[cig-commits] r13652 - doc/cigma/manual
luis at geodynamics.org
luis at geodynamics.org
Thu Dec 11 04:52:42 PST 2008
Author: luis
Date: 2008-12-11 04:52:42 -0800 (Thu, 11 Dec 2008)
New Revision: 13652
Modified:
doc/cigma/manual/appendix.lyx
doc/cigma/manual/cigma.lyx
doc/cigma/manual/error_analysis.lyx
doc/cigma/manual/formats.lyx
doc/cigma/manual/installation.lyx
doc/cigma/manual/interpolation.lyx
doc/cigma/manual/introduction.lyx
doc/cigma/manual/running.lyx
Log:
Clean up notes. Converted htmlUrl -> URL.
Modified: doc/cigma/manual/appendix.lyx
===================================================================
--- doc/cigma/manual/appendix.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/appendix.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -1,11 +1,12 @@
-#LyX 1.5.5 created this file. For more info see http://www.lyx.org/
-\lyxformat 276
+#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 345
\begin_document
\begin_header
\textclass book
\begin_preamble
\newcommand{\mynote}[1]{}
\end_preamble
+\use_default_options false
\language english
\inputencoding auto
\font_roman default
@@ -16,9 +17,11 @@
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
+
\graphics default
\paperfontsize default
\spacing single
+\use_hyperref false
\papersize default
\use_geometry false
\use_amsmath 1
@@ -42,32 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Standard
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Standard
-
-XXX: Content moved to formats.lyx, what else do we need in an appendix?
-\end_layout
-
-\begin_layout Standard
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
Data Formats
\end_layout
@@ -121,8 +98,10 @@
node coordinates, which are specified on a global coordinate system, we
have
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
@@ -138,7 +117,7 @@
height_special "totalheight"
status open
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Box Frameless
position "t"
hor_pos "c"
@@ -151,26 +130,26 @@
height_special "totalheight"
status open
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="5" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{no},3)$
\end_inset
@@ -180,11 +159,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Coordinates
\end_layout
@@ -193,7 +172,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{1},y_{1},z_{1}$
\end_inset
@@ -204,19 +183,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{2},y_{2},z_{2}$
\end_inset
@@ -227,19 +206,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -249,20 +228,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{n_{no}},y_{n_{no}},z_{n_{no}}$
\end_inset
@@ -294,26 +273,26 @@
height_special "totalheight"
status open
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="5" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{no},2)$
\end_inset
@@ -323,11 +302,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Coordinates
\end_layout
@@ -336,7 +315,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{1},y_{1}$
\end_inset
@@ -347,19 +326,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{2},y_{2}$
\end_inset
@@ -370,19 +349,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -392,20 +371,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{n_{no}},y_{n_{no}}$
\end_inset
@@ -450,30 +429,32 @@
-degrees of freedom each, then the connectivity array defining our element
block has the form
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(k,m)$
\end_inset
@@ -483,11 +464,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Connectivity Data
\end_layout
@@ -496,7 +477,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $n_{11},n_{12},\ldots,n_{1m}$
\end_inset
@@ -507,19 +488,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $n_{21},n_{22},\ldots,n_{2m}$
\end_inset
@@ -530,19 +511,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -552,20 +533,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $n_{k1},n_{k2},\ldots,n_{km}$
\end_inset
@@ -580,8 +561,10 @@
\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
@@ -592,70 +575,72 @@
are as follows.
Note that the total number of degrees of freedom depends on the rank of
the specific function being represented.
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="4">
<features>
-<column alignment="center" valignment="top" leftline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" width="0">
-<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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Element
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Scalar
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Vector
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Tensor
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
tet4
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
4
\end_layout
@@ -664,7 +649,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
12
\end_layout
@@ -673,65 +658,65 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
24
\end_layout
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
tet10
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
10
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
30
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
60
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
hex8
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
8
\end_layout
@@ -740,7 +725,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
24
\end_layout
@@ -749,27 +734,27 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
48
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
hex20
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
20
\end_layout
@@ -778,7 +763,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
60
\end_layout
@@ -787,45 +772,45 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
120
\end_layout
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
hex27
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
27
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
81
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
162
\end_layout
@@ -837,76 +822,80 @@
\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
Similarly for the 2-D elements, we have
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="4">
<features>
-<column alignment="center" valignment="top" leftline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" width="0">
-<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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Element
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Scalar
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Vector
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Tensor
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
tri3
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3
\end_layout
@@ -915,7 +904,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
6
\end_layout
@@ -924,45 +913,45 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
9
\end_layout
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
quad4
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
4
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
8
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
12
\end_layout
@@ -995,33 +984,35 @@
As described in Chapter 4, an integration rule is specified by using the
natural coordinate system of the reference element.
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="5">
<features>
-<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
-<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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Weights:
\begin_inset Formula $(Q,1)$
\end_inset
@@ -1031,10 +1022,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Points:
\begin_inset Formula $(Q,n_{dim})$
\end_inset
@@ -1044,10 +1035,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Points:
\begin_inset Formula $(Q,2)$
\end_inset
@@ -1057,10 +1048,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Points:
\begin_inset Formula $(Q,3)$
\end_inset
@@ -1071,11 +1062,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Rule Definition
\end_layout
@@ -1084,7 +1075,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $w_{1}$
\end_inset
@@ -1093,10 +1084,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{\xi}_{1}$
\end_inset
@@ -1108,7 +1099,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{1},\eta_{1}$
\end_inset
@@ -1120,7 +1111,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{1},\eta_{1},\zeta_{1}$
\end_inset
@@ -1131,19 +1122,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $w_{2}$
\end_inset
@@ -1152,10 +1143,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{\xi}_{2}$
\end_inset
@@ -1164,10 +1155,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{2},\eta_{2}$
\end_inset
@@ -1176,10 +1167,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{2},\eta_{2},\zeta_{2}$
\end_inset
@@ -1190,19 +1181,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1211,10 +1202,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1223,10 +1214,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1235,10 +1226,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1248,20 +1239,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $w_{Q}$
\end_inset
@@ -1270,10 +1261,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{\xi}_{Q}$
\end_inset
@@ -1282,10 +1273,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{Q},\eta_{Q}$
\end_inset
@@ -1294,10 +1285,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\xi_{Q},\eta_{Q},\zeta_{Q}$
\end_inset
@@ -1325,30 +1316,34 @@
\end_inset
shape function values at the expected integration points.
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
+
+
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="3">
<features>
-<column alignment="center" valignment="top" leftline="true" width="0">
-<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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Shape Function Values:
\begin_inset Formula $(n,Q)$
\end_inset
@@ -1358,10 +1353,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Jacobian Determinant:
\begin_inset Formula $(Q,1)$
\end_inset
@@ -1372,20 +1367,20 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Integration Point 1
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $N_{1}(\vec{\xi}_{1}),N_{2}(\vec{\xi}_{1}),\ldots,N_{n}(\vec{\xi}_{1})$
\end_inset
@@ -1397,7 +1392,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $J(\vec{\xi}_{1})$
\end_inset
@@ -1408,19 +1403,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Integration Point 2
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $N_{1}(\vec{\xi}_{2}),N_{2}(\vec{\xi}_{2}),\ldots,N_{n}(\vec{\xi}_{2})$
\end_inset
@@ -1429,10 +1424,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $J(\vec{\xi}_{2})$
\end_inset
@@ -1443,19 +1438,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1464,10 +1459,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1477,11 +1472,11 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Integration Point
\begin_inset Formula $Q$
\end_inset
@@ -1491,10 +1486,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $N_{1}(\vec{\xi}_{Q}),N_{2}(\vec{\xi}_{Q}),\ldots,N_{n}(\vec{\xi}_{Q})$
\end_inset
@@ -1503,10 +1498,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $J(\vec{\xi}_{Q})$
\end_inset
@@ -1530,32 +1525,34 @@
\begin_layout Standard
Given a mesh and an integration rule, we can map the integration points
on each element into a possibly large set of global points.
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="4">
<features>
-<column alignment="center" valignment="top" leftline="true" width="0">
-<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
-<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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Points:
\begin_inset Formula $(n_{pts},n_{dim})$
\end_inset
@@ -1565,10 +1562,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Points:
\begin_inset Formula $(n_{pts},2)$
\end_inset
@@ -1578,10 +1575,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Points:
\begin_inset Formula $(n_{pts},3)$
\end_inset
@@ -1592,20 +1589,20 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Coordinates
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{x}_{1}$
\end_inset
@@ -1614,10 +1611,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{1},y_{1}$
\end_inset
@@ -1629,7 +1626,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{1},y_{1},z_{1}$
\end_inset
@@ -1640,19 +1637,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{x}_{2}$
\end_inset
@@ -1661,10 +1658,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{2},y_{2}$
\end_inset
@@ -1673,10 +1670,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{2},y_{2},z_{2}$
\end_inset
@@ -1687,19 +1684,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1708,10 +1705,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1720,10 +1717,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -1733,20 +1730,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vec{x}_{n_{pts}}$
\end_inset
@@ -1755,10 +1752,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{n_{pts}}y_{n_{pts}}$
\end_inset
@@ -1767,10 +1764,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $x_{n_{pts}},y_{n_{pts}},z_{n_{pts}}$
\end_inset
@@ -1796,40 +1793,44 @@
evaluated, as indicated in the table below.
Note that the fastest varying dimension of the array contains the values
of the function at each point.
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
+
+
\begin_inset Tabular
<lyxtabular version="3" rows="6" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Evaluated Quantity
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Resulting Array Shape
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Scalar
\end_layout
@@ -1838,7 +1839,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{pts},1)$
\end_inset
@@ -1848,11 +1849,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Vector
\end_layout
@@ -1861,7 +1862,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{pts},2)$
\end_inset
@@ -1871,11 +1872,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Vector
\end_layout
@@ -1884,7 +1885,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{pts},3)$
\end_inset
@@ -1894,11 +1895,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
2-D Tensor
\end_layout
@@ -1907,7 +1908,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{pts},3)$
\end_inset
@@ -1917,20 +1918,20 @@
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
3-D Tensor
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(n_{pts},6)$
\end_inset
@@ -1962,30 +1963,32 @@
\end_inset
cells, we have the output array
-\newline
+\begin_inset Newline newline
+\end_inset
+
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Array Shape
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $(k,1)$
\end_inset
@@ -1995,11 +1998,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Residual Value
\end_layout
@@ -2008,7 +2011,7 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\varepsilon_{1}$
\end_inset
@@ -2019,19 +2022,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\varepsilon_{2}$
\end_inset
@@ -2042,19 +2045,19 @@
</cell>
</row>
<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset
@@ -2064,20 +2067,20 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\begin_inset Formula $\varepsilon_{k}$
\end_inset
@@ -2092,11 +2095,17 @@
\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
-\newline
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
These local residual values may be combined in the following form:
\begin_inset Formula \[
\varepsilon_{block}=\sqrt{\varepsilon_{1}^{2}+\varepsilon_{2}^{2}+\cdots+\varepsilon_{k}^{2}}\]
@@ -2125,117 +2134,6 @@
\end_layout
\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Standard
-
-Go over numerical integration in 2d and 3d.
-\end_layout
-
-\begin_layout Standard
-
-Required order of numerical integration.
-\end_layout
-
-\begin_layout Standard
-
-Give references to defining your own points here.
- Explain how to use the scripts here.
-\end_layout
-
-\begin_layout Standard
-
-For each element, give the default quadrature rule employed and its order
- of accuracy.
-\end_layout
-
-\begin_layout Standard
-
-Give more examples of quadrature rules.
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-Mention tabulation of shape function values here.
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-References to mention here:
-\end_layout
-
-\begin_layout Standard
-
- FIAT homepage
-\end_layout
-
-\begin_layout Standard
-
- FILIPPA mathematica notebooks
-\end_layout
-
-\begin_layout Standard
-
- Encyclopedia of Cubature Formulas (url?)
-\end_layout
-
-\begin_layout Standard
-
-}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-The core concepts to get across in this chapter are the following:
-\end_layout
-
-\begin_layout Enumerate
-Each element in Cigma is assigned a default quadrature rule
-\end_layout
-
-\begin_layout Enumerate
-Explain briefly how quadrature rules are obtained (product rules)
-\end_layout
-
-\begin_layout Enumerate
-Error bound on integration (dependent on the discretization size h, and
- the order of integration q).
-\end_layout
-
-\begin_layout Enumerate
-How to obtain more quadrature rules (encyclopedia website, FIAT, mathematica
- scripts -- don't forget to mention caveat about using rules that use different
- reference cells -- points transform according to map, while weights are
- multiplied by the appropriate jacobian factor).
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
In order to calculate the
\begin_inset Formula $L_{2}$
\end_inset
@@ -2249,19 +2147,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-Define integration rule.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
In general, we may define an integration rule as a set of points with associated
weights for which we may approximate an integration procedure by a simple
weighed sum
@@ -2289,19 +2174,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Hughes, pg 143
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
The general Gaussian quadrature rule with
\begin_inset Formula $Q$
\end_inset
@@ -2387,90 +2259,5 @@
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Section
-Quadrilaterals and Hexahedra
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Since these two are very similar, keep them together.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For the reference quadrilateral and hexahedral elements, we can use the
-
-\end_layout
-
-\begin_layout Standard
-For quadrilaterals, we use the same reference region
-\begin_inset Formula $[-1,1]\times[-1,1]$
-\end_inset
-
- as in Section 4.X.
-\end_layout
-
-\begin_layout Standard
-The reference region for this geometry is
-\begin_inset Formula $[-1,1]\times[-1,1]\times[-1,1]$
-\end_inset
-
-, as in Section 4.X.
-
-\end_layout
-
-\begin_layout Section
-Triangles and Tetrahedra
-\end_layout
-
-\begin_layout Standard
-To easily obtain high order accuracy quadrature rules for triangles, we
- can re-use the same rules for quadrilaterals by collapsing two of the nodes
- of the quadrilateral.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Fig.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Similar to the triangle
-\end_layout
-
-\begin_layout Section
-Other Integration Rules
-\end_layout
-
-\begin_layout Standard
-The integration points given in this section were obtained by using the
- FIAT Python module.
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\end_body
\end_document
Modified: doc/cigma/manual/cigma.lyx
===================================================================
--- doc/cigma/manual/cigma.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/cigma.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -166,71 +166,6 @@
\end_layout
\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
- Global TODO Items
-\end_layout
-
-\begin_layout Plain Layout
-
- * Don't forget to change version on cover to version 1.0.0 (done)
-\end_layout
-
-\begin_layout Plain Layout
-
- * Change the cover image to use a newer comparison
-\end_layout
-
-\begin_layout Plain Layout
-
- * Add description of basic ExodusII format in file_formats.lyx (delay
- for version 1.1 -- use Scientific.IO.NetCDF for now)
-\end_layout
-
-\begin_layout Plain Layout
-
- * grep for 'Chapter' and 'Section' and make sure that all such numbers
- are relative references.
-\end_layout
-
-\begin_layout Plain Layout
-
- * Fix alignment of tables where appropriate (left/center/right justified)
-\end_layout
-
-\begin_layout Plain Layout
-
- * Fix alignment of table cells where appropriate (left/center/right
- justified)
-\end_layout
-
-\begin_layout Plain Layout
-
- * Figure out how to reference equation numbers in lyx (how to give them
- a label?)
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
\begin_inset CommandInset include
LatexCommand include
filename "introduction.lyx"
@@ -315,71 +250,6 @@
\end_layout
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
-References:
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-* Hughes, Thomas J.R., The Finite Element Method: Linear Static and Dynamic
- Finite Element Analysis, Prentice-Hall 1987 (use Dover ref instead)
-\end_layout
-
-\begin_layout Plain Layout
-
-* Zienkiewicz, O.C., Taylor, R.L.
- The Finite Element Method: The Basis (Vol.
- 1)
-\end_layout
-
-\begin_layout Plain Layout
-
-* Akin, J.E., Finite Element Analysis with Error Estimators, Elsevier 2005
- (ISBN 0750667222)
-\end_layout
-
-\begin_layout Plain Layout
-
-* Johnson, Claes - Numerical Solutions of Partial Differential Equations
- by the Finite Element Method, Cambridge University Press 1987
-\end_layout
-
-\begin_layout Plain Layout
-
-* Carlos Felippa, A Compendium of FEM integration formulas for symbolic
- work, Engineering Computation, Volume 21, Number 8, 2004, pages 867-890
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
Modified: doc/cigma/manual/error_analysis.lyx
===================================================================
--- doc/cigma/manual/error_analysis.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/error_analysis.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -45,128 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
-Purpose of this chapter is to provide a high-level description of cigma,
- and just reference later chapters if we need to.
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-In reference to error analysis, we introduce the topics in the following
- order
-\end_layout
-
-\begin_layout Plain Layout
-
- - Quick reference to distance measures, both pointwise and global L2
-\end_layout
-
-\begin_layout Plain Layout
-
- - Define function as used in cigma
-\end_layout
-
-\begin_layout Plain Layout
-
- - Define integration rule in this chapter
-\end_layout
-
-\begin_layout Plain Layout
-
- * in general (1D, 2D, 3D)
-\end_layout
-
-\begin_layout Plain Layout
-
- * as applied to a discretization (sum over cells)
-\end_layout
-
-\begin_layout Plain Layout
-
- * generating own integration points (XXX: moved to integration.lyx) --
- give references
-\end_layout
-
-\begin_layout Plain Layout
-
- (give warning about using a different reference element -- weights,
- not just points, need to be adjusted -- perhaps this warning belongs in
- the next chapter)
-\end_layout
-
-\begin_layout Plain Layout
-
- - Mention the interpolation functions that are available (XXX: moved to
- interpolation.lyx)
-\end_layout
-
-\begin_layout Plain Layout
-
- * global functions (predefined: zero, scalar.one, ...)
-\end_layout
-
-\begin_layout Plain Layout
-
- * FEM on a given discretization (local interpolations on tet4, hex8,
- tri3, quad3, ...
- elements)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Other tasks:
-\end_layout
-
-\begin_layout Plain Layout
-
- Change name of chapter to something else (no longer necessary)
-\end_layout
-
-\begin_layout Plain Layout
-
- Give formula in the last section
-\end_layout
-
-\begin_layout Plain Layout
-
- Move discussion of convergence order from examples.lyx and merge it at
- the end of this chapter
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
\begin_inset CommandInset label
LatexCommand label
@@ -322,20 +200,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-Briefer discussion here.
- Move this to Chapter 5.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
In order to evaluate the integral for our
\begin_inset Formula $L_{2}$
\end_inset
@@ -444,29 +308,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-FIGURE refmap.png:
-\backslash
-chi_i:
-\backslash
-hat{
-\backslash
-Omega}
-\backslash
-to
-\backslash
-Omega_i
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
Note that a given discretization may contain cells of different shapes,
which would require us to define an appropriate number of reference cells
for each type of cell.
@@ -740,297 +581,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-Suppose the domain
-\begin_inset Formula $\Omega$
-\end_inset
-
- into an appropriate set of cells
-\begin_inset Formula $\Omega_{1},\Omega_{2},\ldots,\Omega_{n_{el}}$
-\end_inset
-
-, we can compute the global error
-\begin_inset Formula $\varepsilon^{2}$
-\end_inset
-
- as a sum over localized cell contributions,
-\begin_inset Formula $\varepsilon^{2}=\sum_{e}\varepsilon_{e}^{2}$
-\end_inset
-
-, where each cell residual
-\begin_inset Formula $\varepsilon_{e}^{2}$
-\end_inset
-
- is given by
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Formula \begin{eqnarray*}
-\varepsilon_{e}^{2} & = & \int_{\Omega_{e}}||u(\vec{x})-v(\vec{x})||^{2}d\vec{x}\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-In general, we won't be able to integrate each cell residual
-\begin_inset Formula $\varepsilon_{e}^{2}$
-\end_inset
-
- exactly since either of the functions
-\begin_inset Formula $u$
-\end_inset
-
- and
-\begin_inset Formula $v$
-\end_inset
-
- may have an incompatible representation relative to the finite element
- space on each domain
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
-.
- However, we can still calculate an approximation of each cell residual
- by applying an appropriate quadrature rule with a tolerable truncation
- error
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Encyclopaedia of Cubature Formulas 2005"
-
-\end_inset
-
-.
-
-\end_layout
-
-\begin_layout Plain Layout
-To obtain an approximation to the integral of a function
-\begin_inset Formula $F(\vec{x})$
-\end_inset
-
- over a cell
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
-, we simply apply the quadrature rule with weights
-\begin_inset Formula $w_{e,1},w_{e,2},\ldots,w_{e,n_{Q}}$
-\end_inset
-
- and integration points
-\begin_inset Formula $\vec{x}_{e,1},\vec{x}_{e,2},\ldots,\vec{x}_{e,n_{Q}}$
-\end_inset
-
- appropriate for the physical element
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
-:
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Formula \[
-\int_{\Omega_{e}}\ F(\vec{x})\ d\vec{x}=\sum_{q=1}^{n_{Q}}w_{e,q}F(\vec{x}_{e,q})\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-Applying this quadrature rule directly over the entire physical domain
-\begin_inset Formula $\Omega=\cup\Omega_{e}$
-\end_inset
-
- gives us
-\begin_inset Formula \[
-\int_{\Omega}\ F(\vec{x})\ d\vec{x}=\sum_{e=1}^{n_{el}}\sum_{q=1}^{n_{Q}}w_{e,q}F(\vec{x}_{e,q})\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-For efficiency reasons, it is undesirable in finite element applications
- to perform calculations in a global coordinate system.
- To avoid duplication of work, shape function evaluations may be performed
- once on a reference cell
-\begin_inset Formula $\hat{\Omega}$
-\end_inset
-
- and then transformed back into the corresponding physical cell
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
- as needed.
-\end_layout
-
-\begin_layout Plain Layout
-To compute integrals of
-\begin_inset Formula $F$
-\end_inset
-
- in a reference coordinate system, we need to apply a change of variables:
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Formula \[
-\int_{\Omega_{e}}\ F(\vec{x})\ d\vec{x}=\int_{\hat{\Omega}}\ F(\vec{x}_{e}(\vec{\xi}))J_{e}(\vec{\xi})\ d\vec{\xi}\]
-
-\end_inset
-
-where
-\color none
-the additional factor
-\begin_inset Formula $J_{e}(\vec{\xi})=\det\left[\frac{d\vec{x}_{e}}{d\vec{\xi}}\right]$
-\end_inset
-
- is the Jacobian determinant of the reference map
-\begin_inset Formula $\vec{x}_{e}(\vec{\xi}):\hat{\Omega}\to\Omega_{e}$
-\end_inset
-
-.
- This map describes how the physical points
-\begin_inset Formula $\vec{x}\in\Omega_{e}$
-\end_inset
-
- are transformed from the reference points
-\begin_inset Formula $\vec{\xi}\in\hat{\Omega}$
-\end_inset
-
-.
- Put another way, the inverse reference map
-\color inherit
-
-\begin_inset Formula $\vec{\xi}=\vec{x}_{e}^{-1}(\vec{x})$
-\end_inset
-
- tells us how the physical domain
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
- maps into the reference cell
-\begin_inset Formula $\hat{\Omega}$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Plain Layout
-At this point, we can assume without loss of generality that every physical
- cell
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
- can be derived from a single reference cell
-\begin_inset Formula $\hat{\Omega}$
-\end_inset
-
-, so that our quadrature rule becomes simply a set of weights
-\begin_inset Formula $w_{1},\ldots,w_{n_{Q}}$
-\end_inset
-
- and points
-\begin_inset Formula $\vec{\xi}_{1},\ldots,\vec{\xi}_{n_{Q}}$
-\end_inset
-
- over
-\begin_inset Formula $\hat{\Omega}$
-\end_inset
-
-.
- After changing variables, we end up with the final form of the quadrature
- rule that we can use to integrate the global residual field:
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Formula \[
-\int_{\hat{\Omega}}\ F(\vec{x}_{e}(\vec{\xi}))J_{e}(\vec{\xi})\ d\vec{\xi}=\sum_{q=1}^{n_{Q}}w_{q}F(\vec{x}_{e}(\vec{\xi}_{q}))J_{e}(\vec{\xi}_{q})\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-If we let
-\begin_inset Formula $F(\vec{x})=||u(\vec{x})-v(\vec{x})||^{2}$
-\end_inset
-
- in the above expression, we can find the cell residual contribution over
-
-\begin_inset Formula $\Omega_{e}$
-\end_inset
-
- from
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Formula \begin{eqnarray*}
-\varepsilon_{e}^{2} & = & \int_{\Omega_{e}}\ ||u(\vec{x})-v(\vec{x})||^{2}\ d\vec{x}\\
- & = & \int_{\hat{\Omega}}\ ||u(\vec{x}_{e}(\vec{\xi}))-v(\vec{x}_{e}(\vec{\xi}))||^{2}J_{e}(\vec{\xi})\ d\vec{\xi}\\
- & = & \sum_{q=1}^{\mathrm{n_{Q}}}w_{q}||u(\vec{x}_{e}(\vec{\xi}_{q}))-v(\vec{x}_{e}(\vec{\xi}_{q}))||^{2}J_{e}(\vec{\xi}_{q})\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-The global error
-\begin_inset Formula $\varepsilon=\sqrt{\sum_{e}\varepsilon_{e}^{2}}$
-\end_inset
-
- is then approximated by the expression
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Box Boxed
-position "t"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 0
-width "100text%"
-special "none"
-height "1in"
-height_special "totalheight"
-status open
-
-\begin_layout Plain Layout
-\begin_inset Formula \begin{eqnarray*}
-\varepsilon & = & \sqrt{\sum_{e=1}^{\mathrm{n_{el}}}\sum_{q=1}^{\mathrm{n_{Q}}}w_{q}||u(\vec{x}_{e}(\vec{\xi}_{q}))-v(\vec{x}_{e}(\vec{\xi}_{q}))||^{2}J_{e}(\vec{\xi}_{q})}\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-We can make a number of observations based on our final expression for the
- global error.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
In this section we show the formula used by Cigma to compute the
\begin_inset Formula $L_{2}$
\end_inset
@@ -1369,50 +919,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-TODO: Move discussion of convergence from old running.lyx into this section.
-\end_layout
-
-\begin_layout Plain Layout
-Standard error estimate (Hughes, pg 190; Johnson, pg 97)
-\end_layout
-
-\begin_layout Plain Layout
-Give formula for
-\begin_inset Formula $\alpha$
-\end_inset
-
- for when we know the exact solution (only need two levels), and we are
- testing our numerical code.
-\end_layout
-
-\begin_layout Plain Layout
-Give formula for
-\begin_inset Formula $\alpha$
-\end_inset
-
- for when we have three levels (same formula), and we are testing our code
- for convergence.
-\end_layout
-
-\begin_layout Plain Layout
-Talk about least squares fit for when we have more than three levels.
- (mention scipy script, and reproduce it here, since it's short)
-\end_layout
-
-\begin_layout Plain Layout
-SciPy script for optimizing least squares fit into the formula y = a*x^b
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
Even if the exact solution
\begin_inset Formula $u(\vec{x})$
\end_inset
@@ -1447,38 +953,10 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-Here we define what we mean by Benchmark, and how we can use.
-\end_layout
-
-\begin_layout Plain Layout
-Give URLs for benchmark repositories on CIG svn tree.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
As we saw in Section 3.5, it is easier to calculate the convergence rate
on a sequence of meshes if we have access to the exact solution.
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-Since one of our goals is to provide an easy means of calculating these
- comparisons,
\end_layout
-\end_inset
-
-
-\end_layout
-
\end_body
\end_document
Modified: doc/cigma/manual/formats.lyx
===================================================================
--- doc/cigma/manual/formats.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/formats.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -45,548 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
-TODO: Rename file_formats.lyx to formats.lyx (done)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-TODO: What about NodeNumberMap?
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Define the dimensions for every object in the file
-\end_layout
-
-\begin_layout Plain Layout
-
- Mesh Coordinates
-\end_layout
-
-\begin_layout Plain Layout
-
- Mesh Connectivity (list of Element Blocks)
-\end_layout
-
-\begin_layout Plain Layout
-
- Field Variables (Global, Nodal, Element)
-\end_layout
-
-\begin_layout Plain Layout
-
- Element Tabulation (Shape function, Shape Function Derivatives)
-\end_layout
-
-\begin_layout Plain Layout
-
- Integration Rule (Weights and Local Points)
-\end_layout
-
-\begin_layout Plain Layout
-
- Global Integration Points
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Explain structure of each file format:
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- Text Format
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- All arrays specified explicitly in several text files containing a list
- of floating point numbers.
-\end_layout
-
-\begin_layout Plain Layout
-
- The first two numbers indicate the dimensions of the array, followed
- by a list of floats
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --integration-mesh-coordinates=imesh_coords.dat
-\end_layout
-
-\begin_layout Plain Layout
-
- --integration-mesh-connectivity=imesh_connect.dat
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --integration-rule-points=tet4_order10_points.dat
-\end_layout
-
-\begin_layout Plain Layout
-
- --integration-rule-weights=tet4_order10_weights.dat
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --first-mesh-coordinates=first_coords.dat
-\end_layout
-
-\begin_layout Plain Layout
-
- --first-mesh-connectivity=first_connect.dat
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --second-mesh-coordinates=first_coords.dat
-\end_layout
-
-\begin_layout Plain Layout
-
- --second-mesh-connectivity=first_connect.dat
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --first-dofs=first_var_stepN.dat
-\end_layout
-
-\begin_layout Plain Layout
-
- --second-dofs=second_var_stepN.dat
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- --integration-rule=tet4_order10.dat <-- (weights in first column)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- Simple Arrays (HDF5)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- Structure of Model Definition
-\end_layout
-
-\begin_layout Plain Layout
-
- root group at /model
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh data at /model/mesh
-\end_layout
-
-\begin_layout Plain Layout
-
- node coordinates as specified on global coordinate system at /model/mesh
-/coordinates
-\end_layout
-
-\begin_layout Plain Layout
-
- list of element blocks at /model/mesh/connectivity
-\end_layout
-
-\begin_layout Plain Layout
-
- note that each element block is tagged by element type in the FE
- attribute
-\end_layout
-
-\begin_layout Plain Layout
-
- degrees-of-freedom data
-\end_layout
-
-\begin_layout Plain Layout
-
- organized by variable at /model/vars/var, or even just /model/var
-\end_layout
-
-\begin_layout Plain Layout
-
- list of steps: /model/var/step{0,1,...,N}
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- Structure of file defining an Integration Rule
-\end_layout
-
-\begin_layout Plain Layout
-
- root group is / by default, but may be specified directly (eg, as
- /rule)
-\end_layout
-
-\begin_layout Plain Layout
-
- root group is tagged with FE string indicating the source element
- (tet4, ...)
-\end_layout
-
-\begin_layout Plain Layout
-
- integration points contained at /rule/points
-\end_layout
-
-\begin_layout Plain Layout
-
- integration points contained at /rule/weights
-\end_layout
-
-\begin_layout Plain Layout
-
- Structure of file with Residuals
-\end_layout
-
-\begin_layout Plain Layout
-
- root group is / by default, but it must exist if specified
-\end_layout
-
-\begin_layout Plain Layout
-
-
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK
-\end_layout
-
-\begin_layout Plain Layout
-
- Basic structure:
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK Grid
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK Dataset consists of the mesh information (node coordinates
- and associated connectivity relations)
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK Data Arrays come in two types (Point Data and Cell Data)
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK Point Data - scalars, vectors, tensors as defined on the
- nodes
-\end_layout
-
-\begin_layout Plain Layout
-
- VTK Cell Data - scalars, vectors, tensors as defined on each
- element
-\end_layout
-
-\begin_layout Plain Layout
-
- Structure of different types
-\end_layout
-
-\begin_layout Plain Layout
-
- Unstructured Grid
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh points: given explicitly in a simple array
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh connectivity: given explicitly in a list of simple arrays
-\end_layout
-
-\begin_layout Plain Layout
-
- element types: Line, Quad, Tetra, Hexahedron, Quadratic Triangle,
- Quadratic Quad, Quadratic Tetra, Quadratic Hexahedron
-\end_layout
-
-\begin_layout Plain Layout
-
- Structured Grid
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh points: given explicitly in a simple array
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh connectivity: derived from dimensions (nx, ny, nz)
-\end_layout
-
-\begin_layout Plain Layout
-
- element types: Quad, Pixel, Hex, Voxel
-\end_layout
-
-\begin_layout Plain Layout
-
- Rectilinear Grid
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh dimensions: (nx, ny, nz)
-\end_layout
-
-\begin_layout Plain Layout
-
- mesh points: derived from 'double xcoords[nx], ycoords[ny], zcoords[n
-z]' arrays
-\end_layout
-
-\begin_layout Plain Layout
-
- element types: Pixel, Voxel
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- UCD
-\end_layout
-
-\begin_layout Plain Layout
-
- Format described in (LINK-TO-DOCUMENT).
-\end_layout
-
-\begin_layout Plain Layout
-
- Using VTK API (vtkAVSucdReader) to read (*.inp) files
-\end_layout
-
-\begin_layout Plain Layout
-
- Just extracts the data into an Unstructured Grid
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- ExodusII
-\end_layout
-
-\begin_layout Plain Layout
-
- This type of mesh can be generated by other programs, such as CUBIT
-\end_layout
-
-\begin_layout Plain Layout
-
- Currently only used to specify an integration mesh, but it is capable
- of storing degree-of-freedom data as well.
-\end_layout
-
-\begin_layout Plain Layout
-
- Utility script for converting *.exo into the appropriate *.h5 file (need
- PyTables, Numpy, Scientific.IO.NetCDF)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
---------------
-\end_layout
-
-\begin_layout Plain Layout
-
-From running.lyx:
-\end_layout
-
-\begin_layout Plain Layout
-
-The underlying data storage format for Cigma is the HDF5 format, due to
- its flexibility for storing and organizing large amounts of data.
- The Hierarchical Data Format (HDF) is designed for storing, retrieving,
- analyzing, visualizing, and converting scientific data.
- It uses a hierarchical structure that provides users a host of options
- for organizing how their data is stored in HDF5 files.
- Using HDF5 datasets in Cigma allows us to avoid having to convert between
- too many distinct formats.
- Moreover, due to the amount of disk I/O, large finite element meshes can
- be handled more efficiently in binary format.
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Another popular format for providing mesh and field inputs.You can easily
- examine the structure of an input file by using the cigma list command,
- which will simply reveal the names and dimensions of all datasets inside
- the specified file.
-\end_layout
-
-\begin_layout Plain Layout
-
-Inputs can be either HDF5 or VTK.
- Specifying the complete path to a dataset consists of the special form
- filepath:dataset, a colon-delimited pair of file path and dataset path.
-\end_layout
-
-\begin_layout Plain Layout
-
-Mesh inputs are currently only unstructured grids.
-\end_layout
-
-\begin_layout Plain Layout
-
-Only exception are the residuals, which are written in legacy VTK format
- as scalar cell data over an unstructured grid.
-\end_layout
-
-\begin_layout Plain Layout
-
-Because Cigma relies on the ability of the user to specify dataset paths,
- we have provided a command called list for viewing the structure of an
- input file.
- Its usage is very simple.
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-This chapter may be summarized by simply stating that most input data can
- be specified as a two-dimensional array.
- The meaning of this array, of course, is dependent on context.
- That is the main concept that we have to get accross in this chapter.
- If the content is similar enough, perhaps the appendix could just be incorporat
-ed into this section.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
Data and File Formats
\end_layout
@@ -1648,27 +1106,6 @@
in the mesh.
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-arrays are subject to interpretation based on their corresponding tag:
-\end_layout
-
-\begin_layout Plain Layout
-by default, interpreted as shape function coefficients (from text and vtk)
-\end_layout
-
-\begin_layout Plain Layout
-can also specify spherical harmonics coefficients.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Shape Function Values
\end_layout
@@ -2223,46 +1660,8 @@
\end_inset
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-A typical point
-\begin_inset Formula $\vec{\xi}_{i}$
-\end_inset
-
- in 2-D is typically written as
-\begin_inset Formula $(\xi_{i},\eta_{i})$
-\end_inset
-
-, and in 3-D we write
-\begin_inset Formula $(\xi_{i},\eta_{i},\zeta_{i})$
-\end_inset
-
-.
- In special cases, integration points may be specified in
\end_layout
-\end_inset
-
-
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-Note: It is important to realize that the integration weights need to be
- adjusted by the appropriate factor when trying to compare rules defined
- on different reference regions.
- It is not sufficient to simply transform the points, as the weights need
- to be adjusted by the jacobian factor as well (see the change of variables
- formula for integrals).
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Integration Points and Values
\end_layout
@@ -2879,21 +2278,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-XXX: The input/output file dichotomy does not seem as necessary now that
- we've added the Data Format section.
- Get rid of those subsection headings.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
A number of file formats are supported for storing and retrieving the above
data structures to and from disk.
The following file extensions are used for these purposes:
@@ -3051,41 +2435,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-There are five different objects you will want to use as input to Cigma,
- all of which can be represented as two-dimensional datasets.
- These are the
-\end_layout
-
-\begin_layout Itemize
-mesh coordinates
-\end_layout
-
-\begin_layout Itemize
-mesh connectivity
-\end_layout
-
-\begin_layout Itemize
-field coefficients (degrees of freedom)
-\end_layout
-
-\begin_layout Itemize
-quadrature rule points
-\end_layout
-
-\begin_layout Itemize
-quadrature rule weights
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
In Section 1.1, we examined what kinds of objects we will be accessing, so
now let's discuss the actual layout in the files in which these objects
will be stored.
@@ -3145,19 +2494,6 @@
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-Mention these assumptions in the corresponding section in running.lyx
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout LyX-Code
model.h5
\end_layout
@@ -3279,19 +2615,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-VTK files are typically designed for visualization purposes,
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
Note that while you typically provide a path (or name) for every dataset,
this is not necessary when specifying a VTK mesh, since this data is taken
from the special Points and Cells arrays, which you cannot rename.
@@ -3322,20 +2645,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-Don't forget about the comment character '#' (which skips everything until
- the next newline)
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
The text files we use in Cigma consist of a simple list of numbers in ASCII
format whose layout corresponds exactly to the simple array layout discussed
earlier in Section 1.1.
@@ -3367,34 +2676,9 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
Depending on the particular operation you perform, there are three different
kinds of output files.
The output format for residuals consists simply of a list of scalars for
- each element in the discretization.
- If you specify a
-\family typewriter
-.vtk
-\family default
- extension for your output file, this will result in an scalar dataset named
- epsilon stored using the legacy VTK file format in the Cell Data section
- of the output file.
- Note that this output consists of the squared values of the local residuals,
- so further post-processing will be necessary.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Depending on the particular operation you perform, there are three different
- kinds of output files.
- The output format for residuals consists simply of a list of scalars for
each element in the discretization, stored using the legacy VTK file format
in the Cell Data section of the output file.
Note that this output consists of the squared values of the local residuals,
Modified: doc/cigma/manual/installation.lyx
===================================================================
--- doc/cigma/manual/installation.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/installation.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -1,11 +1,12 @@
-#LyX 1.5.5 created this file. For more info see http://www.lyx.org/
-\lyxformat 276
+#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 345
\begin_document
\begin_header
\textclass book
\begin_preamble
\newcommand{\mynote}[1]{}
\end_preamble
+\use_default_options false
\language english
\inputencoding auto
\font_roman default
@@ -16,9 +17,11 @@
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
+
\graphics default
\paperfontsize default
\spacing single
+\use_hyperref false
\papersize default
\use_geometry false
\use_amsmath 1
@@ -42,82 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Standard
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Standard
-
-Things to mention:
-\end_layout
-
-\begin_layout Standard
-
- Mention installation from binary (test the binaries from buildbot and
- make sure they install properly)
-\end_layout
-
-\begin_layout Standard
-
- Mention how to obtain a copy of the development tree
-\end_layout
-
-\begin_layout Standard
-
- Add Scientific.IO.NetCDF to list of optional tools
-\end_layout
-
-\begin_layout Standard
-
- Add SciPy to the list of optional tools
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-Portions of Boost that we use
-\end_layout
-
-\begin_layout Standard
-
- boost::filesystem
-\end_layout
-
-\begin_layout Standard
-
- boost::program_options
-\end_layout
-
-\begin_layout Standard
-
- boost::regex (parsing parameters from source strings)
-\end_layout
-
-\begin_layout Standard
-
- boost::python (for wrapping the core library objects)
-\end_layout
-
-\begin_layout Standard
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
Installation and Getting Help
\end_layout
@@ -127,11 +54,15 @@
\end_layout
\begin_layout Standard
-For help, send an e-mail to the
-\begin_inset LatexCommand url
-name "CIG Computational Science Mailing List"
-target "cig-cs at geodynamics.org"
+For help, send an e-mail to the CIG Computational Science Mailing List
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+cig-cs at geodynamics.org
+\end_layout
+
\end_inset
.
@@ -139,20 +70,29 @@
\family typewriter
cig-cs
\family default
- mailing list and view archived discussions at the
-\begin_inset LatexCommand htmlurl
-name "CIG Mail Lists web page"
-target "geodynamics.org/cig/lists"
+ mailing list and view archived discussions at the CIG Mail Lists web page
+
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+geodynamics.org/cig/lists
+\end_layout
+
\end_inset
.
If you encounter any bugs or have problems installing Cigma, please submit
- a report to the
-\begin_inset LatexCommand htmlurl
-name "CIG Bug Tracker"
-target "geodynamics.org/bugs"
+ a report to the CIG Bug Tracker
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+geodynamics.org/bugs
+\end_layout
+
\end_inset
.
@@ -163,11 +103,16 @@
\end_layout
\begin_layout Standard
-To install Cigma, download the source package from the
-\begin_inset LatexCommand htmlurl
-name "CIG Cigma web page"
-target "geodynamics.org/cig/software/packages/cs/cigma"
+To install Cigma, download the source package from the CIG Cigma web page
+
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+geodynamics.org/cig/software/packages/cs/cigma
+\end_layout
+
\end_inset
.
@@ -263,18 +208,27 @@
\begin_layout Standard
The Hierarchical Data Format (HDF5) library is available for download from
-
-\begin_inset LatexCommand htmlurl
-name "The HDF Group"
-target "hdfgroup.org/HDF5"
+ The HDF Group
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+hdfgroup.org/HDF5
+\end_layout
+
\end_inset
.
Binaries can be obtained at
-\begin_inset LatexCommand htmlurl
-target "hdfgroup.org/HDF5/release/obtain5.html"
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+hdfgroup.org/HDF5/release/obtain5.html
+\end_layout
+
\end_inset
.
@@ -320,20 +274,29 @@
library for scientific visualizations.
We recommend that you obtain the binaries from a package manager, making
sure to install the associated development headers along with the library.
- The source for the VTK library is available from
-\begin_inset LatexCommand htmlurl
-name "Kitware, Inc."
-target "www.vtk.org/get-software.php"
+ The source for the VTK library is available from Kitware, Inc.
+
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+www.vtk.org/get-software.php
+\end_layout
+
\end_inset
.
If you decide to compile VTK from source, you will also need the CMake
- build environment, available from
-\begin_inset LatexCommand htmlurl
-name "CMake"
-target "cmake.org"
+ build environment, available from CMake
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+cmake.org
+\end_layout
+
\end_inset
.
@@ -408,11 +371,16 @@
\begin_layout Standard
NumPy is a Python module which adds support for large multi-dimensional
- arrays and matrices, and is available for download from the
-\begin_inset LatexCommand htmlurl
-name "NumPy Home Page"
-target "numpy.scipy.org "
+ arrays and matrices, and is available for download from the NumPy Home
+ Page
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+numpy.scipy.org
+\end_layout
+
\end_inset
.
@@ -444,11 +412,15 @@
PyTables is a Python extension module that builds on top of the HDF5 library.
It provides a convenient scripting interface to manipulate HDF5 files,
which can be used to manipulate the input files needed by Cigma.
- PyTables is available for download from
-\begin_inset LatexCommand htmlurl
-name "PyTables"
-target "www.pytables.org"
+ PyTables is available for download from PyTables
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+www.pytables.org
+\end_layout
+
\end_inset
.
@@ -495,9 +467,14 @@
\begin_layout Standard
ScientificPython is available for download from
-\begin_inset LatexCommand htmlurl
-target "dirac.cnrs-orleans.fr/plone/software/scientificpython"
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+dirac.cnrs-orleans.fr/plone/software/scientificpython
+\end_layout
+
\end_inset
.
@@ -535,9 +512,14 @@
It contains algorithms for optimization, linear algebra, and other common
scientific tasks.
SciPy is available for download from
-\begin_inset LatexCommand url
-target "scipy.org"
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+scipy.org
+\end_layout
+
\end_inset
.
@@ -557,11 +539,15 @@
\end_layout
\begin_layout Standard
-FIAT is available from
-\begin_inset LatexCommand htmlurl
-name "The FEniCS Project"
-target "www.fenics.org/wiki/FIAT"
+FIAT is available from The FEniCS Project
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+www.fenics.org/wiki/FIAT
+\end_layout
+
\end_inset
.
@@ -591,11 +577,15 @@
You can use it for viewing the internal group hierarchy, adding new datasets,
and modifying or deleting existing datasets, or altering metadata on groups
and datasets.
- You can download it from the
-\begin_inset LatexCommand htmlurl
-name "HDFView home page"
-target "hdf.ncsa.uiuc.edu/hdf-java-html/hdfview"
+ You can download it from the HDFView home page
+\begin_inset Flex URL
+status collapsed
+\begin_layout Plain Layout
+
+hdf.ncsa.uiuc.edu/hdf-java-html/hdfview
+\end_layout
+
\end_inset
.
Modified: doc/cigma/manual/interpolation.lyx
===================================================================
--- doc/cigma/manual/interpolation.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/interpolation.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -1,11 +1,12 @@
-#LyX 1.5.5 created this file. For more info see http://www.lyx.org/
-\lyxformat 276
+#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 345
\begin_document
\begin_header
\textclass book
\begin_preamble
\newcommand{\mynote}[1]{}
\end_preamble
+\use_default_options false
\language english
\inputencoding auto
\font_roman default
@@ -16,9 +17,11 @@
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
+
\graphics default
\paperfontsize default
\spacing single
+\use_hyperref false
\papersize default
\use_geometry false
\use_amsmath 1
@@ -46,33 +49,33 @@
\begin_inset ERT
status collapsed
-\begin_layout Standard
+\begin_layout Plain Layout
\backslash
mynote{
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
TODO:
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* Move discussion from error_analysis.lyx and running.lyx here (done)
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* Rename document to interpolation.lyx (done)
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
Note that we place the interpolation chapter before the integration chapter
because we wish to define the isoparametric elements in here (interpolation.lyx)
@@ -80,156 +83,156 @@
rules)
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
Random Notes:
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
For parametrizing the predefined functions we would need to use boost::regex
when initializing the function from a user specified source string
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
Give list of predefined functions here
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- basic:
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* zero
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* scalar.one
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- benchmarks:
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* strikeslip.okada.disloc3d
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* cylinder_extension.{maxwell,non_newtonian}.{displacement,velocity,stress}
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* cylinder_relaxation.{maxwell,non_newtonian}.{displacement,velocity,stress}
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* circular_inclusion.pressure
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
* test.{cube,sphere,square,circle}
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Explain what is needed to define own function
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
Important things to discuss:
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Natural coordinates
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Restricting discussion to isoparametric elements
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Available elements: tet4, tet10, hex8, hex20, hex27, tri3, quad4
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Node orderings for each element type (use figures to illustrate)
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Shape functions
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Shape function derivatives
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Calculation of Jacobian
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Calculation of Volumes
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Deciding if a given point is contained in element
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Default integration rule for each element type
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Mesh Locator for finding element given an arbitrary point -- returns
list of likely elements
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
- Deciding if a given global point is contained in element (need inverse
reference map)
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
\end_layout
-\begin_layout Standard
+\begin_layout Plain Layout
}
\end_layout
@@ -271,19 +274,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-Definition of mesh here
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
A typical discretization will partition the domain of interest into a large
number of cells.
@@ -303,20 +293,6 @@
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Shape functions.
- Interpolant function.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
Once we arrive at a solution on a cell
\begin_inset Formula $\Omega_{e}$
\end_inset
@@ -329,61 +305,14 @@
Available Elements
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Reference domain.
-
-\end_layout
-
-\end_inset
-
-Fig.
- elts.jpg
-\end_layout
-
\begin_layout Subsection
Triangles and Tetrahedra
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Reference domain.
- Shape functions.
- Jacobian determinant and volume.
- Interior test.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Quadrilateral and Hexahedral Elements
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Standard
-Reference cell.
- Shape functions.
- Jacobian determinant & volume.
- Interior test.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Global Functions
\end_layout
@@ -401,497 +330,34 @@
\end_layout
\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Standard
-
-TODO: do we really need to compile every function?
-\end_layout
-
-\begin_layout Standard
-
-If the number of functions becomes unwieldy, maybe this should become a
- configure-time option.
-\end_layout
-
-\begin_layout Standard
-
-For example: we could configure cigma with the following flags:
-\end_layout
-
-\begin_layout Standard
-
- --with-all-functions=yes, --with-gale-functions=no, --with-test-functions,
- --with-foo-functions, etc..
-\end_layout
-
-\begin_layout Standard
-
-TODO: add more to the description of each function
-\end_layout
-
-\begin_layout Standard
-
-}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-TODO: Is there a way to get rid of the internal horizontal rules in the
- second column of a table?
-\end_layout
-
-\begin_layout Standard
-\begin_inset Box Frameless
-position "t"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 0
-width "100col%"
-special "none"
-height "1in"
-height_special "totalheight"
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="18" 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">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Name
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Description
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-zero
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-scalar.one
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-strikeslip.disloc3d.displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Strike-slip benchmark calculation with Okada disloc3d routine
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-strikeslip.disloc3d.velocity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-strikeslip.disloc3d.stress
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.maxwell_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Extension of Cylinder
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.maxwell_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.maxwell_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.non_newt_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Extending a cylinder with a non-newtonian material
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.non_newt_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_ext.non_newt_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.maxwell_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-Gravity relaxation of
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.maxwell_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.maxwell_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.non_newt_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.non_newt_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-cylinder_rel.non_newt_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
By default, we compile a number of functions into Cigma.
We subdivide these into three categories.
- The first class contains only two functions, zero and one, with special
- initialization rules.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-By default, we compile a number of functions into Cigma.
- We subdivide these into three categories.
The first class contains only two functions, zero and one.
The second class of functions consists of test functions intended to verify
the operation of Cigma.
Finally, the third class of functions consists of example benchmark cases
that you may use as a base for defining your own functions.
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
-There are two
- basic functions that are available, listed in the table below.
+
+\begin_inset Newline newline
+\end_inset
+
+There are two basic functions that are available, listed in the table below.
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features>
-<column alignment="left" valignment="top" leftline="true" rightline="true" width="0">
-<column alignment="left" valignment="top" rightline="true" width="0">
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
zero
@@ -899,10 +365,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Always evaluates to 0.
Compatible with scalar, vector, and tensor functions.
\end_layout
@@ -910,11 +376,11 @@
\end_inset
</cell>
</row>
-<row bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
one
@@ -922,10 +388,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Always evaluates to 1.
Only compatible with scalar functions.
\end_layout
@@ -938,9 +404,13 @@
\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
+
+\begin_inset Newline newline
+\end_inset
+
The following functions have short definitions and are available for internal
testing purposes.
Mainly, these are used to make sure Cigma returns consistent results
@@ -950,13 +420,13 @@
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features>
-<column alignment="left" valignment="top" leftline="true" width="0">
-<column alignment="left" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true">
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
test.cube
@@ -967,18 +437,18 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Scalar field in 3-dimensions
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
test.sphere
@@ -989,18 +459,18 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Vector field in 3-dimensions
\end_layout
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
test.square
@@ -1011,18 +481,18 @@
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Scalar field in 2-dimensions
\end_layout
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
test.circle
@@ -1030,10 +500,10 @@
\end_inset
</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
Vector field in 2-dimensions
\end_layout
@@ -1045,9 +515,13 @@
\end_inset
-\newline
+\begin_inset Newline newline
+\end_inset
-\newline
+
+\begin_inset Newline newline
+\end_inset
+
We can also calculate the initial step of the strike-slip benchmark (no
gravity) discussed in Chapter X.
This is based on the Okada (1992) dislocation code[?].
@@ -1057,12 +531,12 @@
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="1">
<features>
-<column alignment="left" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true">
+<column alignment="left" valignment="top" width="0">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
strikeslip.disloc3d.displacement
@@ -1071,11 +545,11 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
strikeslip.disloc3d.velocity
@@ -1084,11 +558,11 @@
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
-\begin_layout Standard
+\begin_layout Plain Layout
\family typewriter
strikeslip.disloc3d.stress
@@ -1102,257 +576,22 @@
\end_inset
-\newline
-
-\newline
-The full list of all pre-defined functions which are available by name are
- given in the appendix.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-Cylinder extension case (maxwell and non-newtonian materials)
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" columns="1">
-<features>
-<column alignment="left" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_ext.maxwell_mat.displacement
-\end_layout
-
+\begin_inset Newline newline
\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-\begin_layout Standard
-\family typewriter
-cylinder_ext.maxwell_mat.velocity
-\end_layout
-
+\begin_inset Newline newline
\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-\begin_layout Standard
-
-\family typewriter
-cylinder_ext.maxwell_mat.stress
+The full list of all pre-defined functions which are available by name are
+ given in the appendix.
\end_layout
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_ext.non_newt_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_ext.non_newt_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_ext.non_newt_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\newline
-
-\newline
-Cylinder relaxation case (maxwell and non-newtonian materials)
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" columns="1">
-<features>
-<column alignment="left" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.maxwell_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.maxwell_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.maxwell_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.non_newt_mat.displacement
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.non_newt_mat.velocity
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-cylinder_rel.non_newt_mat.stress
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\newline
-
-\newline
-Using Gale, we may compute various
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="1" columns="1">
-<features>
-<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
-<row topline="true" bottomline="true">
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-circular_inclusion.pressure
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Defining Your Own Global Function
\end_layout
\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Standard
-Show example subclass of cigma::Function.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
There are three things you need to do in order to register a new function.
These are the steps you need to follow in order to let Cigma know about
your function.
Modified: doc/cigma/manual/introduction.lyx
===================================================================
--- doc/cigma/manual/introduction.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/introduction.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -45,38 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
-Anything to emphasize here?
-\end_layout
-
-\begin_layout Plain Layout
-
- Talk about requirements: quantitative definition, automatic, verification
- of numerical codes
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
Introduction
\end_layout
@@ -155,69 +123,6 @@
vector fields.
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{implementation details -- move contents of this note to other chapters}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-At its core, Cigma draws from a variety of libraries.
- The FInite element Automatic Tabulator (FIAT)
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-www.fenics.org/wiki/FIAT
-\end_layout
-
-\end_inset
-
- Python Library supports generation of arbitrary order instances of the
- Lagrange elements on lines, triangles, and tetrahedra.
- It can also generate higher order instances of Jacobi-type quadrature rules
- on the same element shapes.
- The Approximate Nearest Neighbor (ANN)
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-www.cs.umd.edu/~mount/ANN/
-\end_layout
-
-\end_inset
-
- Library, written in C++, supports data structures and algorithms for both
- exact and nearest-neighbor searching in arbitrarily high dimensions.
-\end_layout
-
-\begin_layout Plain Layout
-Both of these libraries extend and generalize Cigma's functionality so it
- can handle other types of elements, and provide the ability to compare
- vector fields.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Citation
\end_layout
Modified: doc/cigma/manual/running.lyx
===================================================================
--- doc/cigma/manual/running.lyx 2008-12-11 11:21:27 UTC (rev 13651)
+++ doc/cigma/manual/running.lyx 2008-12-11 12:52:42 UTC (rev 13652)
@@ -45,260 +45,6 @@
\begin_body
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-In general, verify that the output of the commands, whenever given, matches
- the actual output when running a similar command
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Do not forget to mention the following:
-\end_layout
-
-\begin_layout Plain Layout
-
- - Default behaviour if a flag or option is not specified (eg., what if
- we omit --output?)
-\end_layout
-
-\begin_layout Plain Layout
-
- - Common flags:
-\end_layout
-
-\begin_layout Plain Layout
-
- Misc options: --quiet and --verbose (misc option)
-\end_layout
-
-\begin_layout Plain Layout
-
- Hidden options: --debug flag to enable logging
-\end_layout
-
-\begin_layout Plain Layout
-
- - Turn off logging if --disable-logging is given to ./configure script
- (logging on by default)
-\end_layout
-
-\begin_layout Plain Layout
-
- - The --output option needs an override flag so we can force the rewriting
- of specific datasets
-\end_layout
-
-\begin_layout Plain Layout
-
- * Default behavior? Exit if output dataset already exists
-\end_layout
-
-\begin_layout Plain Layout
-
- * Possible names if default behavior is to exit: --force-writes, --force-ou
-tput, --overwrite-output
-\end_layout
-
-\begin_layout Plain Layout
-
- * Possible names if default is to allow overwrites: --dont-overwrite
-\end_layout
-
-\begin_layout Plain Layout
-
- - Addition modifiers to compare command?
-\end_layout
-
-\begin_layout Plain Layout
-
- * Try --weighed-residuals={0,1} flag in order to divide the cell residuals
- by the volume
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Given the context of the previous chapter (on file formats), define the
-\end_layout
-
-\begin_layout Plain Layout
-
-'Dataset Path' when discussing the location of datasets within a file
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-XXX: Split the discussion of datasets and I/O into their corresponding chapters
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
- Ensure that most instances of the world 'Field' are replaced by 'Function'
-\end_layout
-
-\begin_layout Plain Layout
-
- Ensure that 'Quadrature Rule' is changed into 'Integration Rule'
-\end_layout
-
-\begin_layout Plain Layout
-
- Reference datasets in HDF5 files as 'Simple Arrays'
-\end_layout
-
-\begin_layout Plain Layout
-
- Discuss ExodusII format
-\end_layout
-
-\begin_layout Plain Layout
-
- Discuss VTK formats: Legacy VTK (.vtk), Unstructured Grid (.vtu), Structured
- Grid (.vts), Rectilinear Grid (.vtr)
-\end_layout
-
-\begin_layout Plain Layout
-
- Discuss Parallel VTK formats: *.pvtu, *.pvts, *.pvtr
-\end_layout
-
-\begin_layout Plain Layout
-
- Discuss UCD format: *.inp, *.ucd -- uses class vtkAVSucdReader from the
- VTK API
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Mention man pages as well -- which also provide an EXAMPLES section
-\end_layout
-
-\begin_layout Plain Layout
-
- Usage string from 'cigma help' displays short form of command -- using
- the positional arguments
-\end_layout
-
-\begin_layout Plain Layout
-
- Commonly used long options are also provided
-\end_layout
-
-\begin_layout Plain Layout
-
- For more advanced usage, 'man cigma-compare' would bring up more examples.
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Don't forget to mention that every positional argument can also be specified
- through the use of a long option
-\end_layout
-
-\begin_layout Plain Layout
-
-Mention common flags, such as --quiet and --verbose for tuning the amount
- of output, and --debug for turning on logging (off by default)
-\end_layout
-
-\begin_layout Plain Layout
-
-In general, --verbose should turn on the progress meter for long-running
- operations, while --quiet will emit the minimal amount of output (none
- for most commands, but the compare command should output just the (L2 norm,
- Linf norm, time in seconds))
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-Command for tracking memory usage of a running process?
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-----------------------------
-\end_layout
-
-\begin_layout Plain Layout
-
-The default data storage format for Cigma is the Hierarchical Data Format
- (HDF5), a portable file format developed at the $X .
- The HDF5 is designed for storing multi-dimensional arrays together with
- meta-data in a portable self-describing format.
- X = [National Center for Supercomputing Applications (NCSA)](hdf.ncsa.uiuc.edu/HDF
-5)
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
------------------------------------------------------
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Chapter
\begin_inset CommandInset label
LatexCommand label
@@ -374,41 +120,10 @@
, with the colon character `:' serving as a separator between the two paths.
\end_layout
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-For example, a VTK file named
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Command Line Interface
\end_layout
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-mynote{Summarize commands.
- Explain 'cigma help foo' and 'man cigma-foo'.
- Include flow diagram showing the relationship between the various commands.}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Comparing Two Finite Element Fields
\end_layout
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