Reference documentation for deal.II version Git 6454e3f 2017-06-26 22:46:01 +0200
Public Member Functions | Public Attributes | Static Private Member Functions | List of all members
PolarManifold< dim, spacedim > Class Template Reference

#include <deal.II/grid/manifold_lib.h>

Inheritance diagram for PolarManifold< dim, spacedim >:
[legend]

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 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 ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=nullptr) const
 
void unsubscribe (const char *identifier=nullptr) 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)
 

Detailed Description

template<int dim, int spacedim = dim>
class PolarManifold< dim, spacedim >

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.

Author
Luca Heltai, Mauro Bardelloni, 2014-2016

Definition at line 59 of file manifold_lib.h.

Constructor & Destructor Documentation

template<int dim, int spacedim>
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 33 of file manifold_lib.cc.

Member Function Documentation

template<int dim, int spacedim>
Point< spacedim > PolarManifold< dim, spacedim >::pull_back ( const Point< spacedim > &  space_point) const
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 85 of file manifold_lib.cc.

template<int dim, int spacedim>
Point< spacedim > PolarManifold< dim, spacedim >::push_forward ( const Point< spacedim > &  chart_point) const
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 54 of file manifold_lib.cc.

template<int dim, int spacedim>
DerivativeForm< 1, spacedim, spacedim > PolarManifold< dim, spacedim >::push_forward_gradient ( const Point< spacedim > &  chart_point) const
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 121 of file manifold_lib.cc.

template<int dim, int spacedim>
Tensor< 1, spacedim > PolarManifold< dim, spacedim >::get_periodicity ( )
staticprivate

Helper function which returns the periodicity associated with this coordinate system, according to dim, chartdim, and spacedim.

Definition at line 40 of file manifold_lib.cc.

Member Data Documentation

template<int dim, int spacedim = dim>
const Point<spacedim> PolarManifold< dim, spacedim >::center

The center of the spherical coordinate system.

Definition at line 107 of file manifold_lib.h.


The documentation for this class was generated from the following files: