# [cig-commits] r13276 - doc/snac

echoi at geodynamics.org echoi at geodynamics.org
Sat Nov 8 17:46:02 PST 2008

Author: echoi
Date: 2008-11-08 17:46:02 -0800 (Sat, 08 Nov 2008)
New Revision: 13276

Modified:
doc/snac/snac.lyx
Log:
The Remeshing section updated.

Modified: doc/snac/snac.lyx
===================================================================
--- doc/snac/snac.lyx	2008-11-08 00:24:07 UTC (rev 13275)
+++ doc/snac/snac.lyx	2008-11-09 01:46:02 UTC (rev 13276)
@@ -1387,8 +1387,8 @@
\end_layout

\begin_layout Standard
-Remeshing becomes necessary in SNAC through the large deformations associated
- with plate tectension.
+Remeshing becomes necessary in SNAC when continued deformation distorts
+ a mesh so severely that the accuracy of solutions are deteriorated.
In SNAC, remeshing is done by moving the nodes back to their original positions
, under the constraint that physically meaningful features such as top and
bottom topography are conserved.
@@ -1399,7 +1399,8 @@
mesh which contains a node of the new mesh.
Then shape (interpolation) functions corresponding to the location of the
new node with respect to the old element is calculated and used to interpolate
- nodal quantities of the old mesh.
+ nodal quantities of the old mdeformed through the large deformations associated
+ with plate tectension.esh.
In the case of the elemental variables (integrated by 1-point Gauss quadrature)
, the quantities are simply transferred to an element of the new mesh from
its closest neighbor tetrahedron of the old mesh, which is found based
@@ -1419,15 +1420,34 @@
\end_inset

demonstrates how remeshing actually works.
- Note that Fig.

+\end_layout
+
+\begin_layout Standard
+This remeshing algorithm, however, has some limitations.
+ Domain decomposition, the parallelism implemented in SNAC, often makes
+ it difficult to map variables between meshes when a parallel boundary of
+ the old mesh has moved too far away from the corresponding one of the new
+ mesh.
+ Also, the current way of remeshing works best in the case of lateral extension
+ because the nodes are moved back to their original positions.
+ If a mesh has shrinked laterally, then it is impossible to remap variables
+ for the regions of a new mesh that do not have corresponding parts in the
+ deformed mesh.
+ In such a case, one would have to
+\emph on
+assume
+\emph default
+ states and properties of material for the unmappable regions.
+ Finally, note that Fig.
+
\begin_inset LatexCommand ref
reference "fig:Remeshing.-Lagrangian-mesh"

\end_inset

(b) shows that remeshing can not only generate a more regular mesh but also
- change the boundary.
+ change the bottom boundary of the domain.
Although useful in some cases, this
\begin_inset Quotes sld
\end_inset
@@ -1436,7 +1456,8 @@
\begin_inset Quotes srd
\end_inset

- technique should be used with caution.
+ technique should be used with caution because it also creates unmappable
+ regions and thus requires to assume the state and properties of material.
SNAC keeps the deformed boundary by default.
\end_layout