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Reference documentation for deal.II version 8.5.1
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Reference documentation for deal.II version 8.5.1
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#include <deal.II/grid/manifold_lib.h>
Public Member Functions | |
| PolarManifold (const Point< spacedim > center=Point< spacedim >()) | |
| virtual Point< spacedim > | pull_back (const Point< spacedim > &space_point) const |
| virtual Point< spacedim > | push_forward (const Point< spacedim > &chart_point) const |
| virtual DerivativeForm< 1, spacedim, spacedim > | push_forward_gradient (const Point< spacedim > &chart_point) const |
 Public Member Functions inherited from ChartManifold< dim, spacedim, spacedim > | |
| ChartManifold (const Tensor< 1, chartdim > &periodicity=Tensor< 1, chartdim >()) | |
| virtual | ~ChartManifold () |
| virtual Point< spacedim > | get_new_point (const Quadrature< spacedim > &quad) const 1 |
| virtual Point< spacedim > | get_new_point (const std::vector< Point< spacedim > > &surrounding_points, const std::vector< double > &weights) const |
| virtual void | add_new_points (const std::vector< Point< spacedim > > &surrounding_points, const Table< 2, double > &weights, std::vector< Point< spacedim > > &new_points) const |
| virtual Point< spacedim > | push_forward (const Point< chartdim > &chart_point) const=0 |
| virtual DerivativeForm< 1, chartdim, spacedim > | push_forward_gradient (const Point< chartdim > &chart_point) const |
| virtual Tensor< 1, spacedim > | get_tangent_vector (const Point< spacedim > &x1, const Point< spacedim > &x2) const |
| const Tensor< 1, chartdim > & | get_periodicity () const |
| Public Member Functions inherited from Manifold< dim, spacedim > | |
| virtual | ~Manifold () |
| virtual Point< spacedim > | get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) const |
| virtual Point< spacedim > | project_to_manifold (const std::vector< Point< spacedim > > &surrounding_points, const Point< spacedim > &candidate) const |
| virtual Point< spacedim > | get_new_point_on_line (const typename Triangulation< dim, spacedim >::line_iterator &line) const |
| virtual Point< spacedim > | get_new_point_on_quad (const typename Triangulation< dim, spacedim >::quad_iterator &quad) const |
| virtual Point< spacedim > | get_new_point_on_hex (const typename Triangulation< dim, spacedim >::hex_iterator &hex) const |
| Point< spacedim > | get_new_point_on_face (const typename Triangulation< dim, spacedim >::face_iterator &face) const |
| Point< spacedim > | get_new_point_on_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const |
| virtual Tensor< 1, spacedim > | normal_vector (const typename Triangulation< dim, spacedim >::face_iterator &face, const Point< spacedim > &p) const |
| virtual void | get_normals_at_vertices (const typename Triangulation< dim, spacedim >::face_iterator &face, FaceVertexNormals &face_vertex_normals) const |
| Public Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) |
| void | subscribe (const char *identifier=0) const |
| void | unsubscribe (const char *identifier=0) const |
| unsigned int | n_subscriptions () const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Public Attributes | |
| const Point< spacedim > | center |
Static Private Member Functions | |
| static Tensor< 1, spacedim > | get_periodicity () |
Additional Inherited Members | |
| Public Types inherited from Manifold< dim, spacedim > | |
| typedef Tensor< 1, spacedim > | FaceVertexNormals[GeometryInfo< dim >::vertices_per_face] |
| Static Public Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, char *arg2, std::string &arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (char *arg1, char *arg2) |
Manifold description for a polar coordinate system.
You can use this Manifold object to describe any sphere, circle, hypersphere or hyperdisc in two or three dimensions, both as a co-dimension one manifold descriptor or as co-dimension zero manifold descriptor, provided that the north and south poles (in three dimensions) and the center (in both two and three dimensions) are excluded from the Manifold (as they are singular points of the polar change of coordinates).
The two template arguments match the meaning of the two template arguments in Triangulation<dim, spacedim>, however this Manifold can be used to describe both thin and thick objects, and the behavior is identical when dim <= spacedim, i.e., the functionality of PolarManifold<2,3> is identical to PolarManifold<3,3>.
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 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 dimensions. These points are singular points of the coordinate transformation, and taking averages around these points does not make any sense.
Definition at line 59 of file manifold_lib.h.
| PolarManifold< dim, spacedim >::PolarManifold | ( | const Point< spacedim > | center = Point<spacedim>() | ) |
The Constructor takes the center of the spherical coordinates system. This class uses the pull_back and push_forward mechanism to transform from Cartesian to spherical coordinate systems, taking into account the periodicity of base Manifold in two dimensions, while in three dimensions it takes the middle point, and project it along the radius using the average radius of the surrounding points.
Definition at line 31 of file manifold_lib.cc.
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virtual |
Pull back the given point from the Euclidean space. Will return the polar coordinates associated with the point space_point. Only used when spacedim = 2.
Implements ChartManifold< dim, spacedim, spacedim >.
Definition at line 83 of file manifold_lib.cc.
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virtual |
Given a point in the spherical coordinate system, this method returns the Euclidean coordinates associated to the polar coordinates chart_point. Only used when spacedim = 3.
Definition at line 52 of file manifold_lib.cc.
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virtual |
Given a point in the spacedim dimensional Euclidean space, this method returns the derivatives of the function \(F\) that maps from the polar coordinate system to the Euclidean coordinate system. In other words, it is a matrix of size \(\text{spacedim}\times\text{spacedim}\).
This function is used in the computations required by the get_tangent_vector() function.
Refer to the general documentation of this class for more information.
Definition at line 119 of file manifold_lib.cc.
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staticprivate |
Helper function which returns the periodicity associated with this coordinate system, according to dim, chartdim, and spacedim.
Definition at line 38 of file manifold_lib.cc.
| const Point<spacedim> PolarManifold< dim, spacedim >::center |
The center of the spherical coordinate system.
Definition at line 107 of file manifold_lib.h.
1.8.14