In the program, we will use a spherical shell as domain. This means
that the inner and outer boundary of the domain are no longer
"straight" (by which we usually mean that they are bilinear surfaces
-that can be represented by the StraightBoundary class). Rather, they
+that can be represented by the FlatManifold class). Rather, they
are curved and it seems prudent to use a curved approximation in the
program if we are already using higher order finite elements for the
velocity. Consequently, we will introduce a member variable of type
template <int spacedim>
void LaplaceBeltrami<spacedim>::make_grid_and_dofs ()
{
- static HyperBallBoundary<dim,spacedim> surface_description;
- triangulation.set_boundary (0, surface_description);
+ static SphericalManifold<dim,spacedim> surface_description;
+ triangulation.set_manifold (0, surface_description);
{
- HyperBallBoundary<spacedim> boundary_description;
+ SphericalManifold<spacedim> boundary_description;
Triangulation<spacedim> volume_mesh;
GridGenerator::half_hyper_ball(volume_mesh);
- volume_mesh.set_boundary (0, boundary_description);
+ volume_mesh.set_manifold (0, boundary_description);
volume_mesh.refine_global (4);
std::set<unsigned char> boundary_ids;
GridGenerator::extract_boundary_mesh (volume_mesh, triangulation,
boundary_ids);
- triangulation.set_boundary (1); /* ** */
- triangulation.set_boundary (0); /* ** */
+ triangulation.set_manifold (1); /* ** */
+ triangulation.set_manifold (0); /* ** */
GridTools::transform (&warp<spacedim>, triangulation); /* ** */
std::ofstream x("x"), y("y");
GridOut().write_gnuplot (volume_mesh, x);
detach the manifold description from the surface mesh, whenever we use a
mapping object in the rest of the program, it has no curves boundary
description to go on any more. Rather, it will have to use the implicit,
-StraightBoundary class that is used on all parts of the boundary not
+FlatManifold class that is used on all parts of the domain not
explicitly assigned a different manifold object. Consequently, whether we use
MappingQ(2), MappingQ(15) or MappingQ1, each cell of our mesh will be mapped
using a bilinear approximation.
possible to access all the sub-shapes (such as vertices, edges and faces)
composing it, along with their geometrical description. In the deal.II
framework, the topological entities composing a shape are used to create
-objects of the Manifold or Boundary classes. In Step-6 we saw how to build a
-HyperBallBoundary and assign it to a set of faces (or cells, for co-dimension
+a corresponding Manifold representation. In Step-6 we saw how to build a
+SphericalManifold and assign it to a set of faces (or cells, for co-dimension
1) of a Triangulation, to have cells and faces refined on a sphere or circle.
The functions of the CAD modeling interface have been designed to retain the
same structure, allowing the user to build a projector object using the
imported CAD shapes, maintaining the very same procedure we use with
-HyperBallBoundary, i.e., assigning such projector object to cells, faces or
+SphericalManifold, i.e., assigning such projector object to cells, faces or
edges of a coarse mesh. At each refinement cycle, the new mesh nodes will be
then automatically generated by projecting a midpoint of an existing object
onto the specified geometry.
Differently from a spherical or circular boundary, a boundary with a complex
geometry poses problems as to where it is best to place the new nodes created
-upon refinement on the prescribed shape. HyperBallBoundary first creates the
-new nodes on the face or edge to be refined by averaging the surrounding
-points in the same way as FlatManifold does. Then, it goes on to project such
-nodes on the circle or sphere along the radial direction. On such a geometry,
-the radial direction ensures that the newly generated nodes remain evenly
-spaced when remaining on a given refinement level.
-
-In the case of an arbitrary and complex shape though, the best direction of
-the projection cannot be identified that easily. The OpenCASCADE wrappers in
-deal.II provide several projector classes that employ different projection
-strategies. A first projector, implemented in the
+upon refinement on the prescribed shape. PolarManifold, for example, transforms
+the surrounding points to polar coordinates, calculates the average in that
+coordinate system (for each coordinate individually) and finally transforms
+the point back to Cartesian coordinates.
+
+In the case of an arbitrary and complex shape though, an appropriate choice for
+the placement of a new node cannot be identified that easily. The OpenCASCADE
+wrappers in deal.II provide several projector classes that employ different
+projection strategies. A first projector, implemented in the
OpenCASCADE::ArclengthProjectionLineManifold class, is to be used only for
edge refinement. It is built assigning it a topological shape of dimension
one, either a <code>TopoDS_Edge</code> or a <code>TopoDS_Wire</code> (which is
* mesh. The surface mesh is then refined in the same way as the faces of
* the volume mesh are. In order to ensure that the surface mesh has the
* same vertices as the volume mesh, it is therefore important that you
- * assign appropriate boundary objects through Triangulation::set_boundary()
- * to the surface mesh object before calling this function. If you don't,
- * the refinement will happen under the assumption that all faces are
- * straight (i.e using the StraightBoundary class) rather than any curved
- * boundary object you may want to use to determine the location of new
- * vertices.
+ * assign appropriate boundary descriptions through
+ * Triangulation::set_manifold() to the surface mesh object before calling
+ * this function. If you don't, the refinement will happen under the
+ * assumption that all faces are straight (i.e using the FlatManifold class)
+ * rather than utilizing the Manifold object you may want to use to determine
+ * the location of new vertices.
*
* @tparam MeshType A type that satisfies the requirements of the
* @ref ConceptMeshType "MeshType concept".
* The face iterator gives an indication which face this function is
* supposed to compute the normal vector for. This is useful if the
* boundary of the domain is composed of different nondifferential
- * pieces (for example when using the StraightBoundary class to
+ * pieces (for example when using the FlatManifold class to
* approximate a geometry that is completely described by the coarse
* mesh, with piecewise (bi-)linear components between the vertices,
* but where the boundary may have a kink at the vertices itself).
*
* This class works by transforming points to polar coordinates (in
* both two and three dimensions), taking the average in that
- * coordinate system, and then transforming back the point to
+ * coordinate system, and then transforming the point back to
* Cartesian coordinates. In order for this manifold to work
* correctly, it cannot be attached to cells containing the center of
* the coordinate system or the north and south poles in three
projects / dealii.git / commitdiff