From f620aedcf5fa5f80c7d506660a1ed51b0fd2e105 Mon Sep 17 00:00:00 2001 From: Peter Schaefer Date: Sun, 14 Apr 2013 17:51:43 +0200 Subject: [PATCH] [doc] plots verbessert [doc] 2DQuad Vergleich der Verfeinerung fertig [doc] implementierung von A angefangen --- .cproject | 29 +++- doc/code.pdf | Bin 395858 -> 535619 bytes doc/code.tex | 18 +- doc/doc.pdf | Bin 368211 -> 446801 bytes doc/doc.tex | 210 ++++++++++++++++++++++- doc/fig/132t05n05_2DQuad_cond.eps | 8 +- doc/fig/132t05n05_2DQuad_error.eps | 8 +- doc/fig/132t05n05_2DQuad_hminmax.eps | 8 +- doc/fig/132t05n05_2DQuad_time.eps | 2 +- doc/fig/132t05n05_3DFichCube_cond.eps | 8 +- doc/fig/132t05n05_3DFichCube_error.eps | 8 +- doc/fig/132t05n05_3DFichCube_hminmax.eps | 8 +- doc/fig/132t05n05_3DFichCube_time.eps | 2 +- doc/fig/1t05n05_2DLShape_cond.eps | 4 +- doc/fig/1t05n05_2DLShape_error.eps | 4 +- doc/fig/1t05n05_2DLShape_hminmax.eps | 4 +- doc/fig/1t05n05_2DLShape_time.eps | 2 +- doc/fig/1t05n05_2DQuad_cond.eps | 4 +- doc/fig/1t05n05_2DQuad_error.eps | 4 +- doc/fig/1t05n05_2DQuad_hminmax.eps | 4 +- doc/fig/1t05n05_2DQuad_time.eps | 2 +- doc/fig/1t05n05_3DFichCube_cond.eps | 4 +- doc/fig/1t05n05_3DFichCube_error.eps | 4 +- doc/fig/1t05n05_3DFichCube_hminmax.eps | 4 +- doc/fig/1t05n05_3DFichCube_time.eps | 2 +- doc/fig/1t05n0_2DQuad_cond.eps | 2 +- doc/fig/1t05n0_2DQuad_error.eps | 2 +- doc/fig/1t05n0_2DQuad_hminmax.eps | 2 +- doc/fig/1t05n0_2DQuad_time.eps | 2 +- doc/fig/1t1n0_2DQuad_cond.eps | 2 +- doc/fig/1t1n0_2DQuad_error.eps | 2 +- doc/fig/1t1n0_2DQuad_hminmax.eps | 2 +- doc/fig/1t1n0_2DQuad_time.eps | 2 +- doc/fig/1tn_2DQuad_cond.eps | 2 +- doc/fig/1tn_2DQuad_error.eps | 2 +- doc/fig/1tn_2DQuad_hminmax.eps | 2 +- doc/fig/1tn_2DQuad_time.eps | 2 +- doc/fig/2222t05n05_2DQuad_cond.eps | 2 +- doc/fig/2222t05n05_2DQuad_error.eps | 2 +- doc/fig/2222t05n05_2DQuad_hminmax.eps | 2 +- doc/fig/2222t05n05_2DQuad_time.eps | 2 +- doc/fig/exmpl11_ref.eps | 2 +- doc/fig/exmpl12_ref.eps | 2 +- doc/fig/exmpl13_nei_part.eps | 2 +- doc/fig/exmpl13_ref.eps | 2 +- doc/fig/exmpl_2DLShape_ref.eps | 2 +- doc/fig/exmpl_2DQuad_ref.eps | 2 +- doc/fig/exmpl_3DCube_ref.eps | 2 +- doc/fig/exmpl_3DFichCube_ref.eps | 2 +- doc/fig/net1.eps | 2 +- doc/fig/net_single.eps | 2 +- doc/fig/net_wrong.eps | 2 +- doc/fig/refType_1.eps | 2 +- doc/fig/refType_2.eps | 2 +- doc/fig/refType_3.eps | 2 +- doc/fig/refType_4.eps | 2 +- doc/fig/refType_full.eps | 2 +- doc/lstings.sty | 4 +- src/A_plots.m | 2 +- src/export_exmpl.m | 3 + src/mex_build_V.cpp | 11 +- src/test_sol.m | 2 +- 62 files changed, 328 insertions(+), 109 deletions(-) diff --git a/.cproject b/.cproject index dbf0e66..13bd80b 100644 --- a/.cproject +++ b/.cproject @@ -1,7 +1,5 @@ - - - + @@ -34,13 +32,13 @@ - + @@ -54,6 +52,9 @@ @@ -78,7 +79,7 @@ - + @@ -100,6 +101,9 @@ @@ -112,6 +116,9 @@ @@ -135,8 +142,13 @@ - - + + + + + + + @@ -157,4 +169,5 @@ + diff --git a/doc/code.pdf b/doc/code.pdf index 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100644 --- a/doc/code.tex +++ b/doc/code.tex @@ -74,15 +74,15 @@ \tableofcontents \clearpage \section{Anhang Code} -% \subsection{C++} -% \subsubsection{mex\_build\_V.cpp} -% \lstinputlisting[language=C++]{../src/mex_build_V.cpp} -% \subsubsection{slpRectangle.hpp} -% \lstinputlisting[language=C++]{../src/slpRectangle.hpp} -% \subsubsection{slpRectangle.cpp} -% \lstinputlisting[language=C++]{../src/slpRectangle.cpp} -% \subsubsection{gauss.hpp} -% \lstinputlisting[language=C++]{../src/gauss.hpp} + \subsection{C++} + \subsubsection{mex\_build\_V.cpp} + \lstinputlisting[language=C++]{../src/mex_build_V.cpp} + \subsubsection{slpRectangle.hpp} + \lstinputlisting[language=C++]{../src/slpRectangle.hpp} + \subsubsection{slpRectangle.cpp} + \lstinputlisting[language=C++]{../src/slpRectangle.cpp} + \subsubsection{gauss.hpp} + \lstinputlisting[language=C++]{../src/gauss.hpp} \subsection{Matlab} \subsubsection{compute.m} \lstinputlisting[language=M]{../src/compute.m} diff --git a/doc/doc.pdf 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$\eta$} +\psfrag{fehler 1t05n05 A}{\tiny Fehler} +\psfrag{Zeit 1t05n05 A}{\tiny Zeit} +\psfrag{cond 1t05n05 A}{\tiny Kondition} +\psfrag{min hmin/max hmax 1t05n05 A}{\tiny $\min (h_{\min})/(\max h_{\max})$} +\psfrag{min hmax/max hmax 1t05n05 A}{\tiny $\min (h_{\max})/(\max h_{\max})$} +\psfrag{min hmin/hmax 1t05n05 A}{\tiny $\min (h_{\min}/h_{\max})$} + + +\psfrag{tmu 132t05n05 A}{\tiny $\tilde \mu$ analytisch} +\psfrag{eta 132t05n05 A}{\tiny $\eta$ analytisch} +\psfrag{fehler 132t05n05 A}{\tiny Fehler analytisch} +\psfrag{Zeit 132t05n05 A}{\tiny Zeit analytisch} +\psfrag{cond 132t05n05 A}{\tiny Kondition analytisch} + +\psfrag{tmu 132t05n05 QEQA}{\tiny $\tilde \mu$ semiquadratur QE} +\psfrag{eta 132t05n05 QEQA}{\tiny $\eta$ semiquadratur QE} +\psfrag{fehler 132t05n05 QEQA}{\tiny Fehler semiquadratur QE} +\psfrag{Zeit 132t05n05 QEQA}{\tiny Zeit semiquadratur QE} +\psfrag{cond 132t05n05 QEQA}{\tiny Kondition semiquadratur QE} + +\psfrag{tmu 132t05n05 QA}{\tiny $\tilde \mu$ semiquadratur Q} +\psfrag{eta 132t05n05 QA}{\tiny $\eta$ semiquadratur Q} +\psfrag{fehler 132t05n05 QA}{\tiny Fehler semiquadratur Q} +\psfrag{Zeit 132t05n05 QA}{\tiny Zeit semiquadratur Q} +\psfrag{cond 132t05n05 QA}{\tiny Kondition semiquadratur Q} + + + + + + + + + + + + \begin{document} \todo{ % \input{titelseite} @@ -1805,10 +1846,13 @@ Da wir im weiteren Verlauf sowohl adaptive also auch anisotrope Netzverfeinerung \end{enumerate} Zusätzlich wurde auch Typ 5. belegt, welcher als Ergebnis eine volle Teilung 2. ausführt, diese aber schrittweise durch eine 3. Teilung und anschließend durch jeweils eine 4. Teilung. Aus Sicherheitsgründen wird auch jede vierte volle 2. Teilung durch eine 5. Teilung ausgeführt, da sonst kurzzeitig Seiten mit mehr als zwei Elementen auftreten könnten. +\noindent Damit jedem Element $T_i$ eine Teilungsart zugeordnet werden kann, haben wir einen Mar\-kierungs\-vektor $marked \in \{1,2,3,4,5\}^M$ eingeführt. Dabei entspricht $marked_i$ der Art der Teilung für das Element $T_i$. Um isotrope und auch uniforme Teilungen zu erleichtern kann statt dem Vektor $marked$ auch nur ein Skalar übergeben werden $marked \in {1,2\dots5}$, wodurch jedes Element mit der gewählten Art verfeinert wird. +\noindent Relevant zum Verfeinern eines Netzes sind also die Koordinaten $COO$, Elemente $ELE$ sowie die Nachbarschaftsrelationen $NEI$ und der Markierungs\-vektor $marked$. +\noindent Da wir später den Fehlerschätzer berechnen wollen, ist es wichtig sich zu jedem Element seine Teilelemente zu merken. Dazu legen wir während der Teilung eine $M \times 4$ Matrix an, in der die maximal vier Elementindizes gespeichert werden. Wenn wir also ein Element in vier gleich große Teile verfeinern, so wird das neue Element links unten das erste sein und alle weiteren folgen gegen den Uhrzeigersinn. Teilen wir ein Element in zwei gleich große Elemente, so werden die doppelt belegten Quadranten auch doppelt eingetragen. Ein gar nicht geteiltes Element wird also vier mal den alten Indizes speichern. Dadurch wird sichergestellt, dass das arithmetische Mittel über die Elemente immer gültig auszuführen ist. (Siehe Abbildung \ref{exmpl13}) \begin{align*} @@ -1825,8 +1869,77 @@ Da wir später den Fehlerschätzer berechnen wollen, ist es wichtig sich zu jede \label{exmpl1:f2s:part} \end{figure} -\subsection{Berechnung der $V$ Matrix} +\subsection{Berechnung der Matrix} +An dieser Stelle wenden wir uns noch ein mal der Berechnung der Matrix $A \in \R^{N\times N}$ zu, deren Einträge bestimmt sind durch das Integral +\begin{align} \label{math:imple:Ajk} + A_{jk} = \int_{T_j} \int_{T_k} \frac 1 {4\pi} \frac 1 {\abs{\bs x - \bs y}} ds_{\bs y} ds_{\bs x}. +\end{align} +Da die Berechnung aller Einträge sehr aufwändig ist, haben wir die entsprechenden Funktionen nicht direkt in \Matlab~implementiert, sondern mithilfe der {\sc mex}-Schnittstelle in \Cpp. \Matlab~benötigt dazu die Bibliothek "`mex.h"' und eine spezielle {\sc mex}-Funktion als Einstiegspunkt mit der Gestalt +\begin{lstlisting}[language=C++, numbers=none] +void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]); +\end{lstlisting} +Dabei steht \lstinline!nlhs! für die erwartete Anzahl der Rückgabe-Parameter, welche im Array \lstinline!*plhs[]! abgespeichert werden müssen. Im Array \lstinline!*prhs[]! werden die Eingabe-Parameter von \Matlab~übergeben, dessen Anzahl über \lstinline!nrhs! abgefragt werden kann. Weiterhin stehen noch wichtige {\sc mex}-Funktionen zum Umwandeln der Parameter, sowie dem Zugriff auf \Matlab-Funktionen und Ausgaben zur Verfügung. +% Innerhalb von \Matlab~kann der Code dann kompiliert werden +% \begin{lstlisting}[language=M, numbers=none] +% mex mexfile.cpp +% \end{lstlisting} +% wobei anschließend noch weitere Dateien und Parameter angegeben werden können. Nach erfolgreichem Kompilieren wurde eine \lstinline!mexfile.mexa64! Datei für ein 64bit System erstellt, welche dann in \Matlab +% \begin{lstlisting}[language=M, numbers=none] +% [pl1] = mexfile(pr1,pr2); +% \end{lstlisting} +% aufgerufen werden kann. + +\noindent +Die Implementierung des Integrals \eqref{math:imple:Ajk} wurde in \lstinline!mex_build_V! \todo{(ref)} mithilfe der beiden Bibliotheken \lstinline!slpRectangle! \todo{(ref, ref)} und \lstinline!gauss! \todo{(ref)} umgesetzt. + +\noindent +Innerhalb von \Matlab~kann der Code dann kompiliert werden +\begin{lstlisting}[language=M, numbers=none] +mex -o 'mex_build_V.cpp' 'slpRectangle.cpp' CFLAGS="\$CFLAGS -fopenmp"... + CXXFLAGS="\$CXXFLAGS -fopenmp" LDFLAGS="\$LDFLAGS -fopenmp" +\end{lstlisting} +Nach erfolgreichem Kompilieren wurde eine \lstinline!mex_build_V.mexa64! Datei für ein 64bit System erstellt, welche dann in \Matlab~über +\begin{lstlisting}[language=M, numbers=none] +A = mex_build_V(coo,ele,zeta,typ); +\end{lstlisting} +aufgerufen werden kann. Hierbei steht wie in der Datenstruktur beschrieben \lstinline!coo! für die Koordinatenmatrix und \lstinline!ele! für die Elementmatrix. Weiterhin sei \lstinline!zeta! ein Array mit den Einträgen \lstinline!zeta! $=(q,\zeta_0,\zeta_1)$. Mithilfe des Parameters $q \in \{0,1,2,3,4,5\}$ kann die Anzahl $2^q$ der Auswertungsstellen für die Gauss-Quadratur gewählt werden. Die beiden Parameter $\zeta_0,\zeta_1 \in \R^+$ werden in den Zulässigkeitsbedingungen verwendet. Der Parameter \lstinline!typ! $\in \{1,2,3\}$ steht für die Art der Berechnung. + +\noindent +Insgesamt wurden vier Arten der Berechnung implementiert. +\begin{enumerate} + \item Bei der voll analytischen Berechnung von $A$ werden + \begin{itemize} + \item alle Elemente analytisch mittels Stammfunktion berechnet. + \end{itemize} + \item In der vollen Quadratur für zulässige Elemente werden + \begin{itemize} + \item $\zeta_0$-zulässige Elemente mit Gauss-Quadratur über alle Integrale + \item und alle anderen analytisch mittels Stammfunktion berechnet. + \end{itemize} + \item Bei der geeigneten Quadratur für zulässige Elemente werden + \begin{itemize} + \item $\zeta_1$-zulässige Elemente mit Gauss-Quadratur über ein Element, + \item $\zeta_0$-zulässige Elemente mit Gauss-Quadratur über alle Integrale + \item und alle anderen analytisch mittels Stammfunktion berechnet. + \end{itemize} + \item In der Quadratur über ein Element für zulässige Elemente werden + \begin{itemize} + \item $\zeta_0$-zulässige Elemente mit Gauss-Quadratur über ein Element + \item und alle anderen analytisch mittels Stammfunktion berechnet. + \end{itemize} +\end{enumerate} + +\noindent +Da der Code sehr umfangreich geworden ist, werden wir an dieser Stelle nur einige Details hervorheben. + +\noindent +Wie schon erwähnt dient die \lstinline!mex_build_V.cpp! als Einstiegspunkt für \Matlab. In ihr haben wir die Auswertung der Parameter, sowie das Ermitteln der Integrationsgrenzen implementiert. Weiterhin iterieren wir hier, mittels \lstinline!for!-Schleifen auch über die Einträge der Matrix, um dann die geeignete Berechnungsfunktion des Eintrags $A_{jk}$ aufzurufen. + +\noindent +Da die Berechnungen der einzelnen Matrixeinträge unabhängig von einander sind, haben wir an dieser Stelle die \lstinline!for!-Schleifen zur Nutzung von paralleler Berechnung auf mehreren Kernen optimiert. Dafür nutzen wir die freie Bibliothek \lstinline!omp.h!. +\noindent +Die Implementierung der Berechnung eines Matrixeintrags befindet sich in der \lstinline!slpRectangle.cpp!. \clearpage @@ -1997,7 +2110,7 @@ Mithilfe der oben Definierten Funktionen ist es uns nun möglich den Ablauf der \subsection{Beispiel Quadrat} Im Folgenden werden wir die Laplace-Gleichung -\begin{align}\label{math:bsp:gls} +\begin{align}\label{math:bsp:Quad:gls} \begin{aligned} - \varDelta u &= 0 \quad\text{ in } \Omega \subset \R^3, \\ u &= g \quad \text{ auf }\Gamma, @@ -2085,8 +2198,97 @@ Anhand der \figLineC[] farbenen Linien, also der "`anisotropen"' Strategie beoba \noindent Um auch die Stabilität der drei Strategien untersuchen zu können, sehen wir in der Abbildung \ref{fig:2DQuad:verfeinern:cond} die Konditionszahlen der $V_{\ell}$ Matrix in Abhängigkeit der Elementanzahl. +\noindent +Weiterhin können wir in Abbildung \ref{fig:2DQuad:verfeinern:time} die benötigte Zeit pro Berechnungsschritt ablesen. Hierbei fällt auf, dass die Wahl der Strategie keinen Einfluss auf die benötigte Zeit hat, sondern nur die Anzahl der Elemente. Für die Berechnung mit 3000 Elementen benötigen alle drei Strategien etwa $10^4s \approx 2h45m$. + +\noindent +Diese Ergebnisse Zeigen also, dass die "`anisotrope"' Strategie die beste Konvergenzrate aufweist, wir dafür jedoch eine schlechtere Konditionsrate in kauf nehmen müssen. Welches letztendlich auf die größen und formen der Elemente zurückzuführen ist. + +\noindent +Ziel wird es nun sein die Instabilitäten, die bei der analytischen Berechnung auftreten durch Quadratur zu vermeiden. Dafür werden wir vorher noch Berechnungen mit verschiedenen Quadraturgraden genauer untersuchen. + \subsubsection{Vergleich verschiedener Quadraturgrade} +Bei der folgenden Berechnung werden wir alle Integrale von $\zeta_Q$-zulässigen Elemente durch die vorgestellte Gauss-Quadratur approximieren. Hierbei werden wir jeweils 1,2,4 oder 8 Auswertungsstellen verwenden. + +\noindent +Siehe Abbildung \ref{fig:2DQuad:quad} + +\begin{figure}[ht] + + +\centering +\subfloat[Fehler und Fehlerschätzer für das Quadrat \label{fig:2DQuad:quad:err}]{\includegraphics[width=0.5\textwidth]{fig/2222t05n05_2DQuad_error}} +% \subfloat[Seitenverhältnisse auf dem Quadrat \label{fig:2DQuad:quad:hminmax}]{\includegraphics[width=0.5\textwidth]{fig/2222t05n05_2DQuad_hminmax}} +% \\ +% \subfloat[Kondition der $V_{\ell}$ Matrix \label{fig:2DQuad:quad:cond}]{\includegraphics[width=0.5\textwidth]{fig/2222t05n05_2DQuad_cond}} +\subfloat[Berechnungszeit für das Quadrat \label{fig:2DQuad:quad:time}]{\includegraphics[width=0.5\textwidth]{fig/2222t05n05_2DQuad_time}} +\caption{Vergleich der Quadraturgrade auf dem Quadrat} +\label{fig:2DQuad:quad} +\end{figure} + \subsubsection{Vergleich verschiedener Berechnungsarten} +Siehe Abbildung \ref{fig:2DQuad:sem}. +\begin{figure}[ht] + + +\centering +\subfloat[Fehler und Fehlerschätzer für das Quadrat \label{fig:2DQuad:sem:err}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_error}} +% \subfloat[Seitenverhältnisse auf dem Quadrat \label{fig:2DQuad:quad:hminmax}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_hminmax}} +\\ +\subfloat[Kondition der $V_{\ell}$ Matrix \label{fig:2DQuad:sem:cond}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_cond}} +\subfloat[Berechnungszeit für das Quadrat \label{fig:2DQuad:sem:time}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_2DQuad_time}} +\caption{Vergleich der Berechnungsarten von $\hat V_{\ell}$} +\label{fig:2DQuad:sem} +\end{figure} + +\subsection{Beispiel Fischer Würfel} +Im Folgenden werden wir die Laplace-Gleichung +\begin{align}\label{math:bsp:FichCube:gls} +\begin{aligned} +- \varDelta u &= 0 \quad\text{ in } \Omega \subset \R^3, \\ +u &= g \quad \text{ auf }\Gamma, +\end{aligned} +\end{align} +mit dem Startnetz aus Abbildung \ref{fig:mesh:3DFichCube}, einem Fischer Würfel genauer betrachten. +Der Fischer Würfel ist gegeben durch einen $[-1, 1]^3$ Würfel aus dem ein $[-1, 0]\times[0,1]^2$ Würfel heraus geschnitten wurde. +% Die vier Eckpunkte des Quadrats sind hierbei gegeben durch +% \begin{align*} +% \{ (0,0,0), (1,0,0), (1,1,0), (0,1,0) \}. +% \end{align*} +\todo{Des Weiteren werden wir als exakte Lösung $\enorm{\phi}^2 = 16.2265$ annehmen.} +\begin{figure}[ht] + \centering + \includegraphics[width=0.5\textwidth]{fig/exmpl_3DFichCube_ref} + \caption{Fischer Würfel} + \label{fig:mesh:3DFichCube} +\end{figure} + + + +Siehe Abbildung \ref{fig:3DFichCube:sem}. +\begin{figure}[ht] + + +\centering +\subfloat[Fehler und Fehlerschätzer für das Quadrat \label{fig:3DFichCube:sem:err}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_3DFichCube_error}} +% \subfloat[Seitenverhältnisse auf dem Quadrat \label{fig:3DFichCube:quad:hminmax}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_3DFichCube_hminmax}} +% \\ +\subfloat[Kondition der $V_{\ell}$ Matrix \label{fig:3DFichCube:sem:cond}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_3DFichCube_cond}} +% \subfloat[Berechnungszeit für das Quadrat \label{fig:3DFichCube:sem:time}]{\includegraphics[width=0.5\textwidth]{fig/132t05n05_3DFichCube_time}} +\caption{Vergleich der Berechnungsarten von $\hat V_{\ell}$} +\label{fig:3DFichCube:sem} +\end{figure} + + + + + + + + + + + % Zum Plotten (Abb.\ref{fig:exmplAA_2DQuad})werden noch folgende Schritte ausgeführt % \begin{itemize} @@ -2134,7 +2336,7 @@ Um auch die Stabilität der drei Strategien untersuchen zu können, sehen wir in \subfloat[2D L Shape\label{fig:mesh:2DLShape}]{\includegraphics[width=0.5\textwidth]{fig/exmpl_2DLShape_ref}} % \subfloat[2D Quad\label{fig:mesh:2DQuad}]{\includegraphics[width=0.5\textwidth]{fig/exmpl_2DQuad_ref}}\\ \subfloat[3D Cube\label{fig:mesh:3DCube}]{\includegraphics[width=0.5\textwidth]{fig/exmpl_3DCube_ref}} -\subfloat[3D FichCube\label{fig:mesh:3DFichCube}]{\includegraphics[width=0.5\textwidth]{fig/exmpl_3DFichCube_ref}} +% \subfloat[3D FichCube\label{fig:mesh:3DFichCube}]{\includegraphics[width=0.5\textwidth]{fig/exmpl_3DFichCube_ref}} \end{figure} \clearpage diff --git a/doc/fig/132t05n05_2DQuad_cond.eps b/doc/fig/132t05n05_2DQuad_cond.eps index f147682..f994caf 100644 --- a/doc/fig/132t05n05_2DQuad_cond.eps +++ b/doc/fig/132t05n05_2DQuad_cond.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_2DQuad_cond.eps -%%CreationDate: 04/13/2013 16:13:47 +%%CreationDate: 04/14/2013 17:43:56 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -779,9 +779,9 @@ gr DA c2 -0 -2769 3963 3041 2 MP stroke -0 -2592 3963 3041 2 MP stroke -0 -2608 3963 3041 2 MP stroke +0 -2769 3847 3041 2 MP stroke +0 -2592 3847 3041 2 MP stroke +0 -2608 3847 3041 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_2DQuad_error.eps b/doc/fig/132t05n05_2DQuad_error.eps index 3e99b7b..293886d 100644 --- a/doc/fig/132t05n05_2DQuad_error.eps +++ b/doc/fig/132t05n05_2DQuad_error.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_2DQuad_error.eps -%%CreationDate: 04/13/2013 16:13:46 +%%CreationDate: 04/14/2013 17:43:55 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -1103,9 +1103,9 @@ DA 45 27 62 37 48 28 52 31 70 41 51 31 90 53 71 42 103 61 123 72 190 113 254 150 560 331 1183 1114 30 MP stroke c2 -0 -2147 3963 2995 2 MP stroke -0 -2144 3963 2992 2 MP stroke -0 -2144 3963 2992 2 MP stroke +0 -2147 3847 2995 2 MP stroke +0 -2144 3847 2992 2 MP stroke +0 -2144 3847 2992 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_2DQuad_hminmax.eps b/doc/fig/132t05n05_2DQuad_hminmax.eps index 4e60d1e..e043a11 100644 --- a/doc/fig/132t05n05_2DQuad_hminmax.eps +++ b/doc/fig/132t05n05_2DQuad_hminmax.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_2DQuad_hminmax.eps -%%CreationDate: 04/13/2013 16:13:46 +%%CreationDate: 04/14/2013 17:43:56 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -1179,9 +1179,9 @@ gr DA c2 -0 -2797 3963 3142 2 MP stroke -0 -2797 3963 3142 2 MP stroke -0 -2797 3963 3142 2 MP stroke +0 -2797 3847 3142 2 MP stroke +0 -2797 3847 3142 2 MP stroke +0 -2797 3847 3142 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_2DQuad_time.eps b/doc/fig/132t05n05_2DQuad_time.eps index 412631e..3d57740 100644 --- a/doc/fig/132t05n05_2DQuad_time.eps +++ b/doc/fig/132t05n05_2DQuad_time.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_2DQuad_time.eps -%%CreationDate: 04/13/2013 16:13:47 +%%CreationDate: 04/14/2013 17:43:57 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK diff --git a/doc/fig/132t05n05_3DFichCube_cond.eps b/doc/fig/132t05n05_3DFichCube_cond.eps index c624731..325ad3a 100644 --- a/doc/fig/132t05n05_3DFichCube_cond.eps +++ b/doc/fig/132t05n05_3DFichCube_cond.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_3DFichCube_cond.eps -%%CreationDate: 04/13/2013 16:13:49 +%%CreationDate: 04/14/2013 17:43:58 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -702,9 +702,9 @@ gr DA c2 -0 -2330 4029 2924 2 MP stroke -0 -2329 4029 2924 2 MP stroke -0 -1947 4029 2924 2 MP stroke +0 -2330 3907 2924 2 MP stroke +0 -2329 3907 2924 2 MP stroke +0 -1947 3907 2924 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_3DFichCube_error.eps b/doc/fig/132t05n05_3DFichCube_error.eps index df72000..89443cb 100644 --- a/doc/fig/132t05n05_3DFichCube_error.eps +++ b/doc/fig/132t05n05_3DFichCube_error.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_3DFichCube_error.eps -%%CreationDate: 04/13/2013 16:13:48 +%%CreationDate: 04/14/2013 17:43:57 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -917,9 +917,9 @@ DA 73 32 99 44 92 41 97 43 131 58 114 51 152 67 120 53 219 98 142 63 245 108 235 105 528 234 1095 1542 22 MP stroke c2 -0 -1805 4029 2690 2 MP stroke -0 -1805 4029 2690 2 MP stroke -0 -1766 4029 2651 2 MP stroke +0 -1805 3907 2690 2 MP stroke +0 -1805 3907 2690 2 MP stroke +0 -1766 3907 2651 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_3DFichCube_hminmax.eps b/doc/fig/132t05n05_3DFichCube_hminmax.eps index dcbf377..d65dc20 100644 --- a/doc/fig/132t05n05_3DFichCube_hminmax.eps +++ b/doc/fig/132t05n05_3DFichCube_hminmax.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_3DFichCube_hminmax.eps -%%CreationDate: 04/13/2013 16:13:48 +%%CreationDate: 04/14/2013 17:43:58 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -936,9 +936,9 @@ gr DA c2 -0 -2353 4029 2726 2 MP stroke -0 -2353 4029 2726 2 MP stroke -0 -2353 4029 2726 2 MP stroke +0 -2353 3907 2726 2 MP stroke +0 -2353 3907 2726 2 MP stroke +0 -2353 3907 2726 2 MP stroke gr c2 diff --git a/doc/fig/132t05n05_3DFichCube_time.eps b/doc/fig/132t05n05_3DFichCube_time.eps index fd323d3..82d3988 100644 --- a/doc/fig/132t05n05_3DFichCube_time.eps +++ b/doc/fig/132t05n05_3DFichCube_time.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/132t05n05_3DFichCube_time.eps -%%CreationDate: 04/13/2013 16:13:50 +%%CreationDate: 04/14/2013 17:43:59 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK diff --git a/doc/fig/1t05n05_2DLShape_cond.eps b/doc/fig/1t05n05_2DLShape_cond.eps index 8b75a27..db70771 100644 --- a/doc/fig/1t05n05_2DLShape_cond.eps +++ b/doc/fig/1t05n05_2DLShape_cond.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/1t05n05_2DLShape_cond.eps -%%CreationDate: 04/13/2013 16:29:51 +%%CreationDate: 04/14/2013 17:43:48 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -670,7 +670,7 @@ gr gs 624 269 3721 2936 MR c np DA c2 -0 -2794 3879 3081 2 MP stroke +0 -2794 3792 3081 2 MP stroke gr c2 diff --git a/doc/fig/1t05n05_2DLShape_error.eps b/doc/fig/1t05n05_2DLShape_error.eps index bf52ff7..66ea6bc 100644 --- a/doc/fig/1t05n05_2DLShape_error.eps +++ b/doc/fig/1t05n05_2DLShape_error.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/1t05n05_2DLShape_error.eps -%%CreationDate: 04/13/2013 16:29:51 +%%CreationDate: 04/14/2013 17:43:48 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -663,7 +663,7 @@ DA 66 39 77 45 62 37 74 44 95 56 95 56 99 59 133 78 147 88 141 83 190 112 254 151 396 234 1067 1045 30 MP stroke c2 -0 -1838 3879 2642 2 MP stroke +0 -1838 3792 2642 2 MP stroke gr c2 diff --git a/doc/fig/1t05n05_2DLShape_hminmax.eps b/doc/fig/1t05n05_2DLShape_hminmax.eps index 0b4e868..172c01f 100644 --- a/doc/fig/1t05n05_2DLShape_hminmax.eps +++ b/doc/fig/1t05n05_2DLShape_hminmax.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/1t05n05_2DLShape_hminmax.eps -%%CreationDate: 04/13/2013 16:29:51 +%%CreationDate: 04/14/2013 17:43:48 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK @@ -739,7 +739,7 @@ gr DA c2 -0 -2797 3879 3142 2 MP stroke +0 -2797 3792 3142 2 MP stroke gr c2 diff --git a/doc/fig/1t05n05_2DLShape_time.eps b/doc/fig/1t05n05_2DLShape_time.eps index d97bfa9..7767750 100644 --- a/doc/fig/1t05n05_2DLShape_time.eps +++ b/doc/fig/1t05n05_2DLShape_time.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/1t05n05_2DLShape_time.eps -%%CreationDate: 04/13/2013 16:29:52 +%%CreationDate: 04/14/2013 17:43:49 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK diff --git a/doc/fig/1t05n05_2DQuad_cond.eps b/doc/fig/1t05n05_2DQuad_cond.eps index b199e1c..82ed9ff 100644 --- a/doc/fig/1t05n05_2DQuad_cond.eps +++ b/doc/fig/1t05n05_2DQuad_cond.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 8.1.0.604 (R2013a). 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Operating System: Linux 3.7.0-7-generic #15-Ubuntu SMP Sat Dec 15 16:34:25 UTC 2012 x86_64. %%Title: ../doc/fig/refType_full.eps -%%CreationDate: 04/13/2013 16:13:32 +%%CreationDate: 04/14/2013 17:43:41 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Extensions: CMYK diff --git a/doc/lstings.sty b/doc/lstings.sty index 4ada06d..065f56d 100644 --- a/doc/lstings.sty +++ b/doc/lstings.sty @@ -62,7 +62,7 @@ mexFunction,mexErrMsgTxt,mxCreateDoubleMatrix,mxGetPr,mxGetM,mxGetN,mexPrintf}, %lib Functions morekeywords=[3]{GAUSS_SIZE,GAUSS_NODES,HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_,DEBUG,PARALLEL, MINSIZE_PER_WORKER,MAX_WORKER}, %Globals - morekeywords=[4]{int,double,void,_gauss,gauss}, %Typen + morekeywords=[4]{int,double,void,_gauss,gauss,mxArray}, %Typen deletekeywords=[1]{int,double,void}, morekeywords=[5]{add,sub,set,dimOfThird,getSCorner,distT,dimOfVec, sign,max,min,switch_site,switch_dim,dist,dist2,dist_s2,dist_s, @@ -74,7 +74,7 @@ \lstdefinelanguage{M}[]{Matlab}{ morecomment=[l]{...}, - morekeywords=[1]{assert,repmat,mod,regexprep,zeros,ones,ismember,scatter3,ylim,xlim,zlim}, + morekeywords=[1]{assert,repmat,mod,regexprep,zeros,ones,ismember,scatter3,ylim,xlim,zlim,mex}, morekeywords=[2]{}, %lib Functions morekeywords=[3]{G_ref_E,G_ref_C,G_ref_N,G_ref_S,G_ref_f2s,G_ref_t,G_ref_tD,G_ref_f2sT,G_D,G_C,G_E,G_N,G_T,G_S}, %Globals morekeywords=[4]{}, %Typen diff --git a/src/A_plots.m b/src/A_plots.m index 758634d..079c9af 100644 --- a/src/A_plots.m +++ b/src/A_plots.m @@ -154,7 +154,7 @@ i=0; % shift2 = shift2+shift2/10; % error*(eta(l)-shift2)/error(l) -first = 1 +find(([ (G_D(2:end,2+rows*i)-G_D(1:end-1,2+rows*i))./G_D(2:end,2+rows*i)])>=0,1); +first = 1 +find(([ (G_D(2:end,2+rows*i)-G_D(1:end-1,2+rows*i))./G_D(2:end,2+rows*i)])>=0,1)-1; Ferr = (X(first,i+1)+X(first-1,i+1))/2; loglog(X(:,i+1),G_D(:,2+rows*i),type2sym(i*3+1), ... diff --git a/src/export_exmpl.m b/src/export_exmpl.m index 3f57427..ffb0496 100644 --- a/src/export_exmpl.m +++ b/src/export_exmpl.m @@ -158,6 +158,9 @@ A_plots({'meshSave/1t1n0_2DQuad_6',... A_plots({'meshSave/132t05n05_2DQuad_30'},'../doc/fig/132t05n05_2DQuad') A_plots({'meshSave/132t05n05_3DFichCube_22'},'../doc/fig/132t05n05_3DFichCube') +A_plots({'meshSave/1432t05n05_3DFichCube_19'},'../doc/fig/1432t05n05_3DFichCube') + A_plots({'meshSave/2222t05n05_2DQuad_30'},'../doc/fig/2222t05n05_2DQuad') + close all \ No newline at end of file diff --git a/src/mex_build_V.cpp b/src/mex_build_V.cpp index 694ebb6..51c2440 100644 --- a/src/mex_build_V.cpp +++ b/src/mex_build_V.cpp @@ -1,11 +1,11 @@ /***************************************************************************/ /* mex_build_v.cpp */ /* */ -/* Definiert die MEX Funktion mex_build_V(coo,ele,zeta,type) */ +/* Definiert die MEX Funktion mex_build_V(coo,ele,zeta,typ) */ /* coo : Koordinaten Matrix */ /* ele : Element Matrix */ /* zeta : Steuerungsvariable der Zulaessigeitsbedingungen */ -/* type : Bestimmt die Art der Berechnung */ +/* typ : Bestimmt die Art der Berechnung */ /* */ /* TYPES---- */ /* 0 : nur die Abstaende der Elemente werden berechnet */ @@ -31,7 +31,7 @@ */ //#define PARALLEL #include -#include "mex.h" +#include #ifdef PARALLEL #include @@ -66,6 +66,8 @@ int inline dimOfThird(int a, int b) { return 1; case 3: return 0; + default: + return -1; } } @@ -308,14 +310,13 @@ void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { //LageInformationen int rx, rxa, rxb, ry, rya, ryb; double tmp; - double x[4][3] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; + double x[4][3] = { { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 } }; double y[4][3] = { { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 } }; double xa[3] = { 0, 0, 0 }; double xb[3] = { 0, 0, 0 }; double ya[3] = { 0, 0, 0 }; double yb[3] = { 0, 0, 0 }; double d[3] = { 0, 0, 0 }; - double dt[3] = { 0, 0, 0 }; /* * Schleife ueber Elemente initialisieren diff --git a/src/test_sol.m b/src/test_sol.m index 7eb66d0..8619361 100644 --- a/src/test_sol.m +++ b/src/test_sol.m @@ -2,7 +2,7 @@ format longG % Matrix MEX Funktion neu Compilieren -mex -o mex_build_V.cpp slpRectangle.cpp CFLAGS="\$CFLAGS -fopenmp" CXXFLAGS="\$CXXFLAGS -fopenmp" LDFLAGS="\$LDFLAGS -fopenmp" +mex -o 'mex_build_V.cpp' 'slpRectangle.cpp' CFLAGS="\$CFLAGS -fopenmp" CXXFLAGS="\$CXXFLAGS -fopenmp" LDFLAGS="\$LDFLAGS -fopenmp" % mex mex_build_V.cpp slpRectangle.cpp -- 2.47.3

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