#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 > >(md::mdspan< const geometry_type, md::extents< std::size_t, 3, md::dynamic_extent > >)> &f, CellRange auto &&cells)
	Interpolate an expression f(x) over a set of cells.
void	interpolate (const std::function< std::pair< std::vector< value_type >, std::vector< std::size_t > >(md::mdspan< const geometry_type, md::extents< std::size_t, 3, md::dynamic_extent > >)> &f)
	Interpolate an expression f(x) on the whole domain.
void	interpolate (const Function< value_type, geometry_type > &u0, CellRange auto &&cells0, CellRange auto &&cells1)
	Interpolate a Function over a subset of cells.
void	interpolate (const Function< value_type, geometry_type > &u, CellRange auto &&cells)
	Interpolate a Function over a subset of cells.
void	interpolate (const Function< value_type, geometry_type > &u)
	Interpolate a Function over all cells.
void	interpolate (const Expression< value_type, geometry_type > &e0, CellRange auto &&cells0, CellRange auto &&cells1)
	Interpolate an Expression over a subset of cells.
void	interpolate (const Expression< value_type, geometry_type > &e0, CellRange auto &&cells)
	Interpolate an Expression over a subset of cells.
void	interpolate (const Expression< value_type, geometry_type > &e)
	Interpolate an Expression on all cells.
void	interpolate (const Function< value_type, geometry_type > &u, CellRange auto &&cells, double tol, int maxit, 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, CellRange auto &&cells, std::span< value_type > u, std::array< std::size_t, 2 > ushape, double tol, int maxit) 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_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.

Member Typedef Documentation

◆ value_type

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

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 = dolfinx::scalar_value_t<T>>

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 = dolfinx::scalar_value_t<T>>

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 = dolfinx::scalar_value_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_t<T>>

void eval	(	std::span< const geometry_type >	x,
		std::array< std::size_t, 2 >	xshape,
		CellRange auto &&	cells,
		std::span< value_type >	u,
		std::array< std::size_t, 2 >	ushape,
		double	tol,
		int	maxit ) 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.
[in]	tol	Tolerance for convergence in Newton method for non-affine pullbacks. If the mesh geometry is affine this argument is ignored.
[in]	maxit	Maximum number of Newton iterations in non-affine pull-back. If the mesh geometry is affine this argument is ignored.

◆ function_space()

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

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

inline

Access the function space.

Returns: The function space.

◆ interpolate() [1/9]

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

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() [2/9]

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

void interpolate	(	const Expression< value_type, geometry_type > &	e0,
		CellRange auto &&	cells )

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]	cells	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.

◆ interpolate() [3/9]

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

void interpolate	(	const Expression< value_type, geometry_type > &	e0,
		CellRange auto &&	cells0,
		CellRange auto &&	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.

Precondition: cells0 cells1 must have the same length.

◆ interpolate() [4/9]

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

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

inline

Interpolate a Function over all cells.

The Functions must be defined on the same mesh.

Parameters

[in] u Function to be interpolated.

◆ interpolate() [5/9]

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

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

inline

Interpolate a Function over a subset of cells.

The Functions must be defined on the same mesh.

Parameters

[in]	u	Function to be interpolated.
[in]	cells	Cells to interpolate from.

◆ interpolate() [6/9]

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

void interpolate	(	const Function< value_type, geometry_type > &	u,
		CellRange auto &&	cells,
		double	tol,
		int	maxit,
		const geometry::PointOwnershipData< U > &	interpolation_data )

inline

Interpolate a Function defined on a different mesh.

Parameters

[in]	u	Function to be interpolated.
[in]	cells	Cells in the mesh associated with this to interpolate into.
[in]	tol	Tolerance for convergence in Newton method for non-affine pullbacks. If the mesh geometry is affine this argument is ignored.
[in]	maxit	Maximum number of Newton iterations in non-affine pull-back. If the mesh geometry is affine this argument is ignored.
[in]	interpolation_data	Data required for associating the interpolation points of this with cells in u. Can be computed with fem::create_interpolation_data.

◆ interpolate() [7/9]

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

void interpolate	(	const Function< value_type, geometry_type > &	u0,
		CellRange auto &&	cells0,
		CellRange auto &&	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.

Precondition: cells0 and cells1 must have the same length.

◆ interpolate() [8/9]

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

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

inline

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

Parameters

[in] f Expression to be interpolated.

◆ interpolate() [9/9]

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

void interpolate	(	const std::function< std::pair< std::vector< value_type >, std::vector< std::size_t > >(md::mdspan< const geometry_type, md::extents< std::size_t, 3, md::dynamic_extent > >)> &	f,
		CellRange auto &&	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 = dolfinx::scalar_value_t<T>>

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/Expression.h
/__w/dolfinx/dolfinx/cpp/dolfinx/fem/Function.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() [1/9]

◆ interpolate() [2/9]

◆ interpolate() [3/9]

◆ interpolate() [4/9]

◆ interpolate() [5/9]

◆ interpolate() [6/9]

◆ interpolate() [7/9]

◆ interpolate() [8/9]

◆ interpolate() [9/9]

◆ sub()