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`, `std::complex<float>`, etc.

using	geometry_type = U
	Geometry type of the Mesh that the Function is defined on.

Public Member Functions
	Function (std::shared_ptr< const FunctionSpace< U > > V)
	Create function on given function space.

	Function (std::shared_ptr< const FunctionSpace< U > > V, std::shared_ptr< la::Vector< T > > x)
	Create function on given function space with a given vector.

	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 sub-function (a view into the Function).

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

std::shared_ptr< const FunctionSpace< U > >	function_space () const
	Access the function space.

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, U > &v, std::span< const std::int32_t > cells, const std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< U >, std::vector< std::int32_t > > &nmm_interpolation_data={})
	Interpolate a provided Function.

void	interpolate (const Function< T, U > &v, const std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< U >, std::vector< std::int32_t > > &nmm_interpolation_data={})
	Interpolate a provided Function.

void	interpolate (const std::function< std::pair< std::vector< T >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const U, MDSPAN_IMPL_STANDARD_NAMESPACE::extents< std::size_t, 3, MDSPAN_IMPL_STANDARD_NAMESPACE::dynamic_extent > >)> &f, std::span< const std::int32_t > cells)
	Interpolate an expression function on a list of cells.

void	interpolate (const std::function< std::pair< std::vector< T >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const U, MDSPAN_IMPL_STANDARD_NAMESPACE::extents< std::size_t, 3, MDSPAN_IMPL_STANDARD_NAMESPACE::dynamic_extent > >)> &f)
	Interpolate an expression function on the whole domain.

void	interpolate (const Expression< T, U > &e, std::span< const std::int32_t > cells)
	Interpolate an Expression (based on UFL)

void	interpolate (const Expression< T, U > &e)
	Interpolate an Expression (based on UFL) on all cells.

void	eval (std::span< const U > 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.

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

Detailed Description

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>
class dolfinx::fem::Function< T, U >

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 \( u_h \).

Template Parameters

T	The function scalar type.
U	The mesh geometry scalar type.

Constructor & Destructor Documentation

◆ Function() [1/2]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

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

inlineexplicit

Create function on given function space.

Parameters

[in] V The function space

◆ Function() [2/2]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

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

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

Function collapse ( ) const

inline

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

Returns: New collapsed Function.

◆ eval()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void eval	(	std::span< const U >	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()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

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

inline

Access the function space.

Returns: The function space

◆ interpolate() [1/6]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void interpolate ( const Expression< T, U > & e )

inline

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

Parameters

[in] e The function to be interpolated

◆ interpolate() [2/6]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

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

inline

Interpolate an Expression (based on UFL)

Parameters

[in]	e	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]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void interpolate	(	const Function< T, U > &	v,
		const std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< U >, std::vector< std::int32_t > > &	nmm_interpolation_data = `{}`
	)

inline

Interpolate a provided Function.

Parameters

[in]	v	The function to be interpolated
[in]	nmm_interpolation_data	Auxiliary data to interpolate on nonmatching meshes. This data can be generated with generate_nonmatching_meshes_interpolation_data (optional).

◆ interpolate() [4/6]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void interpolate	(	const Function< T, U > &	v,
		std::span< const std::int32_t >	cells,
		const std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< U >, std::vector< std::int32_t > > &	nmm_interpolation_data = `{}`
	)

inline

Interpolate a provided Function.

Parameters

[in]	v	The function to be interpolated
[in]	cells	The cells to interpolate on
[in]	nmm_interpolation_data	Auxiliary data to interpolate on nonmatching meshes. This data can be generated with generate_nonmatching_meshes_interpolation_data (optional).

◆ interpolate() [5/6]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void interpolate ( const std::function< std::pair< std::vector< T >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const U, MDSPAN_IMPL_STANDARD_NAMESPACE::extents< std::size_t, 3, MDSPAN_IMPL_STANDARD_NAMESPACE::dynamic_extent > >)> & f )

inline

Interpolate an expression function on the whole domain.

Parameters

[in] f Expression to be interpolated

◆ interpolate() [6/6]

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

void interpolate	(	const std::function< std::pair< std::vector< T >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const U, MDSPAN_IMPL_STANDARD_NAMESPACE::extents< std::size_t, 3, MDSPAN_IMPL_STANDARD_NAMESPACE::dynamic_extent > >)> &	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()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

Function sub ( int i ) const

inline

Extract sub-function (a view into the Function).

Parameters

[in] i Index of subfunction

Returns: The sub-function

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

Public Types

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Function() [1/2]

◆ Function() [2/2]

Member Function Documentation

◆ collapse()

◆ eval()

◆ function_space()

◆ interpolate() [1/6]

◆ interpolate() [2/6]

◆ interpolate() [3/6]

◆ interpolate() [4/6]

◆ interpolate() [5/6]

◆ interpolate() [6/6]

◆ sub()