Function< T > Class Template Reference

This class represents a function \( u_h \) in a finite element function space \( V_h \), given by. More...

#include <Function.h>

Public Types
using	value_type = T
	Field type for the Function, e.g. double.

Public Member Functions
	Function (std::shared_ptr< const FunctionSpace > V)
	Create function on given function space. More...
	Function (std::shared_ptr< const FunctionSpace > V, std::shared_ptr< la::Vector< T >> x)
	Create function on given function space with a given vector. More...
	Function (const Function &v)=delete
	Function (Function &&v)=default
	Move constructor.
	~Function ()=default
	Destructor.
Function &	operator= (Function &&v)=default
	Move assignment.
Function &	operator= (const Function &v)=delete
Function	sub (int i) const
	Extract subfunction (view into the Function) More...
Function	collapse () const
	Collapse a subfunction (view into a Function) to a stand-alone Function. More...
std::shared_ptr< const FunctionSpace >	function_space () const
	Access the function space. More...
std::shared_ptr< const la::Vector< T > >	x () const
	Underlying vector.
std::shared_ptr< la::Vector< T > >	x ()
	Underlying vector.
void	interpolate (const Function< T > &v, std::span< const std::int32_t > cells)
	Interpolate a Function. More...
void	interpolate (const Function< T > &v)
	Interpolate a Function. More...
void	interpolate (const std::function< xt::xarray< T >(const xt::xtensor< double, 2 > &)> &f, std::span< const std::int32_t > cells)
	Interpolate an expression function on a list of cells. More...
void	interpolate (const std::function< xt::xarray< T >(const xt::xtensor< double, 2 > &)> &f)
	Interpolate an expression function on the whole domain. More...
void	interpolate (const Expression< T > &e, std::span< const std::int32_t > cells)
	Interpolate an Expression (based on UFL) More...
void	interpolate (const Expression< T > &e)
	Interpolate an Expression (based on UFL) on all cells. More...
void	eval (std::span< const double > x, std::array< std::size_t, 2 > xshape, std::span< const std::int32_t > cells, std::span< T > u, std::array< std::size_t, 2 > ushape) const
	Evaluate the Function at points. More...

Public Attributes
std::string	name = "u"
	Name.

Detailed Description

template<typename T>
class dolfinx::fem::Function< T >

This class represents a function \( u_h \) in a finite element function space \( V_h \), given by.

\[ u_h = \sum_{i=1}^{n} U_i \phi_i \]

where \( \{\phi_i\}_{i=1}^{n} \) is a basis for \( V_h \), and \( U \) is a vector of expansion coefficients for \( u_h \).

Constructor & Destructor Documentation

Function() [1/2]

Function ( std::shared_ptr< const FunctionSpace >  V )

inlineexplicit

Create function on given function space.

Parameters

[in]

V

The function space

Function() [2/2]

Function ( std::shared_ptr< const FunctionSpace >  V, std::shared_ptr< la::Vector< T >>  x  )

inline

Create function on given function space with a given vector.

Warning

This constructor is intended for internal library use only

Parameters

[in]	V	The function space
[in]	x	The vector

Member Function Documentation

collapse()

Function collapse ( ) const

inline

Collapse a subfunction (view into a Function) to a stand-alone Function.

Returns

New collapsed Function

eval()

void eval ( std::span< const double >  x, std::array< std::size_t, 2 >  xshape, std::span< const std::int32_t >  cells, std::span< T >  u, std::array< std::size_t, 2 >  ushape  ) const

inline

Evaluate the Function at points.

Parameters

[in]	x	The coordinates of the points. It has shape (num_points, 3) and storage is row-major.
[in]	xshape	The shape of x.
[in]	cells	An array of cell indices. cells[i] is the index of the cell that contains the point x(i). Negative cell indices can be passed, and the corresponding point will be ignored.
[out]	u	The values at the points. Values are not computed for points with a negative cell index. This argument must be passed with the correct size. Storage is row-major.
[in]	ushape	The shape of u.

function_space()

std::shared_ptr<const FunctionSpace> function_space ( ) const

inline

Access the function space.

Returns

The function space

interpolate() [1/6]

void interpolate ( const Expression< T > &  e )

inline

Interpolate an Expression (based on UFL) on all cells.

Parameters

[in]

e

The function to be interpolated

interpolate() [2/6]

void interpolate ( const Expression< T > &  e, std::span< const std::int32_t >  cells  )

inline

Interpolate an Expression (based on UFL)

Parameters

[in]	e	The Expression to be interpolated. The Expression must have been created using the reference coordinates FiniteElement::interpolation_points() for the element associated with u.
[in]	cells	The cells to interpolate on

interpolate() [3/6]

void interpolate ( const Function< T > &  v )

inline

Interpolate a Function.

Parameters

[in]

v

The function to be interpolated

interpolate() [4/6]

void interpolate ( const Function< T > &  v, std::span< const std::int32_t >  cells  )

inline

Interpolate a Function.

Parameters

[in]	v	The function to be interpolated
[in]	cells	The cells to interpolate on

interpolate() [5/6]

void interpolate ( const std::function< xt::xarray< T >(const xt::xtensor< double, 2 > &)> &  f )

inline

Interpolate an expression function on the whole domain.

Parameters

[in]

f

The expression to be interpolated

interpolate() [6/6]

void interpolate ( const std::function< xt::xarray< T >(const xt::xtensor< double, 2 > &)> &  f, std::span< const std::int32_t >  cells  )

inline

Interpolate an expression function on a list of cells.

Parameters

[in]	f	The expression function to be interpolated
[in]	cells	The cells to interpolate on

sub()

Function sub ( int  i ) const

inline

Extract subfunction (view into the Function)

Parameters

[in]

i

Index of subfunction

Returns

The subfunction

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

• /__w/dolfinx/dolfinx/cpp/dolfinx/fem/Form.h
• /__w/dolfinx/dolfinx/cpp/dolfinx/fem/Function.h