From 5bafb382f94c06198c2688113254f55218318c6c Mon Sep 17 00:00:00 2001 From: Peter Schaefer Date: Fri, 31 Aug 2012 21:09:17 +0200 Subject: [PATCH] [doc] pinsel pinsel --- doc/doc.pdf | Bin 191957 -> 191940 bytes doc/doc.tex | 25 +++++++++++++---------- doc/fig/exmpl11_ref.eps | 4 ++-- doc/fig/exmpl11_ref.pdf | Bin 5579 -> 5580 bytes doc/fig/exmpl12_ele.tex | 10 +++++----- doc/fig/exmpl12_f2s.tex | 6 +++--- doc/fig/exmpl12_nei.tex | 18 ++++++++--------- doc/fig/exmpl12_ref.eps | 18 ++++++++--------- doc/fig/exmpl12_ref.pdf | Bin 5745 -> 5737 bytes doc/fig/exmpl13_ele.tex | 16 +++++++-------- doc/fig/exmpl13_f2s.tex | 6 +++--- doc/fig/exmpl13_nei.tex | 26 ++++++++++++------------ doc/fig/exmpl13_ref.eps | 28 +++++++++++++------------- doc/fig/exmpl13_ref.pdf | Bin 5880 -> 5872 bytes doc/fig/net1.eps | 12 +++++------ doc/fig/net1.pdf | 42 +++++++++++++++++++-------------------- doc/fig/net_wrong.eps | 4 ++-- doc/fig/net_wrong.pdf | Bin 2861 -> 2862 bytes doc/fig/refType_1.eps | 4 ++-- doc/fig/refType_1.pdf | Bin 3814 -> 3815 bytes doc/fig/refType_2.eps | 4 ++-- doc/fig/refType_2.pdf | Bin 4220 -> 4221 bytes doc/fig/refType_3.eps | 4 ++-- doc/fig/refType_3.pdf | Bin 3960 -> 3962 bytes doc/fig/refType_4.eps | 4 ++-- doc/fig/refType_4.pdf | Bin 3955 -> 3956 bytes doc/fig/refType_full.eps | 4 ++-- doc/fig/refType_full.pdf | Bin 3705 -> 3707 bytes src/exmpl11.mat | Bin 375 -> 375 bytes src/exmpl12.mat | Bin 456 -> 456 bytes src/exmpl13.mat | Bin 505 -> 505 bytes src/export_exmpl.m | 2 +- src/plotShape.m | 4 ++-- 33 files changed, 121 insertions(+), 120 deletions(-) diff --git a/doc/doc.pdf b/doc/doc.pdf index bb49f21e50ca2b703ba5b81511d9af2816f7c507..fd5ea825f7bc17e0199b7b74932a3915390ec785 100644 GIT binary patch delta 76264 zcmV(uKR06=L3;*bl%E zeiw}<0(4M8ptm;3U>EcY85$23xM?PAooTGj!9miJt7u3zPhtul?(&5uQTJJt8mg*i zc+>l_eiYa%m5gYiEcqk)t;DygJ4M61^QK>fsJv+~Y^SEK*DshH3r7=`h%o?67mVAx zrK)bX{ys!L)@?Itlt@z1>8f#wqSYe?QPI0qy 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zJlZ2n$MQr1am^*I4l$ez3+#Kv;+o@uBAzrwb%Ja$=Cr*;nj>eKaEUxPBtF5kl?1c9 zWm`RPcu?#|yP2A5ckj_dRTH!xYL`y`7vp*U^{A|I!^V!AI5ss6UmP*+2C$+4 diff --git a/doc/doc.tex b/doc/doc.tex index 3320d81..7d6876c 100644 --- a/doc/doc.tex +++ b/doc/doc.tex @@ -17,9 +17,12 @@ \usepackage[utf8]{inputenc} %Eingabekodierung \usepackage{fixltx2e} %Deutschsprach Bugs -\definecolor{gray}{gray}{.95} +\definecolor{gray}{gray}{.8} +\definecolor{dred}{rgb}{.8,0,0} +\definecolor{dgreen}{rgb}{0,.8,.4} +\definecolor{dblue}{rgb}{0,.4,.4} -\def\todo#1{\textcolor{red}{#1}} +\def\todo#1{\textcolor{dred}{#1}} \def\why#1{\textcolor{blue}{#1}} \def\Matlab{{\sc Matlab}} \def\q{\Q} @@ -344,10 +347,10 @@ Dann gilt auf isotropen Netzen: \section{Analytische Berechnung der Integrale} Es seien $T_j,T_k \subseteq\R^3$ zwei beschränkte, achsenorientierte Rechtecke in $\R^3$. Die Berechnung der Matrix für das Galerkin-Verfahren benötigt die Auswertung von -\begin{eqnarray*} +\begin{eqnarray}\label{math:V} \frac{1}{4\pi} \int_{T_j} \int_{T_k} \frac{1}{|\bs x- \bs y|} ds_{\bs y} ds_{\bs x} \in \R^3. -\end{eqnarray*} -Wir betrachten zunächst die Berechnung von zwei Integralen, die im Zuge der Berechnungen auftreten werden. +\end{eqnarray} +Wir betrachten zunächst die Berechnung von zwei Integralen, die dabei auftreten werden. \subsection{einfach Integral} Wir bezeichnen \begin{eqnarray*} @@ -387,7 +390,7 @@ Für alle weiteren relevante Fälle $p = -3/2 +k : k \in \N\backslash0$ lässt s \end{align*} \subsection{Integral über zwei Elemente} -Bei der Integration über zwei Seitenelemente \Ta, \Tb $\in \T_{\ell}$ haben wir geometrisch zischen zwei Fällen unterschieden. Entweder die beiden Elemente liegen in parallelen Ebenen oder in orthogonalen Ebenen. +Bei der Berechnung von \ref{math:V} haben wir geometrisch zwischen zwei Fällen zu unterschei den. Entweder die beiden Elemente liegen in parallelen Ebenen oder in orthogonalen Ebenen. \subsubsection{Parallele Elemente} Liegen die beiden Elemente parallel zueinander lassen sie sich Folgendermaßen darstellen: @@ -572,15 +575,15 @@ so so oder so... \subsection{Datenstruktur} Für die Implementierung in \Matlab~und C++ wollen wollen wir eine einheitliche Datenstruktur einführen. -Die für die Partition $\mathcal{T}_{\ell} = \{T_1\ldots T_M\}$ benötigen Knoten $\mathcal{K}_{\ell} = \{C_1\ldots C_N\}$ stellen wir in einer $ N \times 3$ Matrix dar. Dabei enthält die $j$-te Zeile die Koordinaten des Knoten $C_j$ im $\R^3$. +Die für die Partition $\mathcal{T}_{\ell} = \{T_1\ldots T_N\}$ benötigten Knoten $\mathcal{K}_{\ell} = \{C_1\ldots C_M\}$ stellen wir in einer $M \times 3$ Matrix $COO$ dar. Dabei enthält die $j$-te Zeile die Koordinaten des Knoten $C_j$, d.h. : \begin{displaymath} - COO[j,1:3] = C_j := (x_j,y_j,z_j)^{T} \text{ wobei } x,y,z \in \R + COO[j,1:3] = C_j := (x_j,y_j,z_j)^{T} \text{ wobei } x_j,y_j,z_j \in \R. \end{displaymath} -Die Elemente $\mathcal{E}_{\ell}$ werden wir ebenfalls Zeilenweise in einer $M \times 4$ Matrix abspeichern. Dabei soll die $i$-te Zeile den Indizes der Knoten $\{C_j,C_k,C_{\ell},C_m\}$ des Elements $T_j$ entsprechen. +Die Elemente $\mathcal{T}_{\ell}$ werden wir ebenfalls Zeilenweise in einer $N \times 4$ Matrix $ELE$ abspeichern. Dabei soll die $i$-te Zeile den Indizes der Knoten $\{C_j,C_k,C_{\ell},C_m\}$ des Elements $T_i$ entsprechen, also: \begin{displaymath} - ELE[i,1:4] = T_i := (j,k,l,m) + ELE[i,1:4] = T_i := (j,k,l,m). \end{displaymath} -Die Knoten wollen wir gegen den Uhrzeigersinn anordnen und der Knoten $C_j$ soll der kleinste bezüglich der Koordinaten sein. +Die Knoten wollen wir gegen den Uhrzeigersinn anordnen \todo{und der Knoten $C_j$ soll der kleinste bezüglich der Koordinaten sein}. \noindent Für die bessere Handhabung der Elemente beim Verfeinern der Partition, wollen wir auch die Nachbarschaftsrelationen geeignet abspeichern. Dazu überlegen wir uns, dass wir Aufgrund der Netzstabilität maximal zwei Nachbarn pro Kante eines Elements zulassen wollen. diff --git a/doc/fig/exmpl11_ref.eps b/doc/fig/exmpl11_ref.eps index c99aa3a..7e714e2 100644 --- a/doc/fig/exmpl11_ref.eps +++ b/doc/fig/exmpl11_ref.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The MathWorks, Inc. Version 7.14.0.739 (R2012a). 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