[cig-commits] r7112 - cs/cigma/trunk/doc/manual

[sue at geodynamics.org]

Author: sue
Date: 2007-06-08 14:11:54 -0700 (Fri, 08 Jun 2007)
New Revision: 7112

Added:
   cs/cigma/trunk/doc/manual/quadrature-rule-diagram.jpg
   cs/cigma/trunk/doc/manual/various-pieces.lyx
Log:
quadrature rule section and figure

Added: cs/cigma/trunk/doc/manual/quadrature-rule-diagram.jpg
===================================================================
(Binary files differ)


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

Added: cs/cigma/trunk/doc/manual/various-pieces.lyx
===================================================================
--- cs/cigma/trunk/doc/manual/various-pieces.lyx	2007-06-08 20:46:22 UTC (rev 7111)
+++ cs/cigma/trunk/doc/manual/various-pieces.lyx	2007-06-08 21:11:54 UTC (rev 7112)
@@ -0,0 +1,242 @@
+#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 245
+\begin_document
+\begin_header
+\textclass article
+\language english
+\inputencoding auto
+\fontscheme default
+\graphics default
+\paperfontsize default
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Example Session
+\end_layout
+
+\begin_layout LyX-Code
+cigma> open model.h5
+\end_layout
+
+\begin_layout LyX-Code
+cigma> pwd
+\end_layout
+
+\begin_layout LyX-Code
+model.h5:/
+\end_layout
+
+\begin_layout LyX-Code
+cigma> tree
+\end_layout
+
+\begin_layout LyX-Code
+file.h5
+\end_layout
+
+\begin_layout LyX-Code
+`-- model
+\end_layout
+
+\begin_layout LyX-Code
+    |-- mesh
+\end_layout
+
+\begin_layout LyX-Code
+    |   |-- coordinates [4193 x 3]
+\end_layout
+
+\begin_layout LyX-Code
+    |   `-- connectivity [20480 x 4]
+\end_layout
+
+\begin_layout LyX-Code
+    `-- variables
+\end_layout
+
+\begin_layout LyX-Code
+        |-- displacement [4193 x 3]
+\end_layout
+
+\begin_layout LyX-Code
+        `-- velocity [4193 x 3]
+\end_layout
+
+\begin_layout LyX-Code
+cigma> cd /model
+\end_layout
+
+\begin_layout LyX-Code
+cigma> pwd
+\end_layout
+
+\begin_layout LyX-Code
+file.h5:/model
+\end_layout
+
+\begin_layout LyX-Code
+cigma> cd mesh
+\end_layout
+
+\begin_layout LyX-Code
+cigma> pwd
+\end_layout
+
+\begin_layout LyX-Code
+file.h5:/model/mesh
+\end_layout
+
+\begin_layout LyX-Code
+cigma> import variable from /path/to/file.ucd into velocity/0
+\end_layout
+
+\begin_layout LyX-Code
+[4193 x 3]
+\end_layout
+
+\begin_layout LyX-Code
+cigma> import coordinates from /path/to/file.ucd
+\end_layout
+
+\begin_layout LyX-Code
+[4193 x 3]
+\end_layout
+
+\begin_layout LyX-Code
+cigma> import connectivity from /path/to/file.ucd
+\end_layout
+
+\begin_layout LyX-Code
+[20480 x 4]
+\end_layout
+
+\begin_layout LyX-Code
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Quadrature Rule
+\end_layout
+
+\begin_layout Standard
+\noindent
+\begin_inset Graphics
+	filename quadrature-rule-diagram.jpg
+	lyxscale 25
+	scale 25
+	rotateOrigin leftBottom
+
+\end_inset
+
+
+\begin_inset Formula \[
+Q_{\kappa}^{e}\left(\vec{x}\left(\vec{\xi}\right)\right)\]
+
+\end_inset
+
+set of points 
+\begin_inset Formula $\vec{q}_{i}$
+\end_inset
+
+ \InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+\InsetSpace ~
+
+\begin_inset Formula $Q=\left\{ 1,\,\ldots\,,\left|Q\right|\right\} $
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+set of weights 
+\begin_inset Formula $w_{1}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+quadrature rule of degree 
+\begin_inset Formula $\left|Q\right|$
+\end_inset
+
+ \InsetSpace ~
+(
+\begin_inset Formula $\left|Q\right|^{d}$
+\end_inset
+
+ points and weights)
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+F\left(\xi\right),\rightarrow\int_{K_{ref}}\,\, F\left(\vec{\xi}\right)d\vec{\xi}=\begin{array}{c}
+\intop\intop\intop\\
+K_{ref}\end{array}\, F\left(\xi_{1},\xi_{2}\,,\xi_{3}\right)d\xi,\, d\xi_{2},\, d\xi_{3}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+=\sum_{i\epsilon Q}\, F\left(\vec{q}_{i}\right)\cdot w_{i}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\int_{K_{e}}f\left(\vec{x}\right)d\vec{x}=\int_{K_{ref}}f\left(\vec{\xi}\right)\cdot\left|\mathrm{J^{-1}}\left(\vec{\xi}\right)\right|d\vec{\xi}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+=\sum_{i\epsilon Q}\left(f\left(\vec{q}_{i}\right)\left|\mathrm{J^{-1}\left(\vec{q}_{i}\right)}\right|\right)\cdot w_{i}+0\left(\,\,\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document