Reference documentation for deal.II version GIT 0f6eca7a35 2022-05-23 02:45:01+00:00
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Public Types | Public Member Functions | Public Attributes | Static Public Attributes | Private Member Functions | Private Attributes | List of all members
Functions::Spherical< dim > Class Template Reference

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

Inheritance diagram for Functions::Spherical< dim >:
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Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type
 

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
 
virtual std::size_t memory_consumption () const override
 
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
 
virtual void vector_value (const Point< dim > &p, Vector< RangeNumberType > &values) const
 
virtual void value_list (const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
 
virtual void vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const
 
virtual void vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< RangeNumberType >> &values) const
 
virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients) const
 
virtual void gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients, const unsigned int component=0) const
 
virtual void vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const
 
virtual void vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const
 
virtual RangeNumberType laplacian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_laplacian (const Point< dim > &p, Vector< RangeNumberType > &values) const
 
virtual void laplacian_list (const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
 
virtual void vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const
 
virtual void vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &values) const
 
virtual void hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &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, RangeNumberType >>> &values) const
 
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 Attributes

const unsigned int n_components
 

Static Public Attributes

static constexpr unsigned int dimension = dim
 

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
 
numbers::NumberTraits< double >::real_type time
 

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

std::atomic< unsigned int > counter
 
std::map< std::string, unsigned int > counter_map
 
std::vector< std::atomic< bool > * > validity_pointers
 
const std::type_info * object_info
 
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)
 
void check_no_subscribers () const noexcept
 
using map_value_type = decltype(counter_map)::value_type
 
using map_iterator = decltype(counter_map)::iterator
 
static std::mutex mutex
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

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 .

Definition at line 44 of file function_spherical.h.

Member Typedef Documentation

◆ time_type

template<int dim, typename RangeNumberType = double>
using Function< dim, RangeNumberType >::time_type = typename FunctionTime< typename numbers::NumberTraits<RangeNumberType>::real_type>::time_type
inherited

The scalar-valued real type used for representing time.

Definition at line 169 of file function.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 158 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, RangeNumberType >.

Definition at line 170 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, RangeNumberType >.

Definition at line 183 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, RangeNumberType >.

Definition at line 239 of file function_spherical.cc.

◆ memory_consumption()

template<int dim>
std::size_t Functions::Spherical< dim >::memory_consumption
overridevirtual

Return an estimate for the memory consumption, in bytes, of this object.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 310 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 319 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 330 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 341 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 195 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 250 of file function_spherical.cc.

◆ vector_value()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_value ( const Point< dim > &  p,
Vector< RangeNumberType > &  values 
) const
virtualinherited

Return all components of a vector-valued function at a given point.

values shall have the right size beforehand, i.e. n_components.

The default implementation will call value() for each component.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, double >.

◆ value_list()

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

Set values to the point values of the specified component of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array.

By default, this function repeatedly calls value() for each point separately, to fill the output array.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, double >.

◆ vector_value_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_value_list ( const std::vector< Point< dim >> &  points,
std::vector< Vector< RangeNumberType >> &  values 
) const
virtualinherited

Set values to the point values of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array, and that all elements be vectors with the same number of components as this function has.

By default, this function repeatedly calls vector_value() for each point separately, to fill the output array.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, double >.

◆ vector_values()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_values ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< RangeNumberType >> &  values 
) const
virtualinherited

For each component of the function, fill a vector of values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

◆ vector_gradient()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradient ( const Point< dim > &  p,
std::vector< Tensor< 1, dim, RangeNumberType >> &  gradients 
) const
virtualinherited

Return the gradient of all components of the function at the given point.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, double >.

◆ gradient_list()

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

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_gradients()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradients ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &  gradients 
) const
virtualinherited

For each component of the function, fill a vector of gradient values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

◆ vector_gradient_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradient_list ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &  gradients 
) const
virtualinherited

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

Reimplemented in Functions::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ laplacian()

template<int dim, typename RangeNumberType = double>
virtual RangeNumberType Function< dim, RangeNumberType >::laplacian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_laplacian()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_laplacian ( const Point< dim > &  p,
Vector< RangeNumberType > &  values 
) const
virtualinherited

Compute the Laplacian of all components at point p and store them in values.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ laplacian_list()

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

Compute the Laplacian of one component at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_laplacian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_laplacian_list ( const std::vector< Point< dim >> &  points,
std::vector< Vector< RangeNumberType >> &  values 
) const
virtualinherited

Compute the Laplacians of all components at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_hessian()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_hessian ( const Point< dim > &  p,
std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &  values 
) const
virtualinherited

Compute the Hessian of all components at point p and store them in values.

◆ hessian_list()

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

Compute the Hessian of one component at a set of points.

◆ vector_hessian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_hessian_list ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType >>> &  values 
) const
virtualinherited

Compute the Hessians of all components at a set of points.

◆ get_time()

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

Return the value of the time variable.

◆ set_time()

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

Set the time to new_time, overwriting the old value.

◆ advance_time()

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

Advance the time by the given time step delta_t.

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 129 of file function_spherical.h.

◆ dimension

template<int dim, typename RangeNumberType = double>
constexpr unsigned int Function< dim, RangeNumberType >::dimension = dim
staticconstexprinherited

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 159 of file function.h.

◆ n_components

template<int dim, typename RangeNumberType = double>
const unsigned int Function< dim, RangeNumberType >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.

◆ time

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::time
privateinherited

Store the present time.

Definition at line 113 of file function_time.h.


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