#include <Function.h>

Public Types
using	value_type = T

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

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

	Function (std::shared_ptr< const FunctionSpace< geometry_type > > V, std::shared_ptr< la::Vector< value_type > > 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 a 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< geometry_type > >	function_space () const
	Access the function space.

std::shared_ptr< const la::Vector< value_type > >	x () const
	Underlying vector (const version).

std::shared_ptr< la::Vector< value_type > >	x ()
	Underlying vector.

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

void	interpolate (const std::function< std::pair< std::vector< value_type >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const geometry_type, 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 f(x) over a set of cells.

void	interpolate (const Function< value_type, geometry_type > &u)
	Interpolate a Function over all cells.

void	interpolate (const Function< value_type, geometry_type > &u0, std::span< const std::int32_t > cells0, std::span< const std::int32_t > cells1={})
	Interpolate a Function over a subset of cells.

void	interpolate (const Expression< value_type, geometry_type > &e)
	Interpolate an Expression on all cells.

void	interpolate (const Expression< value_type, geometry_type > &e0, std::span< const std::int32_t > cells0, std::span< const std::int32_t > cells1={})
	Interpolate an Expression over a subset of cells.

void	interpolate (const Function< value_type, geometry_type > &v, std::span< const std::int32_t > cells, const geometry::PointOwnershipData< U > &interpolation_data)
	Interpolate a Function defined on a different mesh.

void	eval (std::span< const geometry_type > x, std::array< std::size_t, 2 > xshape, std::span< const std::int32_t > cells, std::span< value_type > 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>
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.

Member Typedef Documentation

◆ value_type

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

using value_type = T

Field type for the Function, e.g. double, std::complex<float>, etc.

Constructor & Destructor Documentation

◆ Function() [1/2]

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

Function ( std::shared_ptr< const FunctionSpace< geometry_type > > 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>

Function	(	std::shared_ptr< const FunctionSpace< geometry_type > >	V,
		std::shared_ptr< la::Vector< value_type > >	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>

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>

void eval	(	std::span< const geometry_type >	x,
		std::array< std::size_t, 2 >	xshape,
		std::span< const std::int32_t >	cells,
		std::span< value_type >	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	Shape of `x`.
[in]	cells	Cell indices such that `cells[i]` is the index of the cell that contains the point x(i). Negative cell indices can be passed, in which case the corresponding point is ignored.
[out]	u	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	Shape of `u`.

◆ function_space()

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

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

inline

Access the function space.

Returns: The function space.

◆ interpolate() [1/7]

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

void interpolate ( const Expression< value_type, geometry_type > & e )

inline

Interpolate an Expression on all cells.

Parameters

[in] e Expression to be interpolated.

Precondition: If a mesh is associated with Function coefficients of e, it must be the same as the mesh::Mesh associated with this.

◆ interpolate() [2/7]

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

void interpolate	(	const Expression< value_type, geometry_type > &	e0,
		std::span< const std::int32_t >	cells0,
		std::span< const std::int32_t >	cells1 = {} )

inline

Interpolate an Expression over a subset of cells.

Parameters

[in]	e0	Expression to be interpolated. The Expression must have been created using the reference coordinates created by FiniteElement::interpolation_points for the element associated with `this`.
[in]	cells0	Cells in the mesh associated with `e0` to interpolate from if `e0` has Function coefficients. If no mesh can be associated with `e0` then the mesh associated with `this` is used.
[in]	cells1	Cell indices associated with the mesh of `this` that will be interpolated to. If `cells0[i]` is the index of a cell in the mesh associated with `u0`, then `cells1[i]` is the index of the same cell but in the mesh associated with `this`. This argument can be empty when `this` and `u0` share the same mesh. Otherwise the length of `cells` and the length of `cells0` must be the same.

◆ interpolate() [3/7]

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

void interpolate ( const Function< value_type, geometry_type > & u )

inline

Interpolate a Function over all cells.

Parameters

[in] u Function to be interpolated.

Precondition: The mesh associated with this and the mesh associated with u must be the same mesh::Mesh.

◆ interpolate() [4/7]

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

void interpolate	(	const Function< value_type, geometry_type > &	u0,
		std::span< const std::int32_t >	cells0,
		std::span< const std::int32_t >	cells1 = {} )

inline

Interpolate a Function over a subset of cells.

The Function being interpolated from and the Function being interpolated into can be defined on different sub-meshes, i.e. views into a subset a cells.

Parameters

[in]	u0	Function to be interpolated.
[in]	cells0	Cells to interpolate from. These are the indices of the cells in the mesh associated with `u0`.
[in]	cells1	Cell indices associated with the mesh of `this` that will be interpolated to. If `cells0[i]` is the index of a cell in the mesh associated with `u0`, then `cells1[i]` is the index of the same cell but in the mesh associated with `this`. This argument can be empty when `this` and `u0` share the same mesh. Otherwise the length of `cells` and the length of `cells0` must be the same.

◆ interpolate() [5/7]

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

void interpolate	(	const Function< value_type, geometry_type > &	v,
		std::span< const std::int32_t >	cells,
		const geometry::PointOwnershipData< U > &	interpolation_data )

inline

Interpolate a Function defined on a different mesh.

Parameters

[in]	v	Function to be interpolated.
[in]	cells	Cells in the mesh associated with `this` to interpolate into.
[in]	interpolation_data	Data required for associating the interpolation points of `this` with cells in `v`. Can be computed with `fem::create_interpolation_data`.

◆ interpolate() [6/7]

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

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

inline

Interpolate an expression f(x) on the whole domain.

Parameters

[in] f Expression to be interpolated.

◆ interpolate() [7/7]

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

void interpolate	(	const std::function< std::pair< std::vector< value_type >, std::vector< std::size_t > >(MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan< const geometry_type, 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 f(x) over a set of cells.

Parameters

[in]	f	Expression function to be interpolated.
[in]	cells	Cells to interpolate on.

◆ sub()

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

Function sub ( int i ) const

inline

Extract a 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
/__w/dolfinx/dolfinx/cpp/dolfinx/fem/interpolate.h
/__w/dolfinx/dolfinx/cpp/dolfinx/io/VTKFile.h
/__w/dolfinx/dolfinx/cpp/dolfinx/io/xdmf_function.h
/__w/dolfinx/dolfinx/cpp/dolfinx/io/xdmf_utils.h
/__w/dolfinx/dolfinx/cpp/dolfinx/io/XDMFFile.h

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ Function() [1/2]

◆ Function() [2/2]

Member Function Documentation

◆ collapse()

◆ eval()

◆ function_space()

◆ interpolate() [1/7]

◆ interpolate() [2/7]

◆ interpolate() [3/7]

◆ interpolate() [4/7]

◆ interpolate() [5/7]

◆ interpolate() [6/7]

◆ interpolate() [7/7]

◆ sub()