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

Inheritance diagram for FunctionManifold< dim, spacedim, chartdim >:

Public Member Functions
	FunctionManifold (const Function< chartdim > &push_forward_function, const Function< spacedim > &pull_back_function, const Tensor< 1, chartdim > &periodicity=Tensor< 1, chartdim >(), const double tolerance=1e-10)

	FunctionManifold (const std::string push_forward_expression, const std::string pull_back_expression, const Tensor< 1, chartdim > &periodicity=Tensor< 1, chartdim >(), const typename FunctionParser< spacedim >::ConstMap=typename FunctionParser< spacedim >::ConstMap(), const std::string chart_vars=FunctionParser< chartdim >::default_variable_names(), const std::string space_vars=FunctionParser< spacedim >::default_variable_names(), const double tolerance=1e-10, const double h=1e-8)

virtual	~FunctionManifold () override

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

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

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

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

Public Member Functions inherited from ChartManifold< dim, spacedim, chartdim >
	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 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

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 (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) 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)

Private Attributes
const FunctionParser< spacedim >::ConstMap	const_map

SmartPointer< const Function< chartdim >, FunctionManifold< dim, spacedim, chartdim > >	push_forward_function

SmartPointer< const Function< spacedim >, FunctionManifold< dim, spacedim, chartdim > >	pull_back_function

const double	tolerance

const bool	owns_pointers

const std::string	push_forward_expression

const std::string	pull_back_expression

const std::string	chart_vars

const std::string	space_vars

const double	finite_difference_step

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, int chartdim = dim>
class FunctionManifold< dim, spacedim, chartdim >

Manifold description derived from ChartManifold, based on explicit Function<spacedim> and Function<chartdim> objects describing the push_forward() and pull_back() functions.

You can use this Manifold object to describe any arbitrary shape domain, as long as you can express it in terms of an invertible map, for which you provide both the forward expression, and the inverse expression.

In debug mode, a check is performed to verify that the transformations are actually one the inverse of the other.

Author: Luca Heltai, 2014

Definition at line 483 of file manifold_lib.h.

Constructor & Destructor Documentation

template<int dim, int spacedim, int chartdim>

FunctionManifold< dim, spacedim, chartdim >::FunctionManifold	(	const Function< chartdim > &	push_forward_function,
		const Function< spacedim > &	pull_back_function,
		const Tensor< 1, chartdim > &	periodicity = `Tensor<1, chartdim>()`,
		const double	tolerance = `1e-10`
	)

Explicit functions constructor. Takes a push_forward function of spacedim components, and a pull_back function of chartdim components. See the documentation of the base class ChartManifold for the meaning of the optional periodicity argument.

The tolerance argument is used in debug mode to actually check that the two functions are one the inverse of the other.

Definition at line 1155 of file manifold_lib.cc.

template<int dim, int spacedim, int chartdim>

FunctionManifold< dim, spacedim, chartdim >::FunctionManifold	(	const std::string	push_forward_expression,
		const std::string	pull_back_expression,
		const Tensor< 1, chartdim > &	periodicity = `Tensor<1, chartdim>()`,
		const typename FunctionParser< spacedim >::ConstMap	const_map = `typename FunctionParser<spacedim>::ConstMap()`,
		const std::string	chart_vars = `FunctionParser<chartdim>::default_variable_names()`,
		const std::string	space_vars = `FunctionParser<spacedim>::default_variable_names()`,
		const double	tolerance = `1e-10`,
		const double	h = `1e-8`
	)

Expressions constructor. Takes the expressions of the push_forward function of spacedim components, and of the pull_back function of chartdim components. See the documentation of the base class ChartManifold for the meaning of the optional periodicity argument.

The strings should be the readable by the default constructor of the FunctionParser classes. You can specify custom variable expressions with the last two optional arguments. If you don't, the default names are used, i.e., "x,y,z".

The tolerance argument is used in debug mode to actually check that the two functions are one the inverse of the other.

Definition at line 1174 of file manifold_lib.cc.

template<int dim, int spacedim, int chartdim>

FunctionManifold< dim, spacedim, chartdim >::~FunctionManifold ( )

overridevirtual

If needed, we delete the pointers we own.

Definition at line 1204 of file manifold_lib.cc.

Member Function Documentation

template<int dim, int spacedim, int chartdim>

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

overridevirtual

Make a clone of this Manifold object.

Implements Manifold< dim, spacedim >.

Definition at line 1222 of file manifold_lib.cc.

template<int dim, int spacedim, int chartdim>

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

overridevirtual

Given a point in the chartdim coordinate system, uses the push_forward_function to compute the push_forward of points in chartdim space dimensions to spacedim space dimensions.

Implements ChartManifold< dim, spacedim, chartdim >.

Definition at line 1258 of file manifold_lib.cc.

template<int dim, int spacedim, int chartdim>

DerivativeForm< 1, chartdim, spacedim > FunctionManifold< dim, spacedim, chartdim >::push_forward_gradient ( const Point< chartdim > & 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 sub_manifold coordinate system to the Euclidean coordinate system. 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. The default implementation calls the get_gradient() method of the FunctionManifold::push_forward_function() member class. If you construct this object using the constructor that takes two string expression, then the default implementation of this method uses a finite difference scheme to compute the gradients(see the AutoDerivativeFunction() class for details), and you can specify the size of the spatial step size at construction time with the h parameter.

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

Reimplemented from ChartManifold< dim, spacedim, chartdim >.

Definition at line 1286 of file manifold_lib.cc.

template<int dim, int spacedim, int chartdim>

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

overridevirtual

Given a point in the spacedim coordinate system, uses the pull_back_function to compute the pull_back of points in spacedim space dimensions to chartdim space dimensions.

Implements ChartManifold< dim, spacedim, chartdim >.

Definition at line 1303 of file manifold_lib.cc.