Reference documentation for deal.II version 9.3.3
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Public Types | Public Member Functions | Public Attributes | Static Public Attributes | Protected Attributes | Private Attributes | List of all members
Functions::CutOffFunctionBase< dim > Class Template Reference
Functions

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

Inheritance diagram for Functions::CutOffFunctionBase< dim >:
[legend]

Public Types

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

Public Member Functions

 CutOffFunctionBase (const double radius=1., const Point< dim > center=Point< dim >(), const unsigned int n_components=1, const unsigned int select=CutOffFunctionBase< dim >::no_component, const bool integrate_to_one=false, const double unitary_integral_value=1.0)
 
virtual ~CutOffFunctionBase ()=default
 
virtual void set_center (const Point< dim > &p)
 
virtual void set_radius (const double r)
 
const Point< dim > & get_center () const
 
double get_radius () const
 
bool integrates_to_one () const
 
virtual RangeNumberType value (const Point< dim > &p, const unsigned int component=0) 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 Tensor< 1, dim, RangeNumberType > gradient (const Point< dim > &p, const unsigned int component=0) 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 SymmetricTensor< 2, dim, RangeNumberType > hessian (const Point< dim > &p, const unsigned int component=0) 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
 
virtual std::size_t memory_consumption () 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 const unsigned int no_component = numbers::invalid_unsigned_int
 
static const unsigned int dimension = dim
 

Protected Attributes

Point< dim > center
 
double radius
 
const unsigned int selected
 
bool integrate_to_one
 
const double unitary_integral_value
 
double rescaling
 

Private Attributes

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.

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)
 
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
 
using map_value_type = decltype(counter_map)::value_type
 
using map_iterator = decltype(counter_map)::iterator
 
static std::mutex mutex
 
static ::ExceptionBase & ExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBase & ExcNoSubscriber (std::string arg1, std::string arg2)
 
void check_no_subscribers () const noexcept
 

Detailed Description

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

Base function for cut-off function. This class stores the center and the radius of the supporting ball of a cut-off function. It also stores the number of the non-zero component, if the function is vector-valued.

This class can also be used for approximated Dirac delta functions. These are special cut-off functions whose integral is always equal to one, independently of the radius of the supporting ball.

Definition at line 925 of file function_lib.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

◆ CutOffFunctionBase()

template<int dim>
Functions::CutOffFunctionBase< dim >::CutOffFunctionBase ( const double  radius = 1.,
const Point< dim >  center = Point<dim>(),
const unsigned int  n_components = 1,
const unsigned int  select = CutOffFunctionBase<dim>::no_component,
const bool  integrate_to_one = false,
const double  unitary_integral_value = 1.0 
)

Constructor.

Parameters
[in]radiusRadius of the ball
[in]centerCenter of the ball
[in]n_componentsNumber of components of this function object
[in]selectIf this is different from CutOffFunctionBase<dim>::no_component, then the function will be non-zero for this component only
[in]integrate_to_oneRescale the value of the function whenever a new radius is set, to guarantee that the integral is equal to one
[in]unitary_integral_valueValue of the integral when the radius is equal to 1.0. Derived classes will need to supply this value, to guarantee that the rescaling is performed correctly.

Definition at line 30 of file function_lib_cutoff.cc.

◆ ~CutOffFunctionBase()

template<int dim>
virtual Functions::CutOffFunctionBase< dim >::~CutOffFunctionBase ( )
virtualdefault

Virtual destructor.

Member Function Documentation

◆ set_center()

template<int dim>
void Functions::CutOffFunctionBase< dim >::set_center ( const Point< dim > &  p)
virtual

Set the center of the ball to the point p.

Reimplemented in Functions::CutOffFunctionTensorProduct< dim >.

Definition at line 54 of file function_lib_cutoff.cc.

◆ set_radius()

template<int dim>
void Functions::CutOffFunctionBase< dim >::set_radius ( const double  r)
virtual

Set the radius of the ball to r

Reimplemented in Functions::CutOffFunctionTensorProduct< dim >.

Definition at line 72 of file function_lib_cutoff.cc.

◆ get_center()

template<int dim>
const Point< dim > & Functions::CutOffFunctionBase< dim >::get_center

Return the center stored in this object.

Definition at line 63 of file function_lib_cutoff.cc.

◆ get_radius()

template<int dim>
double Functions::CutOffFunctionBase< dim >::get_radius

Return the radius stored in this object.

Definition at line 87 of file function_lib_cutoff.cc.

◆ integrates_to_one()

template<int dim>
bool Functions::CutOffFunctionBase< dim >::integrates_to_one

Return a boolean indicating whether this function integrates to one.

Definition at line 96 of file function_lib_cutoff.cc.

◆ value()

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

Return the value of the function at the given point. Unless there is only one component (i.e. the function is scalar), you should state the component you want to have evaluated; it defaults to zero, i.e. the first component.

Reimplemented in Functions::CosineGradFunction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, ScalarFunctionFromFunctionObject< dim, RangeNumberType >, VectorFunctionFromScalarFunctionObject< dim, RangeNumberType >, FunctionFromFunctionObjects< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, FunctionDerivative< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::CutOffFunctionTensorProduct< dim >, Functions::CutOffFunctionLinfty< dim >, Functions::CutOffFunctionW1< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionCinfty< dim >, Functions::Monomial< dim, Number >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::Polynomial< dim >, FunctionParser< dim >, Functions::IncrementalFunction< dim, RangeNumberType >, Functions::ParsedFunction< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >, Functions::CoordinateRestriction< dim >, Functions::CSpline< dim >, Functions::LevelSet::Sphere< dim >, Functions::LevelSet::Plane< dim >, Functions::Spherical< dim >, Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, and Functions::Bessel1< dim >.

◆ 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::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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.

◆ gradient()

template<int dim, typename RangeNumberType = double>
virtual Tensor< 1, dim, RangeNumberType > Function< dim, RangeNumberType >::gradient ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

Return the gradient of the specified component of the function at the given point.

Reimplemented in Functions::LevelSet::Plane< dim >, Functions::CosineGradFunction< dim >, AutoDerivativeFunction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, FunctionFromFunctionObjects< dim, RangeNumberType >, Functions::Bessel1< dim >, Functions::CSpline< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::CutOffFunctionTensorProduct< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionCinfty< dim >, Functions::Monomial< dim, Number >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::Polynomial< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >, Functions::CoordinateRestriction< dim >, and Functions::LevelSet::Sphere< dim >.

◆ 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::ConstantFunction< dim, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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::FEFieldFunction< dim, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ 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::FEFieldFunction< dim, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ laplacian()

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

Compute the Laplacian of a given component at point p.

Reimplemented in Functions::CosineGradFunction< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >, Functions::ConstantFunction< dim, RangeNumberType >, and Functions::ConstantFunction< dim, double >.

◆ 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, DoFHandlerType, VectorType >.

◆ 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, DoFHandlerType, VectorType >.

◆ 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, DoFHandlerType, VectorType >.

◆ hessian()

template<int dim, typename RangeNumberType = double>
virtual SymmetricTensor< 2, dim, RangeNumberType > Function< dim, RangeNumberType >::hessian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

Compute the Hessian of a given component at point p, that is the gradient of the gradient of the function.

Reimplemented in Functions::LevelSet::Plane< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::CosineFunction< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::CoordinateRestriction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, and Functions::LevelSet::Sphere< dim >.

◆ 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.

◆ memory_consumption()

template<int dim, typename RangeNumberType = double>
virtual std::size_t Function< dim, RangeNumberType >::memory_consumption ( ) const
virtualinherited

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

This function is virtual and can be overloaded by derived classes.

Reimplemented in Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, ComponentSelectFunction< dim, RangeNumberType >, Functions::CSpline< dim >, FunctionDerivative< dim >, Functions::JumpFunction< dim >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::Polynomial< dim >, and Functions::Spherical< dim >.

◆ 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 numbers::NumberTraits< double >::real_type  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 numbers::NumberTraits< double >::real_type  delta_t)
virtualinherited

Advance the time by the given time step delta_t.

Member Data Documentation

◆ no_component

template<int dim>
const unsigned int Functions::CutOffFunctionBase< dim >::no_component = numbers::invalid_unsigned_int
static

Value used in the constructor of this and derived classes to denote that no component is selected.

Definition at line 932 of file function_lib.h.

◆ center

template<int dim>
Point<dim> Functions::CutOffFunctionBase< dim >::center
protected

Center of the integration ball.

Definition at line 996 of file function_lib.h.

◆ radius

template<int dim>
double Functions::CutOffFunctionBase< dim >::radius
protected

Radius of the ball.

Definition at line 1001 of file function_lib.h.

◆ selected

template<int dim>
const unsigned int Functions::CutOffFunctionBase< dim >::selected
protected

Component selected. If no_component, the function is the same in all components.

Definition at line 1007 of file function_lib.h.

◆ integrate_to_one

template<int dim>
bool Functions::CutOffFunctionBase< dim >::integrate_to_one
protected

Flag that controls whether we rescale the value when the radius changes.

Definition at line 1012 of file function_lib.h.

◆ unitary_integral_value

template<int dim>
const double Functions::CutOffFunctionBase< dim >::unitary_integral_value
protected

The reference integral value. Derived classes should specify what their integral is when radius = 1.0.

Definition at line 1018 of file function_lib.h.

◆ rescaling

template<int dim>
double Functions::CutOffFunctionBase< dim >::rescaling
protected

Current rescaling to apply the cut-off function.

Definition at line 1023 of file function_lib.h.

◆ dimension

template<int dim, typename RangeNumberType = double>
const unsigned int Function< dim, RangeNumberType >::dimension = dim
staticinherited

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.

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