Reference documentation for deal.II version 9.4.1
Searching...
No Matches
Functions::LSingularityFunction Class Reference

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

Inheritance diagram for Functions::LSingularityFunction:
[legend]

## Public Types

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

## Public Member Functions

virtual double value (const Point< 2 > &p, const unsigned int component=0) const override

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

virtual void vector_value_list (const std::vector< Point< 2 > > &points, std::vector< Vector< double > > &values) const override

virtual Tensor< 1, 2 > gradient (const Point< 2 > &p, const unsigned int component=0) const override

virtual void gradient_list (const std::vector< Point< 2 > > &points, std::vector< Tensor< 1, 2 > > &gradients, const unsigned int component=0) const override

virtual void vector_gradient_list (const std::vector< Point< 2 > > &, std::vector< std::vector< Tensor< 1, 2 > > > &) const override

virtual double laplacian (const Point< 2 > &p, const unsigned int component=0) const override

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

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

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 Tensor< 1, dim, double > gradient (const Point< dim > &p, const unsigned int component=0) 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 SymmetricTensor< 2, dim, double > hessian (const Point< dim > &p, const unsigned int component=0) 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

virtual std::size_t memory_consumption () const

Number get_time () const

virtual void set_time (const Number new_time)

virtual void advance_time (const Number delta_t)

## Public Attributes

const unsigned int n_components

## Static Public Attributes

static constexpr unsigned int dimension

Number 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 intcounter

std::map< std::string, unsigned intcounter_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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

void check_no_subscribers () const noexcept

## Detailed Description

A function that solves the Laplace equation (with specific boundary values but zero right hand side) and that has a singularity at the center of the L-shaped domain in 2D (i.e., at the location of the re-entrant corner of this non-convex domain).

The function is given in polar coordinates by $$r^{\frac{2}{3}} \sin(\frac{2}{3} \phi)$$ with a singularity at the origin and should be used with GridGenerator::hyper_L(). Here, $$\phi$$ is defined as the clockwise angle against the positive $$x$$-axis.

This function is often used to illustrate that the solutions of the Laplace equation

$-\Delta u = 0$

can be singular even if the boundary values are smooth. (Here, if the domain is the L-shaped domain $$(-1,1)^2 \backslash [0,1]^2$$, the boundary values for $$u$$ are zero on the two line segments adjacent to the origin, and equal to $$r^{\frac{2}{3}} \sin(\frac{2}{3} \phi)$$ on the remaining parts of the boundary.) The function itself remains bounded on the domain, but its gradient is of the form $$r^{-1/3}$$ in the vicinity of the origin and consequently diverges as one approaches the origin.

Definition at line 410 of file function_lib.h.

## ◆ time_type

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

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

## ◆ value() [1/2]

 double Functions::LSingularityFunction::value ( const Point< 2 > & p, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1173 of file function_lib.cc.

## ◆ value_list() [1/2]

 void Functions::LSingularityFunction::value_list ( const std::vector< Point< 2 > > & points, std::vector< double > & values, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1190 of file function_lib.cc.

## ◆ vector_value_list() [1/2]

 void Functions::LSingularityFunction::vector_value_list ( const std::vector< Point< 2 > > & points, std::vector< Vector< double > > & values ) const
overridevirtual

Definition at line 1217 of file function_lib.cc.

 Tensor< 1, 2 > Functions::LSingularityFunction::gradient ( const Point< 2 > & p, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1270 of file function_lib.cc.

 void Functions::LSingularityFunction::gradient_list ( const std::vector< Point< 2 > > & points, std::vector< Tensor< 1, 2 > > & gradients, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1290 of file function_lib.cc.

 void Functions::LSingularityFunction::vector_gradient_list ( const std::vector< Point< 2 > > & points, std::vector< std::vector< Tensor< 1, 2 > > > & gradients ) const
overridevirtual

Definition at line 1317 of file function_lib.cc.

## ◆ laplacian() [1/2]

 double Functions::LSingularityFunction::laplacian ( const Point< 2 > & p, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1247 of file function_lib.cc.

## ◆ laplacian_list() [1/2]

 void Functions::LSingularityFunction::laplacian_list ( const std::vector< Point< 2 > > & points, std::vector< double > & values, const unsigned int component = 0 ) const
overridevirtual

Definition at line 1256 of file function_lib.cc.

## ◆ value() [2/2]

 virtual double Function< dim, double >::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.

## ◆ vector_value()

 virtual void Function< dim, double >::vector_value ( const Point< dim > & p, Vector< double > & 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.

## ◆ value_list() [2/2]

 virtual void Function< dim, double >::value_list ( const std::vector< Point< dim > > & points, std::vector< double > & 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.

## ◆ vector_value_list() [2/2]

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

## ◆ vector_values()

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

 virtual Tensor< 1, dim, double > Function< dim, double >::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.

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

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

 virtual void Function< dim, double >::gradient_list ( const std::vector< Point< dim > > & points, std::vector< Tensor< 1, dim, double > > & 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.

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

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

## ◆ laplacian() [2/2]

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

Compute the Laplacian of a given component at point p.

## ◆ vector_laplacian()

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

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

## ◆ laplacian_list() [2/2]

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

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

## ◆ vector_laplacian_list()

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

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

## ◆ hessian()

 virtual SymmetricTensor< 2, dim, double > Function< dim, double >::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.

## ◆ vector_hessian()

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

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

## ◆ hessian_list()

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

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

## ◆ vector_hessian_list()

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

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

## ◆ memory_consumption()

 virtual std::size_t Function< dim, double >::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.

## ◆ get_time()

template<typename Number = double>
 Number FunctionTime< Number >::get_time ( ) const
inherited

Return the value of the time variable.

## ◆ set_time()

template<typename Number = double>
 virtual void FunctionTime< Number >::set_time ( const Number new_time )
virtualinherited

Set the time to new_time, overwriting the old value.

template<typename Number = double>
 virtual void FunctionTime< Number >::advance_time ( const Number delta_t )
virtualinherited

Advance the time by the given time step delta_t.

## ◆ dimension

 constexpr unsigned int Function< dim, double >::dimension
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

 const unsigned int Function< dim, double >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.

## ◆ time

template<typename Number = double>
 Number FunctionTime< Number >::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: