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

Inheritance diagram for EllipticalManifold< dim, spacedim >:

Public Member Functions
	EllipticalManifold (const Point< spacedim > &center, const Tensor< 1, spacedim > &major_axis_direction, const double eccentricity)

virtual std::unique_ptr< Manifold< dim, spacedim > >	clone () const override

virtual Point< spacedim >	pull_back (const Point< spacedim > &space_point) const override

virtual Point< spacedim >	push_forward (const Point< spacedim > &chart_point) const override

virtual DerivativeForm< 1, spacedim, spacedim >	push_forward_gradient (const Point< spacedim > &chart_point) const override

Point< 2 >	push_forward (const Point< 2 > &chart_point) const

Point< 2 >	pull_back (const Point< 2 > &space_point) const

DerivativeForm< 1, 2, 2 >	push_forward_gradient (const Point< 2 > &chart_point) const

Public Member Functions inherited from ChartManifold< dim, dim, dim >
	ChartManifold (const Tensor< 1, chartdim > &periodicity=Tensor< 1, chartdim >())

virtual	~ChartManifold () override=default

virtual Point< spacedim >	get_intermediate_point (const Point< spacedim > &p1, const Point< spacedim > &p2, const double w) const override

virtual Point< spacedim >	get_new_point (const ArrayView< const Point< spacedim >> &surrounding_points, const ArrayView< const double > &weights) const override

virtual void	get_new_points (const ArrayView< const Point< spacedim >> &surrounding_points, const Table< 2, double > &weights, ArrayView< Point< spacedim >> new_points) const override

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 override

const Tensor< 1, chartdim > &	get_periodicity () const

Public Member Functions inherited from Manifold< dim, spacedim >
virtual	~Manifold () override=default

Tensor< 1, 2 >	normal_vector (const Triangulation< 2, 2 >::face_iterator &face, const Point< 2 > &p) const

Tensor< 1, 3 >	normal_vector (const Triangulation< 3, 3 >::face_iterator &face, const Point< 3 > &p) const

void	get_normals_at_vertices (const Triangulation< 2, 2 >::face_iterator &face, FaceVertexNormals &n) const

void	get_normals_at_vertices (const Triangulation< 3, 3 >::face_iterator &face, FaceVertexNormals &n) const

Point< 1 >	get_new_point_on_face (const Triangulation< 1, 1 >::face_iterator &) const

Point< 2 >	get_new_point_on_face (const Triangulation< 1, 2 >::face_iterator &) const

Point< 3 >	get_new_point_on_face (const Triangulation< 1, 3 >::face_iterator &) const

Point< 1 >	get_new_point_on_quad (const Triangulation< 1, 1 >::quad_iterator &) const

Point< 2 >	get_new_point_on_quad (const Triangulation< 1, 2 >::quad_iterator &) const

Point< 3 >	get_new_point_on_quad (const Triangulation< 1, 3 >::quad_iterator &) const

Point< 3 >	get_new_point_on_hex (const Triangulation< 3, 3 >::hex_iterator &hex) const

virtual Point< spacedim >	project_to_manifold (const ArrayView< const 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 &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Protected Attributes
Tensor< 1, spacedim >	direction

const Point< spacedim >	center

const double	cosh_u

const double	sinh_u

Static Private Member Functions
static Tensor< 1, spacedim >	get_periodicity ()

Additional Inherited Members
Public Types inherited from Manifold< dim, spacedim >
using	FaceVertexNormals = std::array< Tensor< 1, spacedim >, GeometryInfo< dim >::vertices_per_face >

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

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

Elliptical manifold description derived from ChartManifold. More information on the elliptical coordinate system can be found at Wikipedia .

This is based on the definition of elliptic coordinates \((u,v)\)

\[ \left\lbrace\begin{aligned} x &= x_0 + c \cosh(u) \cos(v) \\ y &= y_0 + c \sinh(u) \sin(v) \end{aligned}\right. \]

in which \((x_0,y_0)\) are coordinates of the center of the cartesian system.

The current implementation uses coordinates \((c,v)\), instead of \((u,v)\), and fixes \(u\) according to a given eccentricity. Therefore, this choice of coordinates generates an elliptical manifold characterized by a constant eccentricity: \(e=\frac{1}{\cosh(u)}\), with \(e\in\left]0,1\right[\).

The constructor of this class will throw an exception if both dim and spacedim are different from two.

This manifold can be used to produce hyper_shells with elliptical curvature. As an example, the test elliptical_manifold_01 produces the following triangulation:

Author: Stefano Dominici, 2018

Definition at line 508 of file manifold_lib.h.

Constructor & Destructor Documentation

◆ EllipticalManifold()

template<int dim, int spacedim>

EllipticalManifold< dim, spacedim >::EllipticalManifold	(	const Point< spacedim > &	center,
		const Tensor< 1, spacedim > &	major_axis_direction,
		const double	eccentricity
	)

Constructor that takes the center of the manifold system, the direction of the major axis, and the manifold eccentricity. The default major axis is the x-axis. The manifold is rotated in order to align the major axis to the direction specified in input.

Parameters

center	Center of the manifold.
major_axis_direction	Direction of the major axis of the manifold.
eccentricity	Eccentricity of the manifold \(e\in\left]0,1\right[\).

Definition at line 1203 of file manifold_lib.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< Manifold< dim, spacedim > > EllipticalManifold< dim, spacedim >::clone ( ) const

overridevirtual

Return a copy of this manifold.

Every derived class should implement this operation in a sensible manner.

Implements Manifold< dim, spacedim >.

Definition at line 1231 of file manifold_lib.cc.

◆ pull_back() [1/2]

template<int dim, int spacedim>

Point< spacedim > EllipticalManifold< dim, spacedim >::pull_back ( const Point< spacedim > & space_point ) const

overridevirtual

Pull back the given point in spacedim to the Euclidean chartdim dimensional space.

Refer to the general documentation of this class for more information.

Implements ChartManifold< dim, dim, dim >.

Definition at line 1283 of file manifold_lib.cc.

◆ push_forward() [1/2]

template<int dim, int spacedim>

Point< spacedim > EllipticalManifold< dim, spacedim >::push_forward ( const Point< spacedim > & chart_point ) const

overridevirtual

Given a point in the chartdim dimensional Euclidean space, this method returns a point on the manifold embedded in the spacedim Euclidean space.

Refer to the general documentation of this class for more information.

Definition at line 1255 of file manifold_lib.cc.

◆ push_forward_gradient() [1/2]

template<int dim, int spacedim>

DerivativeForm< 1, spacedim, spacedim > EllipticalManifold< dim, spacedim >::push_forward_gradient ( const Point< spacedim > & chart_point ) const

overridevirtual

Given a point in the chartdim dimensional Euclidean space, this method returns the derivatives of the function \(F\) that maps from the chartdim-dimensional to the spacedim-dimensional space. In other words, it is a matrix of size \(\text{spacedim}\times\text{chartdim}\).

This function is used in the computations required by the get_tangent_vector() function. Since not all users of the Manifold class interface will require calling that function, the current function is implemented but will trigger an exception whenever called. This allows derived classes to avoid implementing the push_forward_gradient function if this functionality is not needed in the user program.

Refer to the general documentation of this class for more information.

Definition at line 1325 of file manifold_lib.cc.

◆ get_periodicity()

template<int dim, int spacedim>

Tensor< 1, spacedim > EllipticalManifold< dim, spacedim >::get_periodicity

staticprivate

Return the periodicity associated with the submanifold.

For \(\text{dim}=2\) and \(\text{spacedim}=2\), the first coordinate is non-periodic, while the second coordinate has a periodicity of \(2\pi\).

Definition at line 1242 of file manifold_lib.cc.

◆ push_forward() [2/2]

Point< 2 > EllipticalManifold< 2, 2 >::push_forward ( const Point< 2 > & chart_point ) const

Definition at line 1265 of file manifold_lib.cc.

◆ pull_back() [2/2]

Point< 2 > EllipticalManifold< 2, 2 >::pull_back ( const Point< 2 > & space_point ) const

Definition at line 1293 of file manifold_lib.cc.

◆ push_forward_gradient() [2/2]

DerivativeForm< 1, 2, 2 > EllipticalManifold< 2, 2 >::push_forward_gradient ( const Point< 2 > & chart_point ) const

Definition at line 1336 of file manifold_lib.cc.

Member Data Documentation

◆ direction

template<int dim, int spacedim = dim>

Tensor<1, spacedim> EllipticalManifold< dim, spacedim >::direction

protected

The direction vector of the major axis.

Definition at line 553 of file manifold_lib.h.

◆ center

template<int dim, int spacedim = dim>

const Point<spacedim> EllipticalManifold< dim, spacedim >::center

protected

The center of the manifold.

Definition at line 557 of file manifold_lib.h.

◆ cosh_u

template<int dim, int spacedim = dim>

const double EllipticalManifold< dim, spacedim >::cosh_u

protected

Parameters deriving from the eccentricity of the manifold.

Definition at line 561 of file manifold_lib.h.

◆ sinh_u

template<int dim, int spacedim = dim>

const double EllipticalManifold< dim, spacedim >::sinh_u

protected

Definition at line 562 of file manifold_lib.h.

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

include/deal.II/grid/manifold_lib.h
source/grid/manifold_lib.cc

Public Member Functions

Protected Attributes

Static Private Member Functions

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ EllipticalManifold()

Member Function Documentation

◆ clone()

◆ pull_back() [1/2]

◆ push_forward() [1/2]

◆ push_forward_gradient() [1/2]

◆ get_periodicity()

◆ push_forward() [2/2]

◆ pull_back() [2/2]

◆ push_forward_gradient() [2/2]

Member Data Documentation

◆ direction

◆ center

◆ cosh_u

◆ sinh_u

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