[cig-commits] r7021 - cs/cigma/trunk/doc/manual

[sue at geodynamics.org]

Author: sue
Date: 2007-05-31 14:27:36 -0700 (Thu, 31 May 2007)
New Revision: 7021

Added:
   cs/cigma/trunk/doc/manual/cigma-a2h-cube-with-little-cube.psd
   cs/cigma/trunk/doc/manual/cigma-a2h-cube.jpg
Modified:
   cs/cigma/trunk/doc/manual/cigma.lyx
Log:
edits to equations and another figure

Added: cs/cigma/trunk/doc/manual/cigma-a2h-cube-with-little-cube.psd
===================================================================
(Binary files differ)


Property changes on: cs/cigma/trunk/doc/manual/cigma-a2h-cube-with-little-cube.psd
___________________________________________________________________
Name: svn:mime-type
   + application/octet-stream

Added: cs/cigma/trunk/doc/manual/cigma-a2h-cube.jpg
===================================================================
(Binary files differ)


Property changes on: cs/cigma/trunk/doc/manual/cigma-a2h-cube.jpg
___________________________________________________________________
Name: svn:mime-type
   + application/octet-stream

Modified: cs/cigma/trunk/doc/manual/cigma.lyx
===================================================================
--- cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-31 19:55:12 UTC (rev 7020)
+++ cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-31 21:27:36 UTC (rev 7021)
@@ -308,13 +308,39 @@
 \end_layout
 
 \begin_layout Standard
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Caption
+deal.II
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+	filename cigma-a2h-cube.jpg
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 \begin_inset Formula \[
 \begin{array}{ccccc}
+ &  &  & \phi\\
 (-1, & -1, & -1) & \mapsto & a\\
 (+1, & -1, & -1) & \mapsto & b\\
 (-1, & +1, & -1) & \mapsto & c\\
 (+1, & +1, & -1) & \mapsto & d\end{array}\,\,\,\begin{array}{ccccc}
-(-1, & -1, & +1) & \mapsto & e\\
+\\(-1, & -1, & +1) & \mapsto & e\\
 (+1, & -1, & +1) & \mapsto & f\\
 (-1, & +1, & +1) & \mapsto & g\\
 (+1, & +1, & +1) & \mapsto & h\end{array}\]
@@ -654,7 +680,7 @@
 
 \begin_layout LyX-Code
 \begin_inset Formula \[
-\left[q\times3\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[q\times8\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[8\times3\right]\]
+\left(\left[q\times3\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[q\times8\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[8\times3\right]\right)\]
 
 \end_inset
 
@@ -678,7 +704,7 @@
 \begin_layout Standard
 \begin_inset Graphics
 	filename cigma-abcd-triangle.jpg
-	lyxscale 25
+	lyxscale 50
 	scale 25
 
 \end_inset
@@ -697,7 +723,7 @@
 (-1, & -1, & -1) & \mapsto & a\\
 (+1, & -1, & -1) & \mapsto & b\\
 (-1, & +1, & -1) & \mapsto & c\\
-(+1, & +1, & -1) & \mapsto & d\end{array}$
+(-1, & -1, & +1) & \mapsto & d\end{array}$
 \end_inset
 
 
@@ -735,11 +761,11 @@
 1 & (-1) & (-1) & (-1)\\
 1 & (+1) & (-1) & (-1)\\
 1 & (-1) & (+1) & (-1)\\
-1 & (-1) & (-1) & (-1)\end{array}\right]\left[\begin{array}{c}
+1 & (-1) & (-1) & (+1)\end{array}\right]\left[\begin{array}{c}
 \alpha_{0}\\
 \alpha_{1}\\
 \alpha_{2}\\
-\alpha_{3}\end{array}\right]\left[\begin{array}{c}
+\alpha_{3}\end{array}\right]=\left[\begin{array}{c}
 x_{0}\\
 x_{1}\\
 x_{2}\\
@@ -794,13 +820,13 @@
 \begin{array}{cc}
 x\left(\vec{\xi}\right) & =\alpha_{0}+\alpha_{1}\xi+\alpha_{2}\eta+\alpha_{3}\zeta\\
  & =\left[\frac{1}{2}\left(-x_{0}+x_{1}+x_{2}+x_{3}\right)\right]\\
- & +\left[\frac{1}{2}\left(-x_{0}+x_{1}\right)\right]\xi\\
- & +\left[\frac{1}{2}\left(-x_{0}+x_{2}\right)\right]\eta\\
- & +\left[\frac{1}{2}\left(-x_{0}+x_{3}\right)\right]\zeta\\
+ & +\left[\frac{1}{2}\left(-x_{0}+x_{1}\,\,\,\,\,\,\,\,\,\,\right)\right]\xi\\
+ & +\left[\frac{1}{2}\left(-x_{0}\,\,\,\,\,+x_{2}\,\,\,\,\,\right)\right]\eta\\
+ & +\left[\frac{1}{2}\left(-x_{0}\,\,\,\,\,\,\,\,\,\,+x_{3}\right)\right]\zeta\\
 \\ & =\left[\frac{1}{2}\left(-1-\xi-\eta-\zeta\right)\right]\times0\\
- & +\left[\frac{1}{2}\left(1+\xi\right)\right]\times1\\
- & +\left[\frac{1}{2}\left(1+\eta\right)\right]\times2\\
- & +\left[\frac{1}{2}\left(1+\zeta\right)\right]\times3\\
+ & +\left[\frac{1}{2}\left(1+\xi\,\,\,\,\,\,\,\,\,\,\right)\right]\times1\\
+ & +\left[\frac{1}{2}\left(1\,\,\,\,\,+\eta\,\,\,\,\,\right)\right]\times2\\
+ & +\left[\frac{1}{2}\left(1\,\,\,\,\,\,\,\,\,\,+\zeta\right)\right]\times3\\
 \\\end{array}\]
 
 \end_inset
@@ -815,9 +841,9 @@
 \begin_layout Standard
 \begin_inset Formula \[
 \begin{array}{c}
-x\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)\cdot x_{0}+N_{1}\left(\vec{\xi}\right)\cdot x_{1}+N_{2}\left(\vec{\xi}\right)\cdot x_{2}+N_{3}\left(\vec{\xi}\right)\cdot x_{3}\\
-y\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)\cdot y_{0}+N_{1}\left(\vec{\xi}\right)\cdot y_{1}+N_{2}\left(\vec{\xi}\right)\cdot y_{2}+N_{3}\left(\vec{\xi}\right)\cdot y_{3}\\
-z\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)\cdot z_{0}+N_{1}\left(\vec{\xi}\right)\cdot z_{1}+N_{2}\left(\vec{\xi}\right)\cdot z_{2}+N_{3}\left(\vec{\xi}\right)\cdot z_{3}\\
+x\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)x_{0}+N_{1}\left(\vec{\xi}\right)x_{1}+N_{2}\left(\vec{\xi}\right)x_{2}+N_{3}\left(\vec{\xi}\right)x_{3}\\
+y\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)y_{0}+N_{1}\left(\vec{\xi}\right)y_{1}+N_{2}\left(\vec{\xi}\right)y_{2}+N_{3}\left(\vec{\xi}\right)y_{3}\\
+z\left(\vec{\xi}\right)=N_{0}\left(\vec{\xi}\right)z_{0}+N_{1}\left(\vec{\xi}\right)z_{1}+N_{2}\left(\vec{\xi}\right)z_{2}+N_{3}\left(\vec{\xi}\right)z_{3}\\
 \\\end{array}\]
 
 \end_inset
@@ -871,7 +897,7 @@
 
 \begin_layout LyX-Code
 \begin_inset Formula \[
-\left[q\times3\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[q\times8\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[4\times3\right]\]
+\left[q\times3\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[q\times8\right]\,\,\,\,\,\,\,\,\,\:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[4\times3\right]\]
 
 \end_inset
 
@@ -879,7 +905,7 @@
 \end_layout
 
 \begin_layout Paragraph*
-Summary:
+Summary
 \end_layout
 
 \begin_layout Subparagraph*
@@ -930,17 +956,17 @@
 \begin_inset Tabular
 <lyxtabular version="3" rows="1" columns="2">
 <features>
-<column alignment="center" valignment="top" leftline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true" bottomline="true">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Standard
 \begin_inset Formula $\frac{\partial\vec{x}}{\partial\vec{\xi}}=\left[\begin{array}{ccc}
 \frac{\partial x}{\partial\xi} & \frac{\partial x}{\partial\eta} & \frac{\partial x}{\partial\zeta}\\
-\frac{\partial y}{\partial\xi} & \frac{\partial y}{\partial\eta} & \frac{\partial y}{\partial\xi}\\
-\frac{\partial z}{\partial\xi} & \frac{\partial z}{\partial\eta} & \frac{\partial z}{\partial\xi}\end{array}\right]$
+\frac{\partial y}{\partial\xi} & \frac{\partial y}{\partial\eta} & \frac{\partial y}{\partial\zeta}\\
+\frac{\partial z}{\partial\xi} & \frac{\partial z}{\partial\eta} & \frac{\partial z}{\partial\zeta}\end{array}\right]$
 \end_inset
 
 
@@ -1335,10 +1361,10 @@
 
 \begin_layout Standard
 \begin_inset Formula \[
-J=\left|\frac{2\vec{x}}{2\vec{\xi}}\right|=\left|\begin{array}{c}
+\mathrm{J}=\left|\frac{2\vec{x}}{2\vec{\xi}}\right|=\left|\begin{array}{c}
 \frac{1}{2}\left(x_{1}-x_{0}\right)\,\,\frac{1}{2}\left(x_{2}-x_{0}\right)\,\,\frac{1}{2}\left(x_{3}-x_{0}\right)\\
 \frac{1}{2}\left(y_{1}-y_{0}\right)\,\,\frac{1}{2}\left(y_{2}-y_{0}\right)\,\,\frac{1}{2}\left(y_{3}-y_{0}\right)\\
-\frac{1}{2}\left(z_{1}-z_{0}\right)\,\,\frac{1}{2}\left(x_{2}-x_{0}\right)\,\,\frac{1}{2}\left(x_{3}-x_{0}\right)\end{array}\right|\]
+\frac{1}{2}\left(z_{1}-z_{0}\right)\,\,\frac{1}{2}\left(z_{2}-z_{0}\right)\,\,\frac{1}{2}\left(z_{3}-z_{0}\right)\end{array}\right|\]
 
 \end_inset
 
@@ -1754,7 +1780,7 @@
 \begin_inset Text
 
 \begin_layout Standard
-\begin_inset Formula $\frac{1}{8}\left(+1\right)\left(1-\eta\right)\left(1-\zeta\right)$
+\begin_inset Formula $\frac{1}{8}\left(+1\right)\left(1-\eta\right)\left(1+\zeta\right)$
 \end_inset
 
 
@@ -1766,7 +1792,7 @@
 \begin_inset Text
 
 \begin_layout Standard
-\begin_inset Formula $\frac{1}{8}\left(1+\xi\right)\left(-1\right)\left(1-\zeta\right)$
+\begin_inset Formula $\frac{1}{8}\left(1+\xi\right)\left(-1\right)\left(1+\zeta\right)$
 \end_inset
 
 
@@ -1918,7 +1944,7 @@
 
 \begin_layout LyX-Code
 \begin_inset Formula \[
-J\left(\vec{\xi}\right)=\left|\begin{array}{ccc}
+\mathrm{J}\left(\vec{\xi}\right)=\left|\begin{array}{ccc}
 \frac{\partial x}{\partial\xi}\left(\vec{\xi}\right) & \frac{\partial x}{\partial\eta}\left(\vec{\xi}\right) & \frac{\partial x}{\partial\zeta}\left(\vec{\xi}\right)\\
 \frac{\partial y}{\partial\xi}\left(\vec{\xi}\right) & \frac{\partial y}{\partial\eta}\left(\vec{\xi}\right) & \frac{\partial y}{\partial\zeta}\left(\vec{\xi}\right)\\
 \frac{\partial z}{\partial\xi}\left(\vec{\xi}\right) & \frac{\partial z}{\partial\eta}\left(\vec{\xi}\right) & \frac{\partial z}{\partial\zeta}\left(\vec{\xi}\right)\end{array}\right|\]