#include <deal.II/base/function_spherical.h>

Inheritance diagram for Functions::Spherical< dim >:

Public Member Functions
	Spherical (const Point< dim > &center=Point< dim >(), const unsigned int n_components=1)

virtual double	value (const Point< dim > &point, const unsigned int component=0) const override

virtual Tensor< 1, dim >	gradient (const Point< dim > &p, const unsigned int component=0) const override

virtual SymmetricTensor< 2, dim >	hessian (const Point< dim > &p, const unsigned int component=0) const override

std::size_t	memory_consumption () const

Tensor< 1, 3 >	gradient (const Point< 3 > &p_, const unsigned int component) const

SymmetricTensor< 2, 3 >	hessian (const Point< 3 > &p_, const unsigned int component) const

Public Member Functions inherited from Function< dim >
	Function (const unsigned int n_components=1, const time_type initial_time=0.0)

	Function (const Function &f)=default

virtual	~Function () override=0

Function &	operator= (const Function &f)

virtual void	vector_value (const Point< dim > &p, Vector< double > &values) const

virtual void	value_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const

virtual void	vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const

virtual void	vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const

virtual void	vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double >> &gradients) const

virtual void	gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, double >> &gradients, const unsigned int component=0) const

virtual void	vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const

virtual void	vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const

virtual double	laplacian (const Point< dim > &p, const unsigned int component=0) const

virtual void	vector_laplacian (const Point< dim > &p, Vector< double > &values) const

virtual void	laplacian_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const

virtual void	vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const

virtual void	vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, double >> &values) const

virtual void	hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, double >> &values, const unsigned int component=0) const

virtual void	vector_hessian_list (const std::vector< Point< dim >> &points, std::vector< std::vector< SymmetricTensor< 2, dim, double >>> &values) const

std::size_t	memory_consumption () const

Public Member Functions inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
	FunctionTime (const numbers::NumberTraits< double >::real_type initial_time=numbers::NumberTraits< double >::real_type(0.0))

virtual	~FunctionTime ()=default

numbers::NumberTraits< double >::real_type	get_time () const

virtual void	set_time (const numbers::NumberTraits< double >::real_type new_time)

virtual void	advance_time (const numbers::NumberTraits< double >::real_type delta_t)

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)

Private Member Functions
virtual double	svalue (const std::array< double, dim > &sp, const unsigned int component) const

virtual std::array< double, dim >	sgradient (const std::array< double, dim > &sp, const unsigned int component) const

virtual std::array< double, 6 >	shessian (const std::array< double, dim > &sp, const unsigned int component) const

Private Attributes
const Tensor< 1, dim >	coordinate_system_offset

Additional Inherited Members
Public Types inherited from Function< dim >
using	time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type

Public Types inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
using	time_type = numbers::NumberTraits< double >::real_type

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)

Public Attributes inherited from Function< dim >
const unsigned int	n_components

Static Public Attributes inherited from Function< dim >
static const unsigned int	dimension

Detailed Description

template<int dim>
class Functions::Spherical< dim >

An abstract base class for a scalar-valued function \(f=f(r,\theta,\phi)\) defined in spherical coordinates. This class wraps transformation of values, gradients and hessians from spherical coordinates to the Cartesian coordinate system used by the Function base class. Therefore derived classes only need to implement those functions in spherical coordinates (specifically svalue(), sgradient() and shessian() ). The convention for angles is the same as in GeometricUtilities::Coordinates.

Note: This function is currently only implemented for dim==3 .

Author: Denis Davydov, 2017

Definition at line 45 of file function_spherical.h.

Constructor & Destructor Documentation

◆ Spherical()

template<int dim>

Functions::Spherical< dim >::Spherical	(	const Point< dim > &	center = `Point<dim>()`,
		const unsigned int	n_components = `1`
	)

Constructor which should be provided with center defining the origin of the coordinate system.

Note that components of this function are treated as entirely separate quantities – not as the components of a vector that will be re-interpreted in a different coordinate system.

Definition at line 156 of file function_spherical.cc.

Member Function Documentation

◆ value()

template<int dim>

double Functions::Spherical< dim >::value	(	const Point< dim > &	point,
		const unsigned int	component = `0`
	)		const

overridevirtual

Return the value of the function at the given point.

This function converts the given point to spherical coordinates, calls svalue() with it, and returns the result.

Reimplemented from Function< dim >.

Definition at line 168 of file function_spherical.cc.

◆ gradient() [1/2]

template<int dim>

Tensor< 1, dim > Functions::Spherical< dim >::gradient	(	const Point< dim > &	p,
		const unsigned int	component = `0`
	)		const

overridevirtual

Return the gradient with respect to the Cartesian coordinates at point p.

This function converts the given point to spherical coordinates, calls sgradient() with it, and converts the result into Cartesian coordinates.

Reimplemented from Function< dim >.

Definition at line 181 of file function_spherical.cc.

◆ hessian() [1/2]

template<int dim>

SymmetricTensor< 2, dim > Functions::Spherical< dim >::hessian	(	const Point< dim > &	p,
		const unsigned int	component = `0`
	)		const

overridevirtual

Return the Hessian with respect to the Cartesian coordinates at point p.

This function converts the given point to spherical coordinates, calls sgradient and shessian() with it, and converts the result into Cartesian coordinates.

Reimplemented from Function< dim >.

Definition at line 237 of file function_spherical.cc.

◆ memory_consumption()

template<int dim>

std::size_t Functions::Spherical< dim >::memory_consumption

Definition at line 308 of file function_spherical.cc.

◆ svalue()

template<int dim>

double Functions::Spherical< dim >::svalue	(	const std::array< double, dim > &	sp,
		const unsigned int	component
	)		const

privatevirtual

Return the value at point sp. Here, sp is provided in spherical coordinates.

Definition at line 317 of file function_spherical.cc.

◆ sgradient()

template<int dim>

std::array< double, dim > Functions::Spherical< dim >::sgradient	(	const std::array< double, dim > &	sp,
		const unsigned int	component
	)		const

privatevirtual

Return the gradient in spherical coordinates.

The returned object should contain derivatives in the following order: \(\{ f_{,r},\, f_{,\theta},\, f_{,\phi}\}\).

Definition at line 328 of file function_spherical.cc.

◆ shessian()

template<int dim>

std::array< double, 6 > Functions::Spherical< dim >::shessian	(	const std::array< double, dim > &	sp,
		const unsigned int	component
	)		const

privatevirtual

Return the Hessian in spherical coordinates.

The returned object should contain derivatives in the following order: \(\{ f_{,rr},\, f_{,\theta\theta},\, f_{,\phi\phi},\, f_{,r\theta},\, f_{,r\phi},\, f_{,\theta\phi}\}\).

Definition at line 339 of file function_spherical.cc.

◆ gradient() [2/2]

Tensor< 1, 3 > Functions::Spherical< 3 >::gradient	(	const Point< 3 > &	p_,
		const unsigned int	component
	)		const

Definition at line 193 of file function_spherical.cc.

◆ hessian() [2/2]

SymmetricTensor< 2, 3 > Functions::Spherical< 3 >::hessian	(	const Point< 3 > &	p_,
		const unsigned int	component
	)		const

Definition at line 248 of file function_spherical.cc.

Member Data Documentation

◆ coordinate_system_offset

template<int dim>

const Tensor<1, dim> Functions::Spherical< dim >::coordinate_system_offset

private

A vector from the origin to the center of spherical coordinate system.

Definition at line 127 of file function_spherical.h.

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

include/deal.II/base/function_spherical.h
source/base/function_spherical.cc

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim> class Functions::Spherical< dim >

Constructor & Destructor Documentation

◆ Spherical()

Member Function Documentation

◆ value()

◆ gradient() [1/2]

◆ hessian() [1/2]

◆ memory_consumption()

◆ svalue()

◆ sgradient()

◆ shessian()

◆ gradient() [2/2]

◆ hessian() [2/2]

Member Data Documentation

◆ coordinate_system_offset

template<int dim>
class Functions::Spherical< dim >