From: heltai <heltai@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Wed, 20 Nov 2013 15:52:46 +0000 (+0000)
Subject: Made a module for manifold.
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a110a018e05b6f57a5f654db455dc558106977f0;p=dealii-svn.git

Made a module for manifold.

git-svn-id: https://svn.dealii.org/branches/branch_manifold_id@31729 0785d39b-7218-0410-832d-ea1e28bc413d
---

diff --git a/deal.II/doc/doxygen/headers/glossary.h b/deal.II/doc/doxygen/headers/glossary.h
index ae354e18fa..d2e256d624 100644
--- a/deal.II/doc/doxygen/headers/glossary.h
+++ b/deal.II/doc/doxygen/headers/glossary.h
@@ -423,7 +423,6 @@
  *
  * @see @ref manifold "The module on Manifolds"
  *
- *
  * <dt class="glossary">@anchor GlossComponent <b>Component</b></dt>
  *
  * <dd> When considering systems of equations in which the solution is not
diff --git a/deal.II/doc/doxygen/headers/manifold.h b/deal.II/doc/doxygen/headers/manifold.h
new file mode 100644
index 0000000000..f03fd15208
--- /dev/null
+++ b/deal.II/doc/doxygen/headers/manifold.h
@@ -0,0 +1,78 @@
+// ---------------------------------------------------------------------
+// $Id: manifold.h 30130 2013-07-23 13:01:18Z heltai $
+//
+// Copyright (C) 2003 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+/**
+ * @defgroup manifold Boundary description for triangulations
+ *
+ * The classes in this module are concerned with the description of the
+ * manifold of a domain in which a Triangulation lives. This manifold
+ * description is necessary in two contexts:
+ * <ul>
+ *
+ *   <li> Mesh refinement: Whenever a cell is refined, it is necessary
+ *   to introduce some new vertices in the Triangulation. In the
+ *   simplest case, one assumes that the objects that make up the
+ *   Triangulation are straight line segments, a bi-linear surface or
+ *   a tri-linear volume, the next vertex is simply put into the
+ *   middle of the old ones. This is the default behavior of the
+ *   Triangulation class, and is described by the FlatManifold class.
+ *
+ *   On the other hand, if one deals with curved geometries, or
+ *   geometries which require a denser refinement in some direction,
+ *   this is not the appropriate thing to do. The classes derived from
+ *   the Manifold base class therefore describe the geometry of a
+ *   domain. One can then attach an object of a class derived from
+ *   this base class to the Triangulation object using the
+ *   Triangulation::set_manifold() function, and the Triangulation
+ *   will ask the manifold object where a new vertex should be located
+ *   upon mesh refinement. Several classes already exist to support
+ *   the most common geometries, e.g., CylinderManifold, or
+ *   PolarManifold, which represent respectively the geometry obtained
+ *   when describing your space in cylindrical coordintes or in polar
+ *   coordinates.
+ *
+ *   <li> Integration: When using higher order finite element methods, it is
+ *   often necessary to compute cell terms (like cell contributions to the
+ *   matrix and right hand side of the linear system) using curved
+ *   approximations of the boundary, rather than the straight line
+ *   approximation. The actual implementation of such curved elements happens
+ *   in the Mapping class (see the @ref mapping module), which however obtains
+ *   its information about the boundary of the domain from the classes
+ *   described here. The same is, of course, true when integrating boundary
+ *   terms (e.g., inhomogenous Neumann boundary conditions).
+ *
+ * </ul>
+ *
+ * In deal.II, a Manifold is seen as a collection of points, together
+ * with a notion of distance between points (on the manifold). New
+ * points are obtained by providing a local coordinate system on the
+ * manifold, identifying existing points in the local coordinate
+ * system (pulling them back using the local map to obtain their local
+ * coordinates), find the new point in the local coordinate system by
+ * weighted sums of the existing points, and transforming back the
+ * point in the real space (pushing it forward using the local map).
+ *
+ * While this process is non trivial in most cases of interest, for
+ * most of the trivial geometries, like cylinders, spheres or shells,
+ * we provide reasonable implementations. 
+ *
+ * @see @ref GlossManifoldIndicator "Glossary entry on manifold
+ * indicators"
+ *
+ * @ingroup grid
+ * @author Luca Heltai, 2013
+ */