\usepackage{fullpage} %Seiten etwas Größer
\usepackage[ngerman]{babel} %Sprachpacket für Überschriften
-% \usepackage[utf8]{inputenc} %Eingabekodierung
+\usepackage[utf8x]{inputenc} %Eingabekodierung
+\usepackage{fixltx2e} %Deutschsprach Bugs
+
+\usepackage{psfrag}
\usepackage{graphicx}
+\usepackage{subfig}
+\usepackage{hyperref} %Links im Inhaltsverzeichnis
+\hypersetup{linkbordercolor={1 1 1},citebordercolor={1 1 1},urlbordercolor={1 1 1}}
+\def\T{\mathcal{T}}
\newcommand{\comment}[1]{}
-\usepackage{xcolor}
-% \selectcolormodel{gray}
+
+
+\psfrag{T}{\scriptsize $T$}
+\psfrag{T1}{\scriptsize $T_1$}
+\psfrag{T2}{\scriptsize $T_2$}
+\psfrag{T3}{\scriptsize $T_3$}
+\psfrag{T4}{\scriptsize $T_4$}
+
+\psfrag{x}{\scriptsize $x$}
+\psfrag{y}{\scriptsize $y$}
+\psfrag{z}{\scriptsize $z$}
+
+\psfrag{Elementanzahl}{\scriptsize Elementanzahl}
+\psfrag{Schaetzer}{\scriptsize Fehler}
+\psfrag{Verhaeltnis}{\scriptsize Verhältnis}
+\psfrag{Kondition}{\scriptsize Kondition}
+\psfrag{Sekunden}{\scriptsize Zeit in $s$}
+
+\psfrag{tmu 1t05n05 A}{\tiny $\tilde \mu$}
+\psfrag{eta 1t05n05 A}{\tiny $\eta$}
+\psfrag{fehler 1t05n05 A}{\tiny Fehler}
+
+
+\psfrag{erste Fehler}{\tiny erste Fehler}
+
+\psfrag{Zeit 1t05n05 A}{\tiny Zeit}
+
+
+\psfrag{N-12}{\tiny $N^{-1/2}$}
+\psfrag{N-14}{\tiny $N^{-1/4}$}
+\psfrag{N-34}{\tiny $N^{-3/4}$}
+
\usepackage{lstings}
\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}
- \subsubsection{refineQuad.m}
- \lstinputlisting[language=M]{../src/refineQuad.m}
- \subsubsection{areaQuad.m}
- \lstinputlisting[language=M]{../src/areaQuad.m}
- \subsubsection{mark.m}
- \lstinputlisting[language=M]{../src/mark.m}
- \subsubsection{plotShape.m}
- \lstinputlisting[language=M]{../src/plotShape.m}
- \subsubsection{plotMark.m}
- \lstinputlisting[language=M]{../src/plotMark.m}
+% \subsection{Matlab}
+% \subsubsection{compute.m}
+% \lstinputlisting[language=M]{../src/compute.m}
+% \subsubsection{refineQuad.m}
+% \lstinputlisting[language=M]{../src/refineQuad.m}
+% \subsubsection{areaQuad.m}
+% \lstinputlisting[language=M]{../src/areaQuad.m}
+% \subsubsection{mark.m}
+% \lstinputlisting[language=M]{../src/mark.m}
+
+% \subsubsection{plotShape.m}
+% \lstinputlisting[language=M]{../src/plotShape.m}
+% \subsubsection{plotMark.m}
+% \lstinputlisting[language=M]{../src/plotMark.m}
% \lstinputlisting{}
+
+\section{Plots}
+\begin{figure}[ht]
+\caption{Objekt Beispiele}
+\centering
+\label{fig:objects}
+\subfloat[2D L Shape]{\includegraphics[width=0.5\textwidth]{fig/exmpl_2DLShape_ref}}
+\subfloat[2D Quad]{\includegraphics[width=0.5\textwidth]{fig/exmpl_2DQuad_ref}}\\
+\subfloat[3D Cube]{\includegraphics[width=0.5\textwidth]{fig/exmpl_3DCube_ref}}
+\subfloat[3D FichCube]{\includegraphics[width=0.5\textwidth]{fig/exmpl_3DFichCube_ref}}
+\end{figure}
+
+\begin{figure}[ht]
+\caption{2D Quad adaptiv anisotrop vollanalytisch $V\phi = 1$}
+\centering
+\label{fig:exmplAA_2DQuad}
+\subfloat[Fehler]{\includegraphics[width=0.7\textwidth]{fig/1t05n05_2DQuad_error}}\\
+\subfloat[Seitenverhältnis]{\includegraphics[width=0.5\textwidth]{fig/1t05n05_2DQuad_hminmax}}
+\subfloat[Kondition]{\includegraphics[width=0.5\textwidth]{fig/1t05n05_2DQuad_cond}}
+% \subfloat[Zeit]{\includegraphics[width=0.33\textwidth]{fig/1t05n05_2DQuad_time}}
+\end{figure}
+
+\begin{figure}[ht]
+
+\psfrag{tmu 1t1n0 A}{\tiny $\tilde \mu$ (uniform)}
+\psfrag{eta 1t1n0 A}{\tiny $\eta$ (uniform)}
+\psfrag{fehler 1t1n0 A}{\tiny Fehler (uniform)}
+\psfrag{Zeit 1t1n0 A}{\tiny Zeit (uniform)}
+
+\psfrag{tmu 1t05n0 A}{\tiny $\tilde \mu$ (isotrop)}
+\psfrag{eta 1t05n0 A}{\tiny $\eta$ (isotrop)}
+\psfrag{fehler 1t05n0 A}{\tiny Fehler (isotrop)}
+\psfrag{Zeit 1t05n0 A}{\tiny Zeit (isotrop)}
+
+\psfrag*{tmu 1t05n05 A}{\tiny \quad (anisotrop)}
+\psfrag*{eta 1t05n05 A}{\tiny \quad (anisotrop)}
+\psfrag*{fehler 1t05n05 A}{\tiny \qquad\quad (anisotrop)}
+\psfrag*{Zeit 1t05n05 A}{\tiny \qquad (anisotrop)}
+
+\caption{2D Quad im Vergleich vollanalytisch $V\phi = 1$}
+\centering
+\label{fig:exmpl_2DQuad_tn}
+\subfloat[Fehler]{\includegraphics[width=0.5\textwidth]{fig/1tn_2DQuad_error}}
+\subfloat[Seitenverhältnis]{\includegraphics[width=0.5\textwidth]{fig/1tn_2DQuad_hminmax}}\\
+\subfloat[Kondition]{\includegraphics[width=0.5\textwidth]{fig/1tn_2DQuad_cond}}
+ \subfloat[Zeit]{\includegraphics[width=0.5\textwidth]{fig/1tn_2DQuad_time}}
+\end{figure}
+
+\begin{figure}[ht]
+\caption{3D FichCube adaptiv anisotrop vollanalytisch $V\phi = 1$}
+\centering
+\label{fig:exmplAA_3DQuad}
+\subfloat[Fehler]{\includegraphics[width=0.5\textwidth]{fig/1t05n05_3DFichCube_error}}
+\subfloat[Seitenverhältnis]{\includegraphics[width=0.5\textwidth]{fig/1t05n05_3DFichCube_hminmax}}\\
+\subfloat[Kondition]{\includegraphics[width=0.5\textwidth]{fig/1t05n05_3DFichCube_cond}}
+\end{figure}
\end{document}
\usepackage{fullpage} %Seiten etwas Größer
\usepackage[ngerman]{babel} %Sprachpacket für Überschriften
-\usepackage[utf8]{inputenc} %Eingabekodierung
+\usepackage[utf8x]{inputenc} %Eingabekodierung
\usepackage{fixltx2e} %Deutschsprach Bugs
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% \numberwithin{bew}{section}
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1166 620 mt 1200 654 L
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1726 620 mt 1760 654 L
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0 sg
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25 25 1743 1932 FO
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25 25 3992 429 FO
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PP
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gs 1044 1239 3259 1314 MR c np
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+end %%Color Dict
+
+eplot
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+
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+end
+
+showpage
+
+%%Trailer
+%%EOF
--- /dev/null
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+
+ 537 616 mt
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+/Helvetica /ISOLatin1Encoding 83.3333 FMSR
+
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+/Helvetica /ISOLatin1Encoding 55.5556 FMSR
+
+ 537 249 mt
+(5) s
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+ 624 3206 mt 624 270 L
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+gs 624 270 3721 2937 MR c np
+/c8 { 0.000000 0.300000 0.300000 sr} bdef
+c8
+560 -634 560 -625 560 -296 560 -434 560 185 1183 2538 6 MP stroke
+gs 1132 683 2903 2092 MR c np
+ 25 25 1183 2538 FO
+ 25 25 1743 2723 FO
+ 25 25 2303 2289 FO
+ 25 25 2863 1993 FO
+ 25 25 3423 1368 FO
+ 25 25 3983 734 FO
+gr
+
+/c9 { 0.000000 0.600000 0.600000 sr} bdef
+c9
+126 -145 151 -167 119 -137 161 -181 117 -128 163 -185 121 -150 163 -222
+136 -141 176 -146 160 -133 247 -72 255 -182 305 -230 560 -75 1183 2848 16 MP stroke
+gs 1132 503 3063 2397 MR c np
+0 j
+29 50 -58 0 29 -50 1183 2881 4 MP
+DP
+29 50 -58 0 29 -50 1743 2806 4 MP
+DP
+29 50 -58 0 29 -50 2048 2576 4 MP
+DP
+29 50 -58 0 29 -50 2303 2394 4 MP
+DP
+29 50 -58 0 29 -50 2550 2322 4 MP
+DP
+29 50 -58 0 29 -50 2710 2189 4 MP
+DP
+29 50 -58 0 29 -50 2886 2043 4 MP
+DP
+29 50 -58 0 29 -50 3022 1902 4 MP
+DP
+29 50 -58 0 29 -50 3185 1680 4 MP
+DP
+29 50 -58 0 29 -50 3306 1530 4 MP
+DP
+29 50 -58 0 29 -50 3469 1345 4 MP
+DP
+29 50 -58 0 29 -50 3586 1217 4 MP
+DP
+29 50 -58 0 29 -50 3747 1036 4 MP
+DP
+29 50 -58 0 29 -50 3866 899 4 MP
+DP
+29 50 -58 0 29 -50 4017 732 4 MP
+DP
+29 50 -58 0 29 -50 4143 587 4 MP
+DP
+gr
+
+/c10 { 0.600000 0.000000 0.600000 sr} bdef
+c10
+65 -75 95 -108 107 -126 99 -115 97 -112 94 -99 87 -102 72 -86
+55 -79 84 -124 54 -72 64 -87 60 -41 61 -80 61 -63 45 -37
+62 -15 48 -70 52 -37 70 4 51 -81 90 -78 71 -14 103 -74
+123 -88 190 187 254 -312 560 407 1183 2247 29 MP stroke
+gs 1132 619 2977 2087 MR c np
+1166 2230 mt 1200 2264 L
+1200 2230 mt 1166 2264 L
+1726 2637 mt 1760 2671 L
+1760 2637 mt 1726 2671 L
+1980 2325 mt 2014 2359 L
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+3269 1555 mt 3303 1589 L
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+3324 1476 mt 3358 1510 L
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+3396 1390 mt 3430 1424 L
+3430 1390 mt 3396 1424 L
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+3517 1288 mt 3483 1322 L
+3577 1189 mt 3611 1223 L
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+3674 1077 mt 3708 1111 L
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+3773 962 mt 3807 996 L
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+4009 728 mt 3975 762 L
+4040 653 mt 4074 687 L
+4074 653 mt 4040 687 L
+gr
+
+gr
+
+c10
+0 sg
+%%IncludeResource: font Helvetica
+/Helvetica /ISOLatin1Encoding 83.3333 FMSR
+
+2207 3432 mt
+(Elementanzahl) s
+ 388 1927 mt -90 rotate
+(Sekunden) s
+90 rotate
+ 612 3237 mt
+( ) s
+4333 300 mt
+( ) s
+1 sg
+0 333 894 0 0 -333 665 645 4 MP
+PP
+-894 0 0 333 894 0 0 -333 665 645 5 MP stroke
+2.77778 w
+DO
+SO
+4.16667 w
+0 sg
+ 665 645 mt 1559 645 L
+ 665 645 mt 665 312 L
+ 980 407 mt
+(Zeit 1t1n0 A) s
+gs 665 312 895 334 MR c np
+c8
+242 0 713 376 2 MP stroke
+gs 783 325 103 103 MR c np
+ 25 25 834 376 FO
+gr
+
+gr
+
+c8
+0 sg
+ 980 509 mt
+(Zeit 1t05n0 A) s
+gs 665 312 895 334 MR c np
+c9
+242 0 713 478 2 MP stroke
+gs 783 427 103 103 MR c np
+0 j
+29 50 -58 0 29 -50 834 511 4 MP
+DP
+gr
+
+gr
+
+c9
+0 sg
+ 980 611 mt
+(Zeit 1t05n05 A) s
+gs 665 312 895 334 MR c np
+c10
+242 0 713 580 2 MP stroke
+gs 783 529 103 103 MR c np
+ 817 563 mt 851 597 L
+ 851 563 mt 817 597 L
+gr
+
+gr
+
+c10
+
+end %%Color Dict
+
+eplot
+%%EndObject
+
+epage
+end
+
+showpage
+
+%%Trailer
+%%EOF
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% type2str = {'Analytisch ' 'Quad Element' 'Quad Achse ' 'Quad Seite '};
type2str = {'A ' 'QA' 'QEQA' 'QA ' 'QS '};
-type2sym = {'-o' '-x' '-*' '-+' '-.'};
-type2color = [[0 .3 .3]; [0 .6 .6]; [0 0 .6 ]; [.9 0 0]];
+type2sym = {'o-' 'v-' 'x-' '.-' '^-','+-','p-','s-','d-'};
+type2color = [[0 .3 .3]; [0 .6 .6]; [.6 0 .6 ]; [.9 0 0]];
set(0,'DefaultAxesColorOrder',type2color,...
- 'DefaultAxesLineStyleOrder','-o|-x|-*|-.|--|:')
+ 'DefaultAxesLineStyleOrder','o-|v-|x-')
- set(4,'DefaultAxesColorOrder',type2color(1,:),...
- 'DefaultAxesLineStyleOrder','-o|-x|-*|-.|--|:')
- set(6,'DefaultAxesColorOrder',type2color(1,:),...
- 'DefaultAxesLineStyleOrder','-o|-x|-*|-.|--|:')
+ set(4,'DefaultAxesColorOrder',type2color(1,:)...
+... ,'DefaultAxesLineStyleOrder','.-|-o|-x|-*|-.|--|:'...
+ );
+ set(6,'DefaultAxesColorOrder',type2color(1,:)...
+... ,'DefaultAxesLineStyleOrder','.-|-o|-x|-*|-.|--|:'...
+ );
G_D=[];
X = [];
l1 = {type2str{data(1,[2+(0:step-1)*rows])}};
for i = 1:step
leg0 = {leg0{:}...
- ['t\mu ' l0 l1{i}]...
+ ['tmu ' l0 l1{i}]...
... ['tilde \mu_2 ' l0 l1{i}]...
- ['\eta ' l0 l1{i}]...
+ ['eta ' l0 l1{i}]...
['fehler ' l0 l1{i}]...
... ['\mu ' l0 l1{i}]...
... ['\kappa ' l0 l1{i}]...
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);
Ferr = (X(first,i+1)+X(first-1,i+1))/2;
-loglog(repmat(X(:,i+1),1,3),[G_D(:,2+rows*i) ...
+loglog(X(:,i+1),G_D(:,2+rows*i),type2sym{i*3+1}, ...
... G_D(:,2+8+rows*i)...
- G_D(:,2+1+rows*i)...*(G_D(k,2)-shift)/G_D(k,3)...*G_D(1,2)/G_D(1,2+1+rows*i) ...
- sqrt(abs(sol - G_D(:,2+2+rows*i)))...*(G_D(k,2)-shift)/G_D(k,3)...
+ X(:,i+1),G_D(:,2+1+rows*i),type2sym{i*3+2},...*(G_D(k,2)-shift)/G_D(k,3)...*G_D(1,2)/G_D(1,2+1+rows*i) ...
+ X(:,i+1),sqrt(abs(sol - G_D(:,2+2+rows*i))),type2sym{i*3+3},...*(G_D(k,2)-shift)/G_D(k,3)...
... G_D(:,2+3+rows*i)...*G_D(1,2)/G_D(1,2+3+rows*i) ...
... [ 0; sqrt(G_D(2:end,2+9+rows*i)-G_D(1:end-1,2+9+rows*i))]...
... [ 0; sqrt(G_D(2:end,2+2+rows*i)-G_D(1:end-1,2+2+rows*i))]...
... G_D(:,2+10+rows*i)...
- ],'color', type2color(i+1,:));
+ 'color', type2color(i+1,:));
hold on
for i = 1:step-1
-loglog(repmat(X(:,i+1),1,3),[G_D(:,2+rows*i) ...
+loglog(X(:,i+1),G_D(:,2+rows*i),type2sym{i*3+1}, ...
... G_D(:,2+8+rows*i)...
- G_D(:,2+1+rows*i)...*G_D(1,2)/G_D(1,2+1+rows*i) ...
- sqrt(abs(sol - G_D(:,2+2+rows*i)))...*G_D(1,2)/sqrt(abs(sol - G_D(1,2+2+rows*i)))...
+ X(:,i+1),G_D(:,2+1+rows*i),type2sym{i*3+2},...*(G_D(k,2)-shift)/G_D(k,3)...*G_D(1,2)/G_D(1,2+1+rows*i) ...
+ X(:,i+1),sqrt(abs(sol - G_D(:,2+2+rows*i))),type2sym{i*3+3},...*(G_D(k,2)-shift)/G_D(k,3)...
... G_D(:,2+3+rows*i)...*G_D(1,2)/G_D(1,2+3+rows*i) ...
... [ 0; sqrt(G_D(2:end,2+9+rows*i)-G_D(1:end-1,2+9+rows*i))]...
... [ 0; sqrt(G_D(2:end,2+2+rows*i)-G_D(1:end-1,2+2+rows*i))]...
... G_D(:,2+10+rows*i)...
- ],'color', type2color(i+1,:));
+ 'color', type2color(i+1,:));
end
-loglog(X(:,1),7*X(:,1).^(-1/2),'-.',...
+loglog(X(:,1),9*X(:,1).^(-1/2),'-.',...
X(:,1),3*X(:,1).^(-1/4),':',...
X(:,1),2*X(:,1).^(-3/4),'--','color', [.9 .6 0])
+if(~isempty(Ferr))
loglog([Ferr; Ferr],...
[min(G_D(:,3+rows*[0:step-1]))*0.6; max(G_D(:,2+rows*[0:step-1]))*1.3],...
'--','color',[.9 0 0]);
+end
hold off
% title(['Fehler ' t0])
-xlabel('Elemente');
+xlabel('Elementanzahl');
ylabel('Schaetzer');
legend({leg0{:} ...
- 'N^{-1/2}' 'N^{-1/4}' 'N^{-3/4}'...
+ 'N-12' 'N-14' 'N-34'...
'erste Fehler' ...
} ,'location','southwest','box', 'off');
print('-r600','-depsc',[printt '_error.eps'])
-%% Plotte eNorm
-figure(5)
-loglog(repmat(X(:,1),1,1),G_D(:,2+2),type2sym{1});
-hold on
-for i = 1:step-1
- loglog(repmat(X(:,i+1),1,1),G_D(:,2+2+i*rows),'color', type2color(i+1,:));
-end
-loglog(X(:,1),repmat(sol,size(X,1),1),'-.', 'color', [.9 0 0])
-loglog([Ferr; Ferr],...
- [min(G_D(:,4+rows*[0:step-1]))*0.6; max(G_D(:,4+rows*[0:step-1]))*1.1],...
- '--','color',[.9 0 0]);
-hold off
-ylim([min(min(G_D(:,[4+(0:step-1)*rows]))) 1.005*max(max(G_D(:,[4+(0:step-1)*rows])))])
-% title(['Energie Norm ' t0])
-xlabel('Elemente');
-ylabel('eNorm^2');
-legend({leg1{:} , 'extrapoliert', 'erste Fehler' },'location','SouthEast');
-
-
-print('-r600','-depsc',[printt '_norm.eps'])
+% %% Plotte eNorm
+% figure(5)
+% loglog(repmat(X(:,1),1,1),G_D(:,2+2),type2sym{1});
+% hold on
+% for i = 1:step-1
+% loglog(repmat(X(:,i+1),1,1),G_D(:,2+2+i*rows),'color', type2color(i+1,:));
+% end
+% loglog(X(:,1),repmat(sol,size(X,1),1),'-.', 'color', [.9 0 0])
+% if(~isempty(Ferr))
+% loglog([Ferr; Ferr],...
+% [min(G_D(:,4+rows*[0:step-1]))*0.6; max(G_D(:,4+rows*[0:step-1]))*1.1],...
+% '--','color',[.9 0 0]);
+% end
+% hold off
+% ylim([min(min(G_D(:,[4+(0:step-1)*rows]))) 1.005*max(max(G_D(:,[4+(0:step-1)*rows])))])
+% % title(['Energie Norm ' t0])
+% xlabel('Elementanzahl');
+% ylabel('eNorm^2');
+% legend({leg1{:} , 'extrapoliert', 'erste Fehler' },'location','SouthEast');
+%
+%
+% print('-r600','-depsc',[printt '_norm.eps'])
%% Plotte HMIN HMAX
figure(6)
i=0;
-loglog(repmat(X(:,i+1),1,3),[...
- G_D(:,2+4+rows*i)...
- G_D(:,2+5+rows*i)...
- G_D(:,2+6+rows*i)...
- ],'color', type2color(i+1,:));
+loglog(...
+ X(:,i+1),G_D(:,2+4+rows*i),type2sym{i*3+1},...
+ X(:,i+1),G_D(:,2+5+rows*i),type2sym{i*3+2},...
+ X(:,i+1),G_D(:,2+6+rows*i),type2sym{i*3+3},...
+ 'color', type2color(i+1,:));
hold on
for i = 1:step-1
-loglog(repmat(X(:,i+1),1,3),[...
- G_D(:,2+4+rows*i)...
- G_D(:,2+5+rows*i)...
- G_D(:,2+6+rows*i)...
- ],'color', type2color(i+1,:));
+loglog(...
+ X(:,i+1),G_D(:,2+4+rows*i),type2sym{i*3+1},...
+ X(:,i+1),G_D(:,2+5+rows*i),type2sym{i*3+2},...
+ X(:,i+1),G_D(:,2+6+rows*i),type2sym{i*3+3},...
+ 'color', type2color(i+1,:));
end
% loglog(X(:,1),[7*X(:,1).^(-1/2),3*X(:,1).^(-1/4),2*X(:,1).^(-3/4)],'-.')
+if(~isempty(Ferr))
loglog([Ferr; Ferr],...
[min(G_D(:,6+rows*[0:step-1]))*0.6; max(G_D(:,6+rows*[0:step-1]))*1.3],...
'--','color',[.9 0 0]);
+end
+
+% ylim([min(min(G_D(:,[5+(0:step-1)*rows])))*0.8 1.2*max(max(G_D(:,[5+(0:step-1)*rows])))])
+
hold off
% title(['hmin hmax ' t0])
-xlabel('Elemente');
-ylabel('Schaetzer');
+xlabel('Elementanzahl');
+ylabel('Verhaeltnis');
legend({leg2{:} ...
'erste Fehler' ...
% 'N^{-1/2}' 'N^{-1/4}' 'N^{-3/4}'...
print('-r600','-depsc',[printt '_hminmax.eps'])
-%% Plotte cond
+%% Plotte Kond
figure(7)
i=0;
-loglog(repmat(X(:,i+1),1,1),[...
+loglog(repmat(X(:,i+1),1,1),...
G_D(:,2+7+rows*i)...
- ],'color', type2color(i+1,:));
+ ,type2sym{i+1},'color', type2color(i+1,:));
hold on
for i = 1:step-1
-loglog(repmat(X(:,i+1),1,1),[...
+loglog(repmat(X(:,i+1),1,1),...
G_D(:,2+7+rows*i)...
- ],'color', type2color(i+1,:));
+ ,type2sym{i+1},'color', type2color(i+1,:));
end
% loglog(X(:,1),[7*X(:,1).^(-1/2),3*X(:,1).^(-1/4),2*X(:,1).^(-3/4)],'-.')
+if(~isempty(Ferr))
loglog([Ferr; Ferr],...
[min(G_D(:,9+rows*[0:step-1]))*0.6; max(G_D(:,9+rows*[0:step-1]))*1.3],...
'--','color',[.9 0 0]);
+end
hold off
% title(['KonditionierungsZahlen von V ' t0])
-xlabel('Elemente');
-ylabel('Condition');
+xlabel('Elementanzahl');
+ylabel('Kondition');
legend({leg3{:} ...
'erste Fehler' ...
% 'N^{-1/2}' 'N^{-1/4}' 'N^{-3/4}'...
i=0;
loglog(repmat(X(:,i+1),1,1),[...
G_D(:,2+11+rows*i)...
- ],'color', type2color(i+1,:));
+ ],type2sym{i+1},'color', type2color(i+1,:));
hold on
for i = 1:step-1
loglog(repmat(X(:,i+1),1,1),[...
G_D(:,2+11+rows*i)...
- ],'color', type2color(i+1,:));
+ ],type2sym{i+1},'color', type2color(i+1,:));
end
% loglog(X(:,1),[7*X(:,1).^(-1/2),3*X(:,1).^(-1/4),2*X(:,1).^(-3/4)],'-.')
hold off
% title(['Benoetigte Zeit ' t0])
-xlabel('Elemente');
+xlabel('Elementanzahl');
ylabel('Sekunden');
legend({leg4{:} ...
% 'N^{-1/2}' 'N^{-1/4}' 'N^{-3/4}'...
-
clear
close all
%% voll Analytisch
A_plots({'meshSave/1t05n05_3DFichCube_23'},'../doc/fig/1t05n05_3DFichCube')
-A_plots({'meshSave/1t05n05_2DQuad_28'},'../doc/fig/1t05n05_2DQuad')
+A_plots({'meshSave/1t05n05_2DQuad_32'},'../doc/fig/1t05n05_2DQuad')
+
+%% Isotrop Uniform
+A_plots({'meshSave/1t1n0_2DQuad_6'},'../doc/fig/1t1n0_2DQuad')
+A_plots({'meshSave/1t05n0_2DQuad_16'},'../doc/fig/1t05n0_2DQuad')
+
+A_plots({'meshSave/1t1n0_2DQuad_6',...
+ 'meshSave/1t05n0_2DQuad_16',...
+ 'meshSave/1t05n05_2DQuad_29'},'../doc/fig/1tn_2DQuad')
+
+
close all
\ No newline at end of file
/* type : Bestimmt die Art der Berechnung */\r
/* */\r
/* TYPES---- */\r
+/* 0 : nur die Abstaende der Elemente werden berechnet */\r
+/* zeta wird ignoriert */\r
+/* */\r
/* 1 : Voll Analytisch */\r
/* zeta wird ignoriert */\r
/* */\r
/* 3 : Semianalytisch wie (2) und Quadratur ueber eine Achse */\r
/* Quadratur bei : min{x[1],y[1]} < zeta[0] * dist(x[1],y[1]) */\r
/* */\r
-/* 4 : Semianalytisch wie (2) und Quadratur ueber ein Element */\r
-/* Quadratur bei : min{dia(T1),dia(T2)} < zeta[0] * dist(T1,T2) */\r
/* */\r
/***************************************************************************/\r
/* Author: Peter Schaefer schaeferpm@gmail.com */\r
/* Version: 1.0 (2012) */\r
/***************************************************************************/\r
\r
-#define DEBUG 1\r
-#define PARALLEL\r
-\r
-//#include <iostream>\r
+/*\r
+ * wenn gesetzt wird paralleles Rechnen benutzt\r
+ */\r
+//#define PARALLEL\r
#include <cmath>\r
-//#include <cassert>\r
#include "mex.h"\r
-/*/#include <stdlib.h>\r
\r
- //#include "gauss.hpp"\r
- */\r
-//#define M_EPS 10e-8\r
+#ifdef PARALLEL\r
#include <omp.h>\r
+#endif\r
\r
#include "slpRectangle.hpp"\r
-//using namespace slpR;\r
\r
-// Gibt vom Vektor vec die Dimension != 0 zurueck\r
+/*\r
+ * Gibt vom Vektor vec die Dimension != 0 zurueck\r
+ */\r
int inline dimOfVec(double* vec) {\r
if (vec[2] != 0)\r
return 2;\r
}\r
}\r
\r
-//// Gibt von [0 1 2] die Fehlende Zahl zurueck\r
-//int inline dimOfThird(int a, int b) {\r
-// return ((-(a + b) % 3) + 3) % 3;\r
-//}\r
-\r
-// Gibt von [0 1 2] die Fehlende Zahl zurueck\r
+/*\r
+ * Gibt von [0 1 2] die fehlende Zahl zurueck\r
+ */\r
int inline dimOfThird(int a, int b) {\r
switch (a + b) {\r
case 1:\r
}\r
}\r
\r
+/*\r
+ * addiert Vektor b zu Vektor a\r
+ */\r
void inline add(double* a, double* b) {\r
for (int i = 0; i < 3; ++i)\r
a[i] += b[i];\r
}\r
\r
+/*\r
+ * vergleicht zwei Vektoren a, b\r
+ */\r
bool inline iseq(double* a, double* b) {\r
for (int i = 0; i < 3; ++i)\r
if (a[i] != b[i])\r
return true;\r
}\r
\r
+/*\r
+ * vergleicht Vektor a mit Konstante b\r
+ */\r
bool inline iseq(double* a, double b) {\r
for (int i = 0; i < 3; ++i)\r
if (a[i] != b)\r
return true;\r
}\r
\r
+/*\r
+ * speichert die Summe der Vektoren a,b in Vektor c\r
+ */\r
void inline add(double* a, double* b, double* c) {\r
for (int i = 0; i < 3; ++i)\r
a[i] = b[i] + c[i];\r
}\r
\r
+/*\r
+ * subtrahiert Vektor b von Vektor a\r
+ */\r
void inline sub(double* a, double* b) {\r
for (int i = 0; i < 3; ++i)\r
a[i] -= b[i];\r
}\r
+\r
+/*\r
+ * speichert die Differenz der Vektoren a,b in Vektor c\r
+ */\r
void inline sub(double* a, double* b, double* c) {\r
for (int i = 0; i < 3; ++i)\r
a[i] = b[i] - c[i];\r
}\r
\r
+/*\r
+ * speichert Vektor b in Vektor a\r
+ */\r
void inline set(double* a, double* b) {\r
for (int i = 0; i < 3; ++i)\r
a[i] = b[i];\r
}\r
\r
+/*\r
+ * setzt alle Werte in Vektor a auf Konstante b\r
+ */\r
void inline set(double* a, double b) {\r
for (int i = 0; i < 3; ++i)\r
a[i] = b;\r
}\r
\r
-//gibt die kleinste Ecke zurueck\r
+/*\r
+ * speichert die kleinste Zeile von Matrix x in Vektor d\r
+ */\r
void inline getSCorner(double* d, double x[4][3]) {\r
set(d, x[0]);\r
for (int i = 1; i < 4; ++i) {\r
}\r
}\r
\r
+/*\r
+ * berechnet den Abstand von zwei parallelen Elementen * 4Pi\r
+ */\r
double inline distT_par(double b, double d, double t, double v, double d1,\r
double d2, double d3, double * dummy) {\r
double dis1 = 0, dis2 = 0;\r
+\r
if (d1 < 0)\r
dis1 = -d1 - t;\r
- else if(d1 > 0)\r
+ else if (d1 > 0)\r
dis1 = d1 - b;\r
if (dis1 < 0)\r
dis1 = 0;\r
\r
if (d2 < 0)\r
dis2 = -d2 - v;\r
- else if(d2 > 0)\r
+ else if (d2 > 0)\r
dis2 = d2 - d;\r
if (dis2 < 0)\r
dis2 = 0;\r
\r
-// if(d3!=0)\r
-// mexErrMsgTxt("expected d3 == 0");\r
-\r
-// return dis1 * dis1 + dis2 * dis2 + d3 * d3;\r
return sqrt(dis1 * dis1 + dis2 * dis2 + d3 * d3) * (4 * M_PI);\r
}\r
+\r
+/*\r
+ * berechnet den Abstand von zwei orthogonalen Elementen * 4Pi\r
+ */\r
double inline distT_ort(double b, double d, double t, double v, double d1,\r
double d2, double d3, double * dummy) {\r
double dis1 = 0, dis2 = 0, dis3 = 0;\r
if (dis3 < 0)\r
dis3 = 0;\r
\r
-// return dis1 * dis1 + dis2 * dis2 + dis3 * dis3;\r
return sqrt(dis1 * dis1 + dis2 * dis2 + dis3 * dis3) * (4 * M_PI);\r
}\r
+\r
+/*\r
+ * mexFunktion zum aufbauen der Galerkin Matrix\r
+ */\r
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {\r
- /*\r
- mexPrintf("%d",omp_get_max_threads());\r
- omp_set_num_threads(3);\r
- mexPrintf("%d",omp_get_num_threads());\r
- */\r
\r
int i, j, k; //Schleifenindizes\r
- int count;\r
\r
-//Sicherheitsabfragen zu Datengroessen\r
+ /*\r
+ * Sicherheitsueberpruefung der Parameter\r
+ */\r
if ((nrhs != 4))\r
mexErrMsgTxt(\r
- "expected (coordinates(Nx3),elements(Mx4),zeta(double),type(int))");\r
+ "erwarte (coordinates(Nx3), elements(Mx4), zeta(double), type(int))");\r
if (nlhs > 1)\r
- mexErrMsgTxt("has only one output argument");\r
+ mexErrMsgTxt("Funktion hat nur einen Rueckgabewert");\r
\r
int cm = mxGetM(prhs[0]);\r
int cn = mxGetN(prhs[0]);\r
if (cn != 3)\r
- mexErrMsgTxt("expected coordinates (Nx3)");\r
-// cout << " Koordinaten:" << cm << endl;\r
+ mexErrMsgTxt("erwarte Koordinatenmatrix im (Nx3) Format");\r
\r
int em = mxGetM(prhs[1]);\r
int en = mxGetN(prhs[1]);\r
if (en != 4)\r
- mexErrMsgTxt("expected elements (Mx4)\n");\r
-// cout << " Elemente:" << em << endl;\r
+ mexErrMsgTxt("erwarte Elementmatrix im (Mx4) Format");\r
+\r
+ /*\r
+ * Parameter fuer parallele Berechnung setzen\r
+ */\r
+#ifdef PARALLEL\r
+#define MINSIZE_PER_WORKER 3\r
+#define MAX_WORKER 10\r
\r
-//Auslesen der Parameter\r
+ int actualNumberOfThreads = omp_get_max_threads();\r
\r
+ if (MAX_WORKER < actualNumberOfThreads)\r
+ actualNumberOfThreads = MAX_WORKER;\r
+\r
+ int firstRow = 0, lastRow = -1;\r
+ int targetSize = em * (em + 1) / (2 * actualNumberOfThreads);\r
+\r
+ if (targetSize < MINSIZE_PER_WORKER) {\r
+ actualNumberOfThreads = (int) em * (em + 1) / (2 * MINSIZE_PER_WORKER);\r
+ if (actualNumberOfThreads < 1) {\r
+ actualNumberOfThreads = 1;\r
+ targetSize = em;\r
+ } else {\r
+ targetSize = MINSIZE_PER_WORKER;\r
+ }\r
+ }\r
+#endif\r
+\r
+ /*\r
+ * Variablen initialisieren\r
+ */\r
plhs[0] = mxCreateDoubleMatrix(em, em, mxREAL);\r
double * A = mxGetPr(plhs[0]);\r
double * C = mxGetPr(prhs[0]);\r
int type = (int) *(mxGetPr(prhs[3]));\r
double * zeta = { 0 };\r
\r
-#if DEBUG >= 4\r
- mexPrintf("ZetaM:%d\nZetaN:%d\n",mxGetM(prhs[2]),mxGetN(prhs[2]));\r
-#endif\r
if (mxGetN(prhs[2]) > 1)\r
zeta = mxGetPr(prhs[2]) + 1;\r
\r
+ //setzen der Quadraturpunkte\r
int quad = (int) *mxGetPr(prhs[2]);\r
quad = setQuad(quad);\r
-#if DEBUG >= 3\r
- mexPrintf("Berechnungstyp:%d\nQuadpunkte:%d\n",type,quad);\r
-#endif\r
\r
-// Welche Funktion soll verwendet werden\r
+ //Art der Berechnung bestimmen\r
double (*ctypeP)(double, double, double, double, double, double, double,\r
double*);\r
double (*ctypeO)(double, double, double, double, double, double, double,\r
double*);\r
\r
-//Art der Berechnung bestimmen\r
-// cout << " Typ:" << type << endl;\r
switch (type) {\r
default: // Voll Analytisch\r
ctypeP = cParO1;\r
ctypeP = cParO3;\r
ctypeO = cOrtO3;\r
break;\r
- case 4: // Analytisch oder Qx1x2\r
- ctypeP = cParO4;\r
- ctypeO = cOrtO1;\r
- break;\r
- case 0:\r
+ case 0: // Distanz der Elemente\r
ctypeP = distT_par;\r
ctypeO = distT_ort;\r
break;\r
}\r
\r
- count = 0;\r
-// omp_set_dynamic(1);\r
-\r
//LageInformationen\r
int rx, rxa, rxb, ry, rya, ryb;\r
double tmp;\r
double d[3] = { 0, 0, 0 };\r
double dt[3] = { 0, 0, 0 };\r
\r
-#define MINSIZE_PER_WORKER 3\r
-#define MAX_WORKER 10\r
-\r
- int actualNumberOfThreads = omp_get_max_threads();\r
-\r
- if (MAX_WORKER < actualNumberOfThreads)\r
- actualNumberOfThreads = MAX_WORKER;\r
-\r
- int firstRow = 0, lastRow = -1;\r
- int targetSize = em * (em + 1) / (2 * actualNumberOfThreads);\r
-\r
- if (targetSize < MINSIZE_PER_WORKER) {\r
- actualNumberOfThreads = (int) em * (em + 1) / (2 * MINSIZE_PER_WORKER);\r
- if (actualNumberOfThreads < 1) {\r
- actualNumberOfThreads = 1;\r
- targetSize = em;\r
- } else {\r
- targetSize = MINSIZE_PER_WORKER;\r
- }\r
- }\r
-#if DEBUG >= 3\r
- mexPrintf("matrixSize (em) : %d\n"\r
- "targetSize : %d\n"\r
- "actualNumberOfThreads: %d\n", em, targetSize,\r
- actualNumberOfThreads);\r
-#endif\r
-\r
-//Ausrechnen\r
+ /*\r
+ * Schleife ueber Elemente initialisieren\r
+ */\r
#ifdef PARALLEL\r
-//#pragma omp parallel p\r
{\r
#pragma omp parallel for schedule(static,1) private(i,j,k,tmp,x,y,xa,xb,ya,yb,d,dt,rx,rxa,rxb,ry,rya,ryb,lastRow,firstRow) shared(C,E,ctypeO,ctypeP,em,targetSize,actualNumberOfThreads)\r
\r
-#endif\r
- for (i = 0; i < actualNumberOfThreads; ++i) {\r
- firstRow = (int) sqrt(2 * i * targetSize);\r
- if (i == actualNumberOfThreads - 1) {\r
- lastRow = em - 1;\r
- } else {\r
- lastRow = (int) sqrt(2 * (i + 1) * targetSize) - 1;\r
- }\r
-\r
-#if DEBUG >= 4\r
-#pragma omp critical\r
- mexPrintf("thread Nr.: (%d) | firstRow/lastRow: [%d / %d] \n",\r
+ for (i = 0; i < actualNumberOfThreads; ++i) {\r
+ firstRow = (int) sqrt(2 * i * targetSize);\r
+ if (i == actualNumberOfThreads - 1) {\r
+ lastRow = em - 1;\r
+ } else {\r
+ lastRow = (int) sqrt(2 * (i + 1) * targetSize) - 1;\r
+ }\r
\r
-#ifdef PARALLEL\r
- omp_get_thread_num()\r
+ for (j = firstRow; j <= lastRow; ++j) {\r
#else\r
- i\r
-#endif\r
- , firstRow, lastRow);\r
-#pragma omp end critical\r
-#endif\r
+ {\r
{\r
- for (j = firstRow; j <= lastRow; ++j) {\r
+ for (j = 0; j < em; ++i) {\r
+\r
+#endif\r
+ // Eckdaten zwischenspeichern\r
x[0][0] = C[(int) E[j] - 1];\r
x[0][1] = C[cm + (int) E[j] - 1];\r
x[0][2] = C[2 * cm + (int) E[j] - 1];\r
rxb = dimOfVec(xb);\r
rx = dimOfThird(rxa, rxb);\r
\r
- //kleinste Ecke finden und fuer \delta verwenden\r
-// getSCorner(dt, x);\r
-\r
if (xa[rxa] <= 0 || xb[rxb] <= 0)\r
- mexWarnMsgTxt("X Element hat Seitenlängen <=0!");\r
+ mexWarnMsgTxt("X Element hat Seitenlaengen <=0!");\r
\r
- if(rxa == rxb)\r
- mexWarnMsgTxt("X Laenge ist nur in einer Richtung");\r
-\r
-// if (!iseq(dt, x[0]))\r
-// mexWarnMsgTxt("x[0] ist nicht die kleinste Ecke");\r
+ if (rxa == rxb)\r
+ mexWarnMsgTxt("X Laenge ist nur in eine Richtung");\r
\r
for (k = 0; k <= j; ++k) {\r
\r
+ //Eckdaten zwischenspeichern\r
y[0][0] = C[(int) E[k] - 1];\r
y[0][1] = C[cm + (int) E[k] - 1];\r
y[0][2] = C[2 * cm + (int) E[k] - 1];\r
ryb = dimOfVec(yb);\r
ry = dimOfThird(rya, ryb);\r
\r
- //kleinste Ecke finden\r
-// getSCorner(d, y);\r
-\r
if (ya[rya] <= 0 || yb[ryb] <= 0)\r
- mexWarnMsgTxt("Y Element hat Seitenlängen <=0!");\r
+ mexWarnMsgTxt("Y Element hat Seitenlaengen <=0!");\r
\r
- if(rya == ryb)\r
+ if (rya == ryb)\r
mexWarnMsgTxt("Y Laenge ist nur in einer Richtung");\r
\r
-// if (!iseq(d, y[0]))\r
-// mexWarnMsgTxt("y[0] ist nicht die kleinste Ecke");\r
-\r
- //\delta berechnen\r
-// sub(d, dt);\r
-\r
+ //delta berechnen\r
sub(d, y[0], x[0]);\r
\r
-// if(j==1 && k==0){\r
-// mexPrintf("[%d %d](%f,%f)(%f,%f)+(%f,%f,%f)", j, k,\r
-// (xa[rxa]), (xb[rxb]), (ya[rya]),\r
-// (yb[ryb]), d[rxa], d[rxb], d[rx]);\r
-// mexPrintf("{%d,%d;%d,%d}\n",rxa,rxb,rya,rxb);\r
-// }\r
-\r
-#if DEBUG >= 5\r
-#pragma omp critical\r
- mexPrintf("[%d %d](%f,%f)(%f,%f)+(%f,%f,%f)\n", j, k,\r
- (xa[rxa]), (xb[rxb]), (ya[rya]),\r
- (yb[ryb]), d[rxa], d[rxb], d[rx]);\r
-#pragma omp end critical\r
-#endif\r
+ /*\r
+ * Matrix Eintrag berechnen\r
+ */\r
if (rx == ry) {\r
if (rxa == rya) {\r
tmp = ctypeP((xa[rxa]), (xb[rxb]), (ya[rxa]),\r
}\r
\r
}\r
-\r
+#ifdef PARALLEL\r
#pragma omp critical\r
+#endif\r
\r
A[(k * em) + j] = 1. / (4 * M_PI) * tmp;\r
if (k != j)\r
A[(j * em) + k] = 1. / (4 * M_PI) * tmp;\r
\r
+#ifdef PARALLEL\r
#pragma omp end critical\r
-\r
+#endif\r
}\r
}\r
}\r
}\r
-#ifdef PARALLEL\r
-}\r
-#endif\r
\r
return;\r
}\r
/***************************************************************************/\r
/* slpRectangle.cpp */\r
-/* Beschreibung */\r
+/* Implementiert alle Funktionen zum Berechnen der GalerkinMatrix */\r
/* */\r
/* */\r
/* */\r
/* Version: 1.0 (2012) */\r
/***************************************************************************/\r
\r
-//#include <iostream>\r
#include <math.h>\r
-//#include <cassert>\r
-#include <limits>\r
-//#include <cstdlib>\r
\r
#include <mex.h>\r
\r
#include "slpRectangle.hpp"\r
#include "gauss.hpp"\r
\r
-//#define quad 2 // Anzahl der Quadratur Auswertungstellen 2^quad\r
-//int quad = 2;\r
int GAUSS_size = GAUSS_SIZE[2];\r
gauss * GAUSS_nodes = GAUSS_NODES[2];\r
-//using namespace std;\r
\r
+/*\r
+ * setzt den Quadraturgrad, also 2^q Auswertungsstellen\r
+ */\r
int setQuad(int q) {\r
GAUSS_size = GAUSS_SIZE[q];\r
GAUSS_nodes = GAUSS_NODES[q];\r
return GAUSS_size;\r
}\r
\r
-int inline sign(double);\r
-//double arsinh(double);\r
-\r
-/* ============================== */\r
-\r
+/*\r
+ * gibt das signum von x zurueck\r
+ */\r
int inline sign(double x) {\r
return x > 0 ? 1 : (x < 0 ? -1 : 0);\r
}\r
+\r
/*\r
- double inline arsinh(double x) {\r
- return log(x + sqrt(x * x + 1));\r
- }\r
+ * gibt das Maximum der beiden Zahlen x,y zurueck\r
*/\r
-\r
double inline max(double x, double y) {\r
return x < y ? y : x;\r
}\r
\r
+/*\r
+ * gibt das minimum der beiden Zahlen x,y zurueck\r
+ */\r
double inline min(double x, double y) {\r
return x > y ? y : x;\r
}\r
}\r
}\r
\r
+/*\r
+ * kleinere Achse nach vorn\r
+ */\r
void inline switch_dim_par(double& b, double& d, double& t, double& v,\r
double& d1, double& d2) {\r
//\r
return dis1 * dis1;\r
}\r
\r
+/*\r
+ * Kernfunktion 1 /|x-y|\r
+ */\r
double inline f_par(double x1, double x2, double y1, double y2, double d1,\r
double d2, double d3) {\r
return 1.\r
(x1 - y1 - d1) * (x1 - y1 - d1)\r
+ (x2 - y2 - d2) * (x2 - y2 - d2) + d3 * d3);\r
}\r
-\r
+/*\r
+ * Kernfunktion 1 /|x-y|\r
+ */\r
double inline f_ort(double x1, double x2, double y2, double y3, double d1,\r
double d2, double d3) {\r
return 1.\r
+ (y3 + d3) * (y3 + d3));\r
}\r
\r
+/*\r
+ * 1 mal integrierte Kernfunktion int 1 /|x-y| dy (QUADRATUR)\r
+ */\r
double inline g_QY(double p, double y, double x, double l) {\r
-\r
double sol = 0;\r
-\r
for (int i = 0; i < GAUSS_size; ++i) {\r
sol += pow(\r
- (x - GAUSS_nodes[i].n * y)\r
- * (x - GAUSS_nodes[i].n * y) + l * l, p)\r
- * GAUSS_nodes[i].w * y;\r
+ (x - GAUSS_nodes[i].n * y) * (x - GAUSS_nodes[i].n * y) + l * l,\r
+ p) * GAUSS_nodes[i].w * y;\r
}\r
\r
return sol;\r
}\r
\r
-//y-x muss != 0 sein\r
+/*\r
+ * Stammfunktion g\r
+ * 1 mal integrierte Kernfunktion int 1 /|x-y| dy (ANALYTISCH)\r
+ */\r
double inline g_AY(double p, double y, double x, double l) {\r
- //printf("%.1f | %.1f | %.1f | %.1f +",p,x,y,l);\r
-\r
double sol = 0;\r
\r
if (l != 0) {\r
if (p == 0.5) {\r
sol = (y - x) / 2 * sqrt((y - x) * (y - x) + l * l)\r
+ l * l / 2 * asinh((y - x) / fabs(l));\r
- // printf("%.2f |",sol);\r
} else if (p == 0)\r
sol = y - x;\r
else if (p == -0.5)\r
return sol;\r
}\r
\r
+/*\r
+ * 2 mal integrierte Kernfunktion int int 1 /|x-y| dy_2 dy_1 (QUADRATUR)\r
+ */\r
double inline G_QY1Y2(double p, double y1, double y2, double x1, double x2,\r
double l) {\r
\r
for (int i = 0; i < GAUSS_size; ++i) {\r
for (int j = 0; j < GAUSS_size; ++j) {\r
sol += pow(\r
- (x1 - y1 * GAUSS_nodes[i].n)\r
- * (x1 - y1 * GAUSS_nodes[i].n)\r
+ (x1 - y1 * GAUSS_nodes[i].n) * (x1 - y1 * GAUSS_nodes[i].n)\r
+ (x2 - y2 * GAUSS_nodes[j].n)\r
- * (x2 - y2 * GAUSS_nodes[j].n)\r
- + l * l, p) * y1 * GAUSS_nodes[i].w * y2\r
- * GAUSS_nodes[j].w;\r
+ * (x2 - y2 * GAUSS_nodes[j].n) + l * l, p)\r
+ * y1 * GAUSS_nodes[i].w * y2 * GAUSS_nodes[j].w;\r
}\r
}\r
return sol;\r
}\r
\r
+/*\r
+ * 2 mal integrierte Kernfunktion int int 1 /|x-y| dy_2 dx_2 (ANALYTISCH)\r
+ */\r
double inline G_AY2X2(double y1, double y2, double x1, double x2, double d3) {\r
-\r
-// cout << "(" << y1 << "," << y2 << ")(" << x1 << "," << x2 << ")(" << d3 << ")" << endl;\r
-\r
double hlp = ((x1 - y1) * (x1 - y1) + (x2 - y2) * (x2 - y2) + d3 * d3);\r
-\r
double sol = sqrt(hlp);\r
\r
if ((x2 - y2) != 0)\r
- //sol -= (x2 - y2) * g_AY(-0.5,x2,y2, sqrt((x1 - y1) * (x1 - y1) + d3 * d3));\r
sol += (x2 - y2) * log(sqrt(hlp) - (x2 - y2));\r
\r
- if (sol\r
- != sol/* || fabs(sol) == std::numeric_limits<double>::infinity()*/) {\r
- // cout << "G_AY2X2: " << sol << " isn't a Number. (" << y1 << "," << y2\r
- // << ")(" << x1 << "," << x2 << ")(" << d3 << ")" << endl;\r
- // cout << (x2 - y2) << "__" << sqrt(hlp) << endl;\r
- // cout << (x1 - y1) * (x1 - y1) << " " << hlp << endl;\r
- // mexPrintf("G_AY2X2X: nan");\r
- }\r
return sol;\r
}\r
\r
+/*\r
+ * Stammfunktion G\r
+ * 2 mal integrierte Kernfunktion int int 1 /|x-y| dy_2 dy_1 (ANALYTISCH)\r
+ */\r
double inline G_AY1Y2(double p, double y1, double y2, double x1, double x2,\r
double l) {\r
- // printf("%.1f | %.1f %.1f | %.1f %.1f | %.1f +",p,x1,x2,y1,y2,l);\r
double pt = p + 1.5;\r
double sol = 0;\r
if (pt == 0) {\r
* ((y2 - x2) * (y2 - x2) + l * l))\r
+ 1);\r
}\r
-\r
} else if ((pt > 0) && ((int) pt == pt)) {\r
if (l != 0)\r
sol = 2 * p * l * l * G_AY1Y2(p - 1, y1, y2, x1, x2, l);\r
* g_AY(p, y1, x1, sqrt((y2 - x2) * (y2 - x2) + l * l));\r
sol /= 2 * p + 2;\r
} else {\r
+ //Fall wird nicht benoetigt\r
sol = NAN;\r
- // cout << "warning in G_AY1Y2: no case for p=" << p\r
- // << " defined. Possible: [-1.5,-0.5,0.5,...]" << endl;\r
+ mexWarnMsgTxt("G_AY1Y2 fuer Parameter nicht implementiert!");\r
}\r
\r
return sol;\r
}\r
\r
-double inline Gs_AX2Y1Y2(double p, double y1, double y2, double x1, double x2,\r
- double l) {\r
- double sol = 0;\r
- mexWarnMsgTxt("Gs_AX2Y1Y2 nicht implementiert!");\r
- return sol;\r
-}\r
-\r
+/*\r
+ * Stammfunktion F\r
+ * 4 mal integrierte Kernfunktion int int 1 /|x-y| dy dx (ANALYTISCH)\r
+ */\r
double inline F_par(double x1, double x2, double y1, double y2, double d1,\r
double d2, double d3) {\r
-\r
- // printf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f",x1,x2,y1,y2,d1,d2,d3);\r
double sol = (x1 - y1 - d1) * (x2 - y2 - d2);\r
\r
if (sol != 0)\r
return sol;\r
}\r
\r
+/*\r
+ * Stammfunktion F\r
+ * 4 mal integrierte Kernfunktion int int 1 /|x-y| dy dx (ANALYTISCH)\r
+ */\r
double inline F_ort(double x1, double x2, double y2, double y3, double d1,\r
double d2, double d3) {\r
-\r
-// mexPrintf("%.1f %.1f | %.1f %.1f | %.1f %.1f %.1f \n",x1,x2,y2,y3,d1,d2,d3);\r
double sol = -G_AY1Y2(0.5, y3, x1, -d3, d1, x2 - y2 - d2);\r
\r
if ((x1 - d1) * (x2 - y2 - d2) != 0)\r
return sol / 2.;\r
}\r
\r
+/*\r
+ * Stammfunktion (fuer Quadratur)\r
+ * 2 mal integrierte Kernfunktion int int 1 /|x-y| dy_2 dy_1 (ANALYTISCH)\r
+ */\r
double inline FY1Y2_par(double x1, double x2, double y1, double y2, double d1,\r
double d2, double d3) {\r
return G_AY1Y2(-0.5, y1, y2, x1 - d1, x2 - d2, d3);\r
}\r
\r
-//double inline FY2X2_par(double y1, double x1, double y2, double x2, double d1,\r
-// double d2, double d3) {\r
-// return G_AY2X2(y1 + d1, y2 + d2, x1, x2, d3);\r
-//}\r
-\r
+/*\r
+ * Stammfunktion (fuer Quadratur)\r
+ * 2 mal integrierte Kernfunktion int int 1 /|x-y| dy_2 dy_3 (ANALYTISCH)\r
+ */\r
double inline FY2Y3_ort(double x1, double x2, double y2, double y3, double d1,\r
double d2, double d3) {\r
- return G_AY1Y2(-0.5, y2 , y3 , x2-d2, -d3, x1-d1);\r
+ return G_AY1Y2(-0.5, y2, y3, x2 - d2, -d3, x1 - d1);\r
}\r
\r
/*\r
- * Quadratur über zwei Integrale und Grenzen in Stammfunktion über zwei Integrale\r
- * b,d - Grenzen für Quadratur\r
+ * Quadratur ueber zwei Integrale und Grenzen in Stammfunktion ueber zwei Integrale\r
+ * b,d - Grenzen fuer Quadratur\r
* t,v - Grenzen in Stammfunktion\r
*/\r
template<double (F)(double, double, double, double, double, double, double)>\r
}\r
\r
/*\r
- * Quadratur über vier Integrale\r
- * b,d,t,v - Grenzen für Quadratur\r
+ * Quadratur ueber vier Integrale\r
+ * b,d,t,v - Grenzen fuer Quadratur\r
*/\r
template<double (F)(double, double, double, double, double, double, double)>\r
double intQ4(double b, double d, double t, double v, double d1, double d2,\r
}\r
\r
/*\r
- * Grenzen in Stammfunktion über vier Integrale\r
- * b,d,t,v - Grenzen für Stammfunktion\r
+ * Grenzen in Stammfunktion ueber vier Integrale\r
+ * b,d,t,v - Grenzen fuer Stammfunktion\r
*/\r
template<double (F)(double, double, double, double, double, double, double)>\r
double inline intA4(double b, double d, double t, double v, double d1,\r
\r
}\r
\r
+/*\r
+ * fuer parallele Elemente\r
+ * voll Analytisch\r
+ */\r
double cParO1(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
-// if (d3 && fabs(d3)!=2)\r
-// mexPrintf("%f \n", d3);\r
return intA4<F_par>(b, d, t, v, d1, d2, d3);\r
}\r
-\r
+/*\r
+ * fuer orthogonale Elemente\r
+ * voll Analytisch\r
+ */\r
double cOrtO1(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
-// if (!d3)\r
-// mexPrintf("%f \n", d3);\r
return intA4<F_ort>(b, d, t, v, d1, d2, d3);\r
}\r
\r
+/*\r
+ * fuer parallele Elemente\r
+ * voll Analytisch\r
+ */\r
double cParO2(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
double tmp = 0;\r
//kurze Seite nach vorn\r
switch_site_par(b, d, t, v, d1, d2);\r
\r
- //kurze Achse nach vorn\r
-// switch_dim_par(b, d, t, v, d1, d2);\r
-\r
if (zeta[0] * zeta[0] * (t * t + v * v) < dist2_par(b, d, t, v, d1, d2, d3))\r
return intQ4<f_par>(b, d, t, v, d1, d2, d3);\r
\r
return intA4<F_par>(b, d, t, v, d1, d2, d3);\r
}\r
\r
+/*\r
+ * fuer orthogonale Elemente\r
+ * volle Quadratur fuer zeta_1 zulaessige Elemente\r
+ * analytisch sonst\r
+ */\r
double cOrtO2(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
double tmp = 0, dis2 = 0;\r
//kurze Seite nach vorn\r
switch_site_ort(b, d, t, v, d1, d2, d3);\r
\r
- //kurze Achse nach vorn\r
-// switch_dim_par(b, d, t, v, d1, d2);\r
-\r
if (zeta[0] * zeta[0] * (t * t + v * v) < dist2_ort(b, d, t, v, d1, d2, d3))\r
return intQ4<f_ort>(b, d, t, v, d1, d2, d3);\r
\r
return intA4<F_ort>(b, d, t, v, d1, d2, d3);\r
}\r
-\r
+/*\r
+ * fuer parallele Elemente\r
+ * volle Quadratur fuer zeta_1 zulaessige Elemente\r
+ * Quadratur ueber ein Element fuer zeta_2 zulaessige Elemente\r
+ * volle Quadratur fuer zeta_1 zulaessige Elemente\r
+ * analytisch sonst\r
+ */\r
double cParO3(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
\r
//kurze Seite nach vorn\r
switch_site_par(b, d, t, v, d1, d2);\r
\r
- //kurze Achse nach vorn\r
-// switch_dim_par(b, d, t, v, d1, d2);\r
-\r
if (zeta[1] * zeta[1] * (b * b + d * d) < dist2_par(b, d, t, v, d1, d2, d3))\r
return intQ2A2<FY1Y2_par>(b, d, t, v, d1, d2, d3);\r
\r
\r
return intA4<F_par>(b, d, t, v, d1, d2, d3);\r
}\r
-\r
+/*\r
+ * fuer orthogonale Elemente\r
+ * Quadratur ueber ein Element fuer zeta_2 zulaessige Elemente\r
+ * volle Quadratur fuer zeta_1 zulaessige Elemente\r
+ * analytisch sonst\r
+ */\r
double cOrtO3(double b, double d, double t, double v, double d1, double d2,\r
double d3, double* zeta) {\r
double tmp = 0, dis2 = 0;\r
//kurze Seite nach vorn\r
switch_site_ort(b, d, t, v, d1, d2, d3);\r
\r
- //kurze Achse nach vorn\r
-// switch_dim_par(b, d, t, v, d1, d2);\r
-\r
if (zeta[1] * zeta[1] * (b * b + d * d) < dist2_ort(b, d, t, v, d1, d2, d3))\r
return intQ2A2<FY2Y3_ort>(b, d, t, v, d1, d2, d3);\r
\r
return intA4<F_ort>(b, d, t, v, d1, d2, d3);\r
}\r
\r
-double cParO4(double b, double d, double t, double v, double d1, double d2,\r
- double d3, double* zeta) {\r
-\r
- double tmp = 0;\r
-\r
- //kurze Seite nach vorn\r
- switch_site_par(b, d, t, v, d1, d2);\r
-\r
- //kurze Achse nach vorn\r
- switch_dim_par(b, d, t, v, d1, d2);\r
-\r
- if ((t * t + v * v) < zeta[0] * dist2_par(b, d, t, v, d1, d2, d3))\r
- return intQ4<f_par>(b, d, t, v, d1, d2, d3);\r
-\r
-// if ((b * b + d * d) < zeta[0] * dist2_par(b, d, t, v, d1, d2, d3))\r
-// return calcParIntQX1X2(b, d, t, v, d1, d2, d3);\r
-\r
- return intA4<F_par>(b, d, t, v, d1, d2, d3);\r
-}\r
/***************************************************************************/
/* slpRectangle.hpp */
-/* Beschreibung... */
+/* Implementiert alle Funktionen zur Berechnung der Galerkin Matrix */
/* */
/* */
/* */
#ifndef HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_
#define HILBERT3D_LAPLACE_SLPRECTANGLE_HPP_GUARD_
-//namespace slpR {
-
-// sol = g0(p,y,x,l);
-// double g_AY(double, double, double, double);
-// sol = g0(p,y,x,l);
-// double g_QY(double, double, double, double);
-
-// sol = G00(p,y1,y2,x1,x2,l);
-// double G_AY1Y2(double, double, double, double, double, double);
-// sol = G00(p,y1,y2,x1,x2,l);
-// double G_AY2X2(double, double, double, double, double);
-// sol = G00(p,y1,y2,x1,x2,l);
-// double G_QY1Y2(double, double, double, double, double, double);
-// double Gs_AX2Y1Y2(double, double, double, double, double, double);
-
-// sol = F_par(x1,x2,y1,y2,d1,d2,d3);
-// double F_par(double, double, double, double, double, double, double);
-// sol = F_ort(x1,x2,y2,y3,d1,d2,d3);
-// double F_ort(double, double, double, double, double, double, double);
-
-// sol = quad0Int4((F_par/F_ort),b,d,t,v,d1,d2,d3);
-// double apply0Int4(
-//double(*)(double, double, double, double, double, double, double),
-//double, double, double, double, double, double, double);
-// double apply0Int2(
-//double(*)(double, double, double, double, double, double, double),
-//double, double, double, double, double, double, double);
-
-// sol = calcParInt.(b,d,t,v,d1,d2,d3);
-//double calcParIntA(double, double, double, double, double, double, double);
-//double calcParIntQX1X2(double, double, double, double, double, double, double);
-//double calcParIntQY1X1(double, double, double, double, double, double, double);
-//double calcParIntQY1(double, double, double, double, double, double, double);
-//double calcParIntQ(double, double, double, double, double, double, double);
-
-// sol = calcOrtInt.(b,d,t,v,d1,d2,d3);
-//double calcOrtIntA(double, double, double, double, double, double, double);
-//double calcOrtIntQX1X2(double, double, double, double, double, double, double);
-
-//Voll Analytisch
+/*
+ * voll Analytisch rechnen
+ */
double cParO1(double, double, double, double, double, double, double, double*);
double cOrtO1(double, double, double, double, double, double, double, double*);
-//A oder Q
+
+/*
+ * volle Quadratur fuer zeta_1 zulaessige Elemente
+ * analytisch sonst
+ */
double cParO2(double, double, double, double, double, double, double, double*);
double cOrtO2(double, double, double, double, double, double, double, double*);
-//A oder Q oder Qy1x2
+
+/*
+ * Quadratur ueber ein Element fuer zeta_2 zulaessige Elemente
+ * volle Quadratur fuer zeta_1 zulaessige Elemente
+ * analytisch sonst
+ */
double cParO3(double, double, double, double, double, double, double, double*);
double cOrtO3(double, double, double, double, double, double, double, double*);
-// A oder Q oder Qx1x2
-double cParO4(double, double, double, double, double, double, double, double*);
+/*
+ * setzt die 2^Anzahl der Auswertungsstellen
+ */
int setQuad(int);
-//}
#endif
projects / bacc.git / commitdiff