[cig-commits] r16516 - doc/snac

[echoi at geodynamics.org]

Author: echoi
Date: 2010-04-09 07:19:29 -0700 (Fri, 09 Apr 2010)
New Revision: 16516

Modified:
   doc/snac/snac.lyx
Log:
Modified the "Remeshing" and "GNU Scientific Library" section.



Modified: doc/snac/snac.lyx
===================================================================
--- doc/snac/snac.lyx	2010-04-09 13:55:57 UTC (rev 16515)
+++ doc/snac/snac.lyx	2010-04-09 14:19:29 UTC (rev 16516)
@@ -1,4 +1,4 @@
-#LyX 1.6.2 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -2173,6 +2173,13 @@
 
 \begin_layout Subsection
 Remeshing
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Remeshing"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
@@ -2190,18 +2197,20 @@
  new node with respect to the old element is calculated and used to interpolate
  nodal quantities of the old deformed mesh.
  The element-associated variables (integrated by 1-point Gauss quadrature)
- are simply transferred to an element of the new mesh from its closest neighbor
- tetrahedron of the old mesh, which is found based on the distance between
- quadrature locations.
- Such a transfer is proven to be variationally consistent and also preserves
- nonlinear internal constraints as in the case of plasticity 
+ are first ``recovered'' as nodal fields by Superconvergent Patch Recovery
+ method
 \begin_inset CommandInset citation
 LatexCommand cite
-key "OrtiQuig1991"
+key "ZienZhu1992"
 
 \end_inset
 
 .
+ Like other nodal fields, these recovered fields are interpolated onto a
+ new mesh.
+ Then, element-associated variables are evaluated at the new tetrahedron's
+ barycenter, coinciding with 1-point Gauss quadrature, based on the interpolated
+ recovered fields.
  Fig.
 \begin_inset space ~
 \end_inset
@@ -2247,7 +2256,7 @@
  Although useful in some cases, this ``boundary restoring'' technique should
  be used with caution because it also creates unmappable regions and thus
  requires us to assume the state and properties of material.
- SNAC keeps the deformed boundary by default.
+ SNAC retains the deformed boundary by default.
 \end_layout
 
 \begin_layout Standard
@@ -2906,8 +2915,8 @@
 \end_layout
 
 \begin_layout Standard
-GNU Scientific Library (GSL) is a numerical library for C and C++ programmers
- (see 
+GNU Scientific Library (GSL) is ``a numerical library for C and C++ programmers'
+' (
 \begin_inset CommandInset href
 LatexCommand href
 name "http://www.gnu.org/software/gsl"
@@ -2916,21 +2925,24 @@
 \end_inset
 
 ).
- SNAC needs this library for remeshing.
- The Superconvergent Patch Recovery (SPR) method (Zienkiewicz and Zhu, 1992)
- is used to transfer element-based variables from an old mesh to a new one
- and, since based on least square optimization, this method requires a matrix
- inversion.
+ SNAC needs this library for remeshing (see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Remeshing"
+
+\end_inset
+
+) since the recovery method involves matrix inversion operations.
  So, GSL's linear algebra routines are utilized in SNAC's remesher plugin.
- Although remesher is a plugin, it is expected to be used in most geodynamic
+ Although the remesher is a plugin, it is expected to be used in most geodynamic
  applications.
  Also, the use of GSL will be expanded in the future development.
- So, GSL has become a requirment.
+ So, GSL has become a requirement.
 \end_layout
 
 \begin_layout Standard
-SNAC's build scripts will be able to find and link it if the library is
- installed in a standard location.
+SNAC's build scripts will be able to find and link GSL if it is installed
+ in a standard location.
  But if it is installed locally, one should define an environment variable,
  
 \family typewriter
@@ -11385,5 +11397,32 @@
  & Unwin.
 \end_layout
 
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "17"
+key "ZienZhu1992"
+
+\end_inset
+
+Zienkiewicz, O.C.
+ and Zhu, J.Z.
+ (1992), The superconvergent patch recovery and a posteriori error estimates.
+ Part 1: The recovery technique.
+ 
+\shape italic
+Int.
+ J.
+ Num.
+ Meth.
+ Engng.
+\shape default
+, 
+\shape italic
+33
+\shape default
+, 1331-1364.
+\end_layout
+
 \end_body
 \end_document