[src] gauss erklärung

[src] slpR neuen Fall angefangen

diff --git a/doc/doc.pdf b/doc/doc.pdf
index dcddbc097f231b6b96c34e088d150a8f92003583..78e4134c5240d16661c4b465ee6cbf806909f277 100644 (file)
Binary files a/doc/doc.pdf and b/doc/doc.pdf differ

diff --git a/doc/doc.tex b/doc/doc.tex
index 0f628ee8615f20a767c1687c564595f43547511e..7d8b984dafcd1ac6a1e03871aee8d0db046ee77c 100644 (file)
--- a/doc/doc.tex
+++ b/doc/doc.tex
@@ -88,7 +88,7 @@ In dieser Arbeit beschäftigen wir uns mit der Randelementmethode für die homog
  - \varDelta u  &= 0 &\text{ in } \Omega& \subset \R^3,\\
  u &=  f &\text{ auf } \Gamma&:=\partial\Omega,
 \end{align}
-wobei $\varDelta u := \partial_x^2u+\partial_y^2u$ den Laplace-Operator bezeichnet und $\Omega \subset \R^3$ sei eine beschränkte Teilmenge von $\R^3$ mit Dirichlet-Rand $\Gamma := \partial \Omega$.\\
+wobei $\varDelta u := \partial_x^2u+\partial_y^2u$ den Laplace-Operator bezeichnet und $\Omega \subset \R^3$ eine beschränkte Teilmenge von $\R^3$ mit Lipschitz-Rand $\Gamma := \partial \Omega$ ist.\\
 
 \noindent
 Wir wissen, dass die Laplace-Gleichung erfüllt wird durch:
@@ -198,11 +198,11 @@ Damit ist $\phi_{\ell}$ die Galerkinapproximation an $\phi$
 %  \phi_{\ell/2} &= D \cdot y\\
 % \end{align}
 
-\subsection{Netz}
+\subsection{Netze}
 Für die Diskretisierung des Problems wollen wir nun einige Begriffe definieren.
 
-\begin{defi}
- Sei $T \subseteq \R^3$ ein achsenorientiertes Rechteck, wenn sich aus dem Eckpunkt $C \in \R^3$, alle weiteren Knoten schreiben lassen als $\{ C + a\cdot A, C + a \cdot A + b \cdot B , C + b \cdot B\}$, wobei Vektoren $A,B \in \{(1,0,0)^T,(0,1,0)^T,(0,0,1)^T\}$. und Skalare $a,b\neq0$ sind und der Flächeninhalt $|T| > 0$. \todo{Kanten/Seiten definieren? Anmerken, dass ein Kante als Vektor nur eine dim $\neq 0$?}\\Weiterhin sei
+\begin{defi}[Partition]
+ Wir nennen $T \subseteq \R^3$ ein achsenorientiertes Rechteck, wenn sich aus einem Eckpunkt $C \in \R^3$, alle weiteren Knoten schreiben lassen als $\{ C + a\cdot A, C + a \cdot A + b \cdot B , C + b \cdot B\}$, wobei Vektoren $A,B \in \{(1,0,0)^T,(0,1,0)^T,(0,0,1)^T\}$. und Skalare $a,b\neq0$ sind und der Flächeninhalt $|T| > 0$. \todo{Kanten/Seiten definieren? Anmerken, dass ein Kante als Vektor nur eine dim $\neq 0$?}\\Weiterhin sei
  \begin{align}
   C_T &:= \{ c_i:1\leq i \leq 4\}
  \end{align}
@@ -210,11 +210,11 @@ die Menge der Eckpunkte des Rechtecks.
 \end{defi}
 
 \begin{defi}
- Sei $\T_{\ell} = \{T_1,T_2,\dots,T_N\}$ eine \todo{Triangulierung ($\to$ Dreiecke?)} von $\Gamma$. Dann gilt:
+ Wir nennen $\T_{\ell} = \{T_1,T_2,\dots,T_N\}$ eine Partition von $\Gamma$ falls:
 \begin{itemize}
  \item $\overline{\Gamma} = \bigcup_{j=1}^NT_j$
- \item $\forall T_j \in T_{\ell}$ abgeschlossen und nicht null $\abs{T_j}>0$
- \item $\abs{T_j \cap T_k} = 0$ mit $T_j,T_k\in\T_{\ell}$ und $T_j\neq T_k$
+ \item alle Elemente aus $T_{\ell}$ abgeschlossene achsenorientierte Rechtecke
+ \item $\abs{T_j \cap T_k}$ ist entweder ein Knoten, eine Seite oder keines von beiden mit $T_j,T_k\in\T_{\ell}$ und $T_j\neq T_k$
 \end{itemize}
 \end{defi}
 Den Begriff der Triangulierung wollen wir hier noch stärker definieren, da wir pro Seite eines Rechtecks nur einen hängenden Knoten zulassen wollen.
@@ -231,6 +231,9 @@ anliegen können. Weiterhin wollen wir auch verlangen, dass der auf der Kante li
 \todo{+Bild}
 
 \subsubsection{Verfeinern}
+\begin{defi}[Lokale Verfeinerung]
+\end{defi}
+
 \begin{defi}
  Sei $\T_{\ell/2}$ die aus der Verfeinerung von $\T_{\ell}$ resultierende gültige Triangulierung.
 \end{defi}

diff --git a/src/exmplAA_2DQuad_cond.eps b/src/exmplAA_2DQuad_cond.eps
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diff --git a/src/exmplAA_2DQuad_error.eps b/src/exmplAA_2DQuad_error.eps
deleted file mode 100644 (file)
index 4e4a50f..0000000
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diff --git a/src/exmplAA_2DQuad_hminmax.eps b/src/exmplAA_2DQuad_hminmax.eps
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-  25   25 3292 1448 FO
-  25   25 3386 1743 FO
-  25   25 3455 1743 FO
-  25   25 3518 1743 FO
-  25   25 3601 2037 FO
-  25   25 3662 2037 FO
-  25   25 3743 2332 FO
-gr
-
-gs 624 269 3721 2938 MR c np
-/c10 { 1.000000 0.000000 0.000000 sr} bdef
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-81 295 61 294 83 0 63 295 69 0 94 294 68 295 120 0 
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-
-c10
-gs 1319 219 2476 2754 MR c np
-  25   25 1370  270 FO
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-  25   25 3601 2332 FO
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-
-0 sg
-%%IncludeResource: font Helvetica
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-2279  205 mt 
-(hmin hmax) s
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- 612 3237 mt 
-( ) s
-4333  299 mt 
-( ) s
-1 sg
-0 333 1398 0 0 -333 665 3166 4 MP
-PP
--1398 0 0 333 1398 0 0 -333 665 3166 5 MP stroke
-2.77778 w
-DO
-SO
-4.16667 w
-0 sg
- 665 3166 mt 2063 3166 L
- 665 3166 mt  665 2833 L
-1009 2928 mt 
-(min hmin/max hmax tsAA A) s
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-
-gr
-
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-0 sg
-1009 3030 mt 
-(min hmax/max hmax tsAA A) s
-gs 665 2833 1399 334 MR c np
-c9
-264 0 717 2999 2 MP stroke
-gs 798 2948 103 103 MR c np
-  25   25  849 2999 FO
-gr
-
-gr
-
-c9
-0 sg
-1009 3132 mt 
-(min hmin/hmax tsAA A) s
-gs 665 2833 1399 334 MR c np
-c10
-264 0 717 3101 2 MP stroke
-gs 798 3050 103 103 MR c np
-  25   25  849 3101 FO
-gr
-
-gr
-
-c10
-
-end %%Color Dict
-
-eplot
-%%EndObject
-
-epage
-end
-
-showpage
-
-%%Trailer
-%%EOF

diff --git a/src/exmplAA_2DQuad_norm.eps b/src/exmplAA_2DQuad_norm.eps
deleted file mode 100644 (file)
index 270a51a..0000000
--- a/src/exmplAA_2DQuad_norm.eps
+++ /dev/null
@@ -1,562 +0,0 @@
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-c0
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- 624 3206 mt 4344 3206 L
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- 563 3332 mt 
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- 655 3281 mt 
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- 997 3206 mt  997 3187 L
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-3135 3281 mt 
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-4283 3332 mt 
-(10) s
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-
-4375 3281 mt 
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- 400 2938 mt 
-(10) s
-%%IncludeResource: font Helvetica
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-
- 492 2887 mt 
-(0.63) s
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- 400 2197 mt 
-(10) s
-%%IncludeResource: font Helvetica
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- 492 2146 mt 
-(0.64) s
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- 400 1456 mt 
-(10) s
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-
- 492 1405 mt 
-(0.65) s
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- 624 3206 mt  624 3206 L
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- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
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- 624  685 mt  661  685 L
-4344  685 mt 4306  685 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 400  715 mt 
-(10) s
-%%IncludeResource: font Helvetica
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- 492  664 mt 
-(0.66) s
- 624 3206 mt  624 3206 L
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- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt  624 3206 L
- 624 3206 mt 4344 3206 L
- 624  270 mt 4344  270 L
- 624 3206 mt  624  270 L
-4344 3206 mt 4344  270 L
-gs 624 270 3721 2937 MR c np
-/c8 { 0.000000 0.000000 1.000000 sr} bdef
-c8
-81 -6 61 -8 83 -11 63 -15 69 -21 94 -31 68 -43 120 -55 
-94 -92 138 -174 164 -207 253 -338 338 -495 747 -1280 1370 3206 15 MP stroke
-gr
-
-c8
-gs 1319 379 2476 2879 MR c np
-  25   25 1370 3206 FO
-  25   25 2117 1926 FO
-  25   25 2455 1431 FO
-  25   25 2708 1093 FO
-  25   25 2872  886 FO
-  25   25 3010  712 FO
-  25   25 3104  620 FO
-  25   25 3224  565 FO
-  25   25 3292  522 FO
-  25   25 3386  491 FO
-  25   25 3455  470 FO
-  25   25 3518  455 FO
-  25   25 3601  444 FO
-  25   25 3662  436 FO
-  25   25 3743  430 FO
-gr
-
-gs 624 270 3721 2937 MR c np
-DD
-/c9 { 1.000000 0.000000 0.000000 sr} bdef
-c9
-81 0 61 0 83 0 63 0 69 0 94 0 68 0 120 0 
-94 0 138 0 164 0 253 0 338 0 747 0 1370 416 15 MP stroke
-gr
-
-c9
-DD
-0 sg
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-2225  206 mt 
-(Energie Norm) s
-2307 3432 mt 
-(Elemente) s
- 343 1882 mt  -90 rotate
-(eNorm) s
-90 rotate
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 66.6667 FMSR
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- 302 1630 mt  -90 rotate
-(2) s
-90 rotate
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 612 3237 mt 
-( ) s
-4333  300 mt 
-( ) s
-SO
-1 sg
-0 232 764 0 0 -232 3539 3166 4 MP
-PP
--764 0 0 232 764 0 0 -232 3539 3166 5 MP stroke
-2.77778 w
-DO
-SO
-4.16667 w
-0 sg
-3539 3166 mt 4303 3166 L
-3539 2934 mt 4303 2934 L
-3539 3166 mt 3539 2934 L
-4303 3166 mt 4303 2934 L
-3539 3166 mt 4303 3166 L
-3539 3166 mt 3539 2934 L
-3539 3166 mt 4303 3166 L
-3539 2934 mt 4303 2934 L
-3539 3166 mt 3539 2934 L
-4303 3166 mt 4303 2934 L
-3834 3029 mt 
-(tsAA A) s
-gs 3539 2934 765 233 MR c np
-c8
-226 0 3584 2999 2 MP stroke
-gs 3646 2948 103 103 MR c np
-  25   25 3697 2999 FO
-gr
-
-gr
-
-c8
-0 sg
-3834 3132 mt 
-(extrapoliert) s
-gs 3539 2934 765 233 MR c np
-DD
-c9
-226 0 3584 3100 2 MP stroke
-SO
-gr
-
-c9
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diff --git a/src/export_gauss.m b/src/export_gauss.m
index 97ad50f9e863878c95a506038ef6aa8d2c7e91e0..39334168c33e9355473565a8f3106ff0998961fa 100644 (file)
--- a/src/export_gauss.m
+++ b/src/export_gauss.m
@@ -17,7 +17,7 @@ str = ['#ifndef GAUSS_NODES' char(10) ...
 ' * > for(int i=0;i<gauss_size[3];++i)' char(10) ...
 ' * >    sol += sin(gauss_nodes[3][i].n) * gauss_nodes[3][i].w;' char(10) ...
 ' *' char(10) ...
-' * Peter Schaefer (Automatisch generiert durch export_gaus() )' char(10) ...
+' * Peter Schaefer (Automatisch generiert durch export_gaus.m )' char(10) ...
 ' */' char(10)  char(10) ...
 'typedef struct _gauss{' char(10) ...
 '      double n;' char(10) ...
@@ -46,4 +46,4 @@ str = [str str1 char(10) str2 char(10) '#endif' char(10)];
 fid = fopen(file,'w');
 fprintf(fid,'%s',str);
 fclose(fid);
-end
\ No newline at end of file
+end

diff --git a/src/gauss.hpp b/src/gauss.hpp
index 33b4f84822f268b0a2969021fe712d3317fa7fcf..93e62eec2cfe53212dce083f5f0ba8f33cc20458 100644 (file)
--- a/src/gauss.hpp
+++ b/src/gauss.hpp
@@ -15,7 +15,7 @@
  * > for(int i=0;i<gauss_size[3];++i)
  * >    sol += sin(gauss_nodes[3][i].n) * gauss_nodes[3][i].w;
  *
- * Peter Schaefer (Automatisch generiert durch export_gaus() )
+ * Peter Schaefer (Automatisch generiert durch export_gaus.m )
  */
 
 typedef struct _gauss{

diff --git a/src/slpRectangle.cpp b/src/slpRectangle.cpp
index 96543d06fe46e7bc090876279511f69ec946b996..ba053183c13ec5192105fc37827cbb2e3656137b 100644 (file)
--- a/src/slpRectangle.cpp
+++ b/src/slpRectangle.cpp
@@ -563,6 +563,9 @@ double cParO4(double b, double d, double t, double v, double d1, double d2,
        //kurze Seite nach vorn\r
        switch_site(b, d, t, v, d1, d2);\r
 \r
+       //kurze Achse nach vorn\r
+       switch_dim(b, d, t, v, d1, d2);\r
+\r
        if ((t * t + v * v) < zeta[0] * dist2(b, d, t, v, d1, d2, d3))\r
                return calcParIntQ(b, d, t, v, d1, d2, d3);\r
 \r