6 & 18 & 3 & 0 & 0 & 0 & 0\\
+ 12 & 2 & 20 & 11 & 13 & 0 & 0 & 0 & 0\\
+ 13 & 10 & 12 & 3 & 9 & 0 & 0 & 0 & 0\\
+ 14 & 15 & 17 & 22 & 4 & 0 & 0 & 0 & 0\\
+ 15 & 7 & 5 & 14 & 16 & 0 & 0 & 0 & 0\\
+ 16 & 1 & 15 & 4 & 23 & 0 & 0 & 0 & 0\\
+ 17 & 18 & 22 & 14 & 5 & 0 & 0 & 0 & 0\\
+ 18 & 11 & 6 & 17 & 19 & 0 & 0 & 0 & 0\\
+ 19 & 3 & 18 & 5 & 8 & 0 & 0 & 0 & 0\\
+ 20 & 2 & 24 & 6 & 12 & 0 & 0 & 0 & 0\\
+ 21 & 23 & 4 & 24 & 2 & 0 & 0 & 0 & 0\\
+ 22 & 24 & 14 & 17 & 6 & 0 & 0 & 0 & 0\\
+ 23 & 1 & 16 & 21 & 10 & 0 & 0 & 0 & 0\\
+ 24 & 21 & 4 & 22 & 20 & 0 & 0 & 0 & 0
\end{tabular}
\label{exmpl_3DCube: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.
+%%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). Operating System: Linux 3.2.0-39-generic #62-Ubuntu SMP Thu Feb 28 00:28:53 UTC 2013 x86_64.
%%Title: ../doc/fig/exmpl_3DCube_ref.eps
-%%CreationDate: 09/01/2012 16:57:05
+%%CreationDate: 03/21/2013 23:08:03
%%DocumentNeededFonts: Helvetica
%%DocumentProcessColors: Cyan Magenta Yellow Black
%%Extensions: CMYK
8.33333 w
/c8 { 0.000000 0.400000 0.400000 sr} bdef
c8
-4033 2486 mt 2279 2961 L
-4033 2486 mt 4033 1133 L
-2688 514 mt 2688 1866 L
-2688 1866 mt 2688 514 L
-4033 1133 mt 2279 1609 L
-4033 2486 mt 2688 1866 L
-4033 1133 mt 4033 2486 L
-4033 1133 mt 2688 514 L
+4033 2486 mt 3156 2723 L
+4033 1810 mt 3361 1500 L
+4033 1133 mt 4033 1810 L
+4033 2486 mt 3361 2176 L
+4033 1810 mt 4033 2486 L
+4033 1810 mt 4033 1133 L
+3361 824 mt 3361 1500 L
+3361 1500 mt 3361 824 L
+4033 1133 mt 3156 1371 L
+4033 2486 mt 4033 1810 L
+3361 2176 mt 3361 1500 L
+3361 1500 mt 3361 2176 L
+4033 1810 mt 3156 2047 L
+4033 1133 mt 3361 824 L
gr
8.33333 w
/c9 { 1.000000 0.000000 0.000000 sr} bdef
c9
4011 2479 mt
-(2) s
+(18) s
+4011 1803 mt
+(19) s
4011 1127 mt
-(6) s
+(20) s
0 sg
-3361 1530 mt
+3697 1347 mt
(\(4\)) s
+3697 2023 mt
+(\(16\)) s
+3595 1620 mt
+(\(21\)) s
+3595 2296 mt
+(\(23\)) s
+gs 623 269 3721 2937 MR c np
+c8
+3361 2176 mt 4033 2486 L
+3361 824 mt 4033 1133 L
+3361 2176 mt 2483 2414 L
+3361 1500 mt 2688 1190 L
+3361 2176 mt 2688 1866 L
+3361 1500 mt 4033 1810 L
+3361 824 mt 2688 514 L
+2688 514 mt 2688 1190 L
+2688 1190 mt 2688 514 L
+3361 824 mt 2483 1061 L
+gr
+
+c8
+c9
+3338 2169 mt
+(21) s
+3338 1493 mt
+(22) s
+3338 817 mt
+(23) s
+0 sg
+3258 2480 mt
+(\(1\)) s
+3258 1127 mt
+(\(24\)) s
3194 3389 mt
(x) s
-3156 2077 mt
+gs 623 269 3721 2937 MR c np
+c8
+3156 2723 mt 2483 2414 L
+3156 2047 mt 3156 1371 L
+2688 1190 mt 3361 1500 L
+2688 1866 mt 2688 1190 L
+2688 1190 mt 2688 1866 L
+3156 1371 mt 2279 1609 L
+3156 2723 mt 2279 2961 L
+3156 2723 mt 3156 2047 L
+2688 1866 mt 3361 2176 L
+3156 2047 mt 2279 2285 L
+3156 1371 mt 2483 1061 L
+3156 2047 mt 4033 1810 L
+3156 1371 mt 3156 2047 L
+3156 2723 mt 4033 2486 L
+3156 2047 mt 3156 2723 L
+3156 1371 mt 4033 1133 L
+gr
+
+c8
+c9
+3134 2716 mt
+(10) s
+3134 2040 mt
+(11) s
+3134 1364 mt
+(12) s
+0 sg
+3024 1037 mt
+(\(14\)) s
+3024 1713 mt
+(\(15\)) s
+2718 1858 mt
(\(2\)) s
+2718 2534 mt
+(\(10\)) s
gs 623 269 3721 2937 MR c np
c8
-2688 1866 mt 4033 2486 L
-2688 514 mt 4033 1133 L
-2688 1866 mt 933 2342 L
-2688 514 mt 933 989 L
+2688 1866 mt 1811 2104 L
+2688 514 mt 3361 824 L
+2688 1190 mt 1811 1428 L
+2688 514 mt 1811 752 L
gr
c8
c9
2665 1859 mt
-(4) s
+(24) s
+2665 1183 mt
+(25) s
2665 507 mt
-(8) s
+(26) s
0 sg
-2483 2444 mt
-(\(1\)) s
-2483 1091 mt
-(\(6\)) s
+2586 2170 mt
+(\(7\)) s
+2586 818 mt
+(\(22\)) s
+gs 623 269 3721 2937 MR c np
+c8
+2483 2414 mt 3361 2176 L
+2483 1061 mt 1811 752 L
+2483 2414 mt 1811 2104 L
+2483 2414 mt 1606 2651 L
+2483 2414 mt 3156 2723 L
+1811 752 mt 1811 1428 L
+1811 1428 mt 1811 752 L
+2483 1061 mt 1606 1299 L
+2483 1061 mt 3361 824 L
+2483 1061 mt 3156 1371 L
+gr
+
+c8
+c9
+2461 2407 mt
+(13) s
+2461 1055 mt
+(14) s
+0 sg
+2381 2717 mt
+(\(9\)) s
+2381 1365 mt
+(\(20\)) s
gs 623 269 3721 2937 MR c np
c8
-2279 2961 mt 933 2342 L
-2279 2961 mt 4033 2486 L
-2279 1609 mt 2279 2961 L
-2279 2961 mt 2279 1609 L
-2279 1609 mt 933 989 L
-2279 1609 mt 4033 1133 L
+2279 2285 mt 3156 2047 L
+2279 1609 mt 2279 2285 L
+2279 2961 mt 1606 2651 L
+2279 2961 mt 3156 2723 L
+2279 2285 mt 2279 2961 L
+2279 2285 mt 2279 1609 L
+1811 1428 mt 2688 1190 L
+2279 1609 mt 1606 1299 L
+2279 2961 mt 2279 2285 L
+1811 1428 mt 1811 2104 L
+1811 2104 mt 2688 1866 L
+1811 2104 mt 1811 1428 L
+2279 2285 mt 1606 1975 L
+2279 1609 mt 3156 1371 L
gr
c8
c9
2257 2954 mt
(1) s
+2257 2278 mt
+(2) s
2257 1602 mt
-(5) s
+(3) s
0 sg
-1811 1458 mt
+2249 1677 mt
(\(5\)) s
-1606 2005 mt
-(\(3\)) s
+2249 1001 mt
+(\(17\)) s
+1943 1822 mt
+(\(12\)) s
+1943 2498 mt
+(\(13\)) s
+gs 623 269 3721 2937 MR c np
+c8
+1811 752 mt 933 989 L
+1811 2104 mt 2483 2414 L
+1811 752 mt 2688 514 L
+1811 1428 mt 933 1665 L
+1811 2104 mt 933 2342 L
+1811 752 mt 2483 1061 L
+gr
+
+c8
+c9
+1788 2097 mt
+(15) s
+1788 1421 mt
+(16) s
+1788 745 mt
+(17) s
+0 sg
+1708 1055 mt
+(\(6\)) s
+1708 2408 mt
+(\(8\)) s
+gs 623 269 3721 2937 MR c np
+c8
+1606 2651 mt 1606 1975 L
+1606 1975 mt 933 1665 L
+1606 1299 mt 2483 1061 L
+1606 2651 mt 933 2342 L
+1606 2651 mt 2483 2414 L
+1606 1975 mt 1606 1299 L
+1606 1299 mt 933 989 L
+1606 1299 mt 1606 1975 L
+1606 1975 mt 2279 2285 L
+1606 1975 mt 1606 2651 L
+1606 2651 mt 2279 2961 L
+1606 1299 mt 2279 1609 L
+gr
+
+c8
+c9
+1584 2644 mt
+(4) s
+1584 1968 mt
+(5) s
+1584 1292 mt
+(6) s
+0 sg
1363 3346 mt
(y) s
+1372 1239 mt
+(\(18\)) s
+1372 1915 mt
+(\(19\)) s
+1270 2188 mt
+(\(3\)) s
+1270 1512 mt
+(\(11\)) s
gs 623 269 3721 2937 MR c np
c8
- 933 2342 mt 2688 1866 L
- 933 989 mt 933 2342 L
- 933 2342 mt 2279 2961 L
- 933 2342 mt 933 989 L
- 933 989 mt 2688 514 L
- 933 989 mt 2279 1609 L
+ 933 1665 mt 933 2342 L
+ 933 2342 mt 1606 2651 L
+ 933 989 mt 1606 1299 L
+ 933 2342 mt 1811 2104 L
+ 933 989 mt 933 1665 L
+ 933 1665 mt 1606 1975 L
+ 933 1665 mt 933 989 L
+ 933 989 mt 1811 752 L
+ 933 2342 mt 933 1665 L
+ 933 1665 mt 1811 1428 L
gr
c8
c9
911 2335 mt
-(3) s
- 911 983 mt
(7) s
+ 911 1659 mt
+(8) s
+ 911 983 mt
+(9) s
0 sg
380 1673 mt -90 rotate
(z) s
\begin{tabular}{>{\columncolor{gray}}rccc}
\rowcolor{gray}
Index & x1 & x2 & x3\\
- 1 & 0 & 0 & 0\\
- 2 & -1 & 0 & 0\\
- 3 & -1 & 1 & 0\\
- 4 & 0 & 1 & 0\\
- 5 & 0 & 1 & 1\\
- 6 & 0 & 0 & 1\\
- 7 & -1 & 0 & 1\\
- 8 & -1 & -1 & -1\\
- 9 & -1 & 0 & -1\\
- 10 & -1 & 1 & -1\\
- 11 & 0 & 1 & -1\\
- 12 & 1 & 1 & -1\\
- 13 & 1 & 1 & 0\\
- 14 & 1 & 1 & 1\\
- 15 & 1 & 0 & 1\\
- 16 & 1 & -1 & 1\\
- 17 & 0 & -1 & 1\\
- 18 & -1 & -1 & 1\\
- 19 & -1 & -1 & 0\\
- 20 & 1 & -1 & -1
+ 1 & -1 & -1 & -1\\
+ 2 & -1 & -1 & 0\\
+ 3 & -1 & -1 & 1\\
+ 4 & -1 & 0 & -1\\
+ 5 & -1 & 0 & 0\\
+ 6 & -1 & 0 & 1\\
+ 7 & -1 & 1 & -1\\
+ 8 & -1 & 1 & 0\\
+ 9 & 0 & -1 & -1\\
+ 10 & 0 & -1 & 0\\
+ 11 & 0 & -1 & 1\\
+ 12 & 0 & 0 & -1\\
+ 13 & 0 & 0 & 0\\
+ 14 & 0 & 0 & 1\\
+ 15 & 0 & 1 & -1\\
+ 16 & 0 & 1 & 0\\
+ 17 & 0 & 1 & 1\\
+ 18 & 1 & -1 & -1\\
+ 19 & 1 & -1 & 0\\
+ 20 & 1 & -1 & 1\\
+ 21 & 1 & 0 & -1\\
+ 22 & 1 & 0 & 0\\
+ 23 & 1 & 0 & 1\\
+ 24 & 1 & 1 & -1\\
+ 25 & 1 & 1 & 0\\
+ 26 & 1 & 1 & 1
\end{tabular}
\begin{tabular}{>{\columncolor{gray}}rcccc}
\rowcolor{gray}
Index & c1 & c2 & c3 & c4\\
- 1 & 1 & 2 & 3 & 4\\
- 2 & 1 & 4 & 5 & 6\\
- 3 & 1 & 6 & 7 & 2\\
- 4 & 2 & 3 & 10 & 9\\
- 5 & 3 & 10 & 11 & 4\\
- 6 & 4 & 11 & 12 & 13\\
- 7 & 4 & 13 & 14 & 5\\
- 8 & 5 & 14 & 15 & 6\\
- 9 & 6 & 15 & 16 & 17\\
- 10 & 6 & 17 & 18 & 7\\
- 11 & 7 & 18 & 19 & 2\\
- 12 & 2 & 19 & 8 & 9\\
- 13 & 8 & 10 & 12 & 20\\
- 14 & 20 & 12 & 14 & 16\\
- 15 & 20 & 16 & 18 & 8
+ 1 & 5 & 13 & 16 & 8\\
+ 2 & 13 & 14 & 17 & 16\\
+ 3 & 5 & 6 & 14 & 13\\
+ 4 & 4 & 5 & 8 & 7\\
+ 5 & 7 & 8 & 16 & 15\\
+ 6 & 15 & 16 & 25 & 24\\
+ 7 & 16 & 17 & 26 & 25\\
+ 8 & 14 & 23 & 26 & 17\\
+ 9 & 11 & 20 & 23 & 14\\
+ 10 & 3 & 11 & 14 & 6\\
+ 11 & 2 & 3 & 6 & 5\\
+ 12 & 1 & 2 & 5 & 4\\
+ 13 & 9 & 12 & 21 & 18\\
+ 14 & 19 & 22 & 23 & 20\\
+ 15 & 2 & 10 & 11 & 3\\
+ 16 & 12 & 15 & 24 & 21\\
+ 17 & 4 & 7 & 15 & 12\\
+ 18 & 1 & 4 & 12 & 9\\
+ 19 & 18 & 21 & 22 & 19\\
+ 20 & 10 & 19 & 20 & 11\\
+ 21 & 9 & 18 & 19 & 10\\
+ 22 & 1 & 9 & 10 & 2\\
+ 23 & 22 & 25 & 26 & 23\\
+ 24 & 21 & 24 & 25 & 22
\end{tabular}
\label{exmpl_3DFichCube:ele}
\ No newline at end of file
\begin{tabular}{>{\columncolor{gray}}rcccccccc}
\rowcolor{gray}
Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\
- 1 & 3 & 4 & 5 & 2 & 0 & 0 & 0 & 0\\
- 2 & 1 & 7 & 8 & 3 & 0 & 0 & 0 & 0\\
- 3 & 2 & 10 & 11 & 1 & 0 & 0 & 0 & 0\\
- 4 & 1 & 5 & 13 & 12 & 0 & 0 & 0 & 0\\
- 5 & 4 & 13 & 6 & 1 & 0 & 0 & 0 & 0\\
- 6 & 5 & 13 & 14 & 7 & 0 & 0 & 0 & 0\\
- 7 & 6 & 14 & 8 & 2 & 0 & 0 & 0 & 0\\
- 8 & 7 & 14 & 9 & 2 & 0 & 0 & 0 & 0\\
- 9 & 8 & 14 & 15 & 10 & 0 & 0 & 0 & 0\\
- 10 & 9 & 15 & 11 & 3 & 0 & 0 & 0 & 0\\
- 11 & 10 & 15 & 12 & 3 & 0 & 0 & 0 & 0\\
- 12 & 11 & 15 & 13 & 4 & 0 & 0 & 0 & 0\\
- 13 & 12 & 5 & 14 & 15 & 4 & 6 & 0 & 0\\
- 14 & 13 & 6 & 8 & 15 & 0 & 7 & 9 & 0\\
- 15 & 14 & 9 & 11 & 13 & 0 & 10 & 12 & 0
+ 1 & 3 & 2 & 5 & 4 & 0 & 0 & 0 & 0\\
+ 2 & 3 & 8 & 7 & 1 & 0 & 0 & 0 & 0\\
+ 3 & 11 & 10 & 2 & 1 & 0 & 0 & 0 & 0\\
+ 4 & 12 & 1 & 5 & 17 & 0 & 0 & 0 & 0\\
+ 5 & 4 & 1 & 6 & 16 & 0 & 0 & 0 & 13\\
+ 6 & 5 & 7 & 24 & 17 & 0 & 0 & 0 & 0\\
+ 7 & 2 & 8 & 23 & 6 & 0 & 0 & 0 & 0\\
+ 8 & 9 & 23 & 7 & 2 & 0 & 0 & 0 & 0\\
+ 9 & 20 & 14 & 8 & 10 & 0 & 0 & 0 & 0\\
+ 10 & 15 & 9 & 3 & 11 & 0 & 0 & 0 & 0\\
+ 11 & 15 & 10 & 3 & 12 & 0 & 0 & 0 & 0\\
+ 12 & 22 & 11 & 4 & 16 & 0 & 0 & 0 & 0\\
+ 13 & 18 & 16 & 5 & 19 & 0 & 0 & 0 & 0\\
+ 14 & 19 & 23 & 9 & 20 & 0 & 0 & 0 & 0\\
+ 15 & 22 & 20 & 10 & 11 & 0 & 0 & 0 & 0\\
+ 16 & 17 & 12 & 5 & 13 & 0 & 0 & 0 & 0\\
+ 17 & 4 & 6 & 16 & 18 & 0 & 0 & 0 & 0\\
+ 18 & 22 & 17 & 13 & 24 & 21 & 0 & 0 & 0\\
+ 19 & 13 & 24 & 14 & 21 & 0 & 0 & 0 & 0\\
+ 20 & 21 & 14 & 9 & 15 & 0 & 0 & 0 & 0\\
+ 21 & 18 & 19 & 20 & 22 & 0 & 0 & 0 & 0\\
+ 22 & 18 & 21 & 15 & 12 & 0 & 0 & 0 & 0\\
+ 23 & 24 & 7 & 8 & 14 & 0 & 0 & 0 & 0\\
+ 24 & 18 & 6 & 23 & 19 & 0 & 0 & 0 & 0
\end{tabular}
\label{exmpl_3DFichCube:nei}
\ No newline at end of file
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8.33333 w
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gr
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c9
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c8
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gs 623 269 3722 2937 MR c np
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gr
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c8
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gr
c8
-0 sg
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gs 623 269 3722 2937 MR c np
c8
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gr
c8
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gs 623 269 3722 2937 MR c np
c8
-1811 1428 mt 2483 1737 L
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gr
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gs 623 269 3722 2937 MR c np
c8
-1606 1975 mt 933 1665 L
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gr
c8
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0 sg
1363 3346 mt
(y) s
(\(4\)) s
gs 623 269 3722 2937 MR c np
c8
- 933 1665 mt 1811 1428 L
+ 933 1665 mt 1606 1975 L
933 1665 mt 933 2342 L
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933 2342 mt 1811 2104 L
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gr
c8
c9
- 922 1677 mt
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%%Title: ../doc/fig/net_single.eps
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MathWorks begin
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portraitMode 0150 5100 csm
- 0 -33 4372 3413 MR c np
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86 dict begin %Colortable dictionary
/c0 { 0.000000 0.000000 0.000000 sr} bdef
/c1 { 1.000000 1.000000 1.000000 sr} bdef
1 sg
0 0 4801 3603 PR
4.16667 w
-gs 623 269 3721 2937 MR c np
+0 1623 -1616 -744 0 -1622 4344 2635 4 MP
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+%%IncludeResource: font Helvetica
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16.6667 w
/c8 { 0.000000 0.400000 0.400000 sr} bdef
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0 j
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% Test ausführen
%Anzahl der Schritte oder wenn groeßer als 40 der Elemente
-steps = 10^4;
+steps = 5;
%Art der Berechnungen
-type = [1 2];
+type = [1 3];
zeta = { [2 2 2] [2 2 2]};