Finite Element, containing the dof layout on a reference element, and various methods for evaluating and transforming the basis. More...

#include <FiniteElement.h>

Public Member Functions
	FiniteElement (const ufc_finite_element &ufc_element)
	Create finite element from UFC finite element. More...

	FiniteElement (const FiniteElement &element)=delete
	Copy constructor.

	FiniteElement (FiniteElement &&element)=default
	Move constructor.

virtual	~FiniteElement ()=default
	Destructor.

FiniteElement &	operator= (const FiniteElement &element)=delete
	Copy assignment.

FiniteElement &	operator= (FiniteElement &&element)=default
	Move assignment.

std::string	signature () const noexcept
	String identifying the finite element. More...

mesh::CellType	cell_shape () const noexcept
	Cell shape. More...

int	space_dimension () const noexcept
	Dimension of the finite element function space. More...

int	block_size () const noexcept
	Block size of the finite element function space. For VectorElements and TensorElements, this is the number of DOFs colocated at each DOF point. For other elements, this is always 1. More...

int	value_size () const noexcept
	The value size, e.g. 1 for a scalar function, 2 for a 2D vector. More...

int	reference_value_size () const noexcept
	The value size, e.g. 1 for a scalar function, 2 for a 2D vector for the reference element. More...

int	value_rank () const noexcept
	Rank of the value space. More...

int	value_dimension (int i) const
	Return the dimension of the value space for axis i.

std::string	family () const noexcept
	The finite element family. More...

void	evaluate_reference_basis (xt::xtensor< double, 3 > &values, const xt::xtensor< double, 2 > &X) const
	Evaluate all basis functions at given points in reference cell.

void	transform_reference_basis (xt::xtensor< double, 3 > &values, const xt::xtensor< double, 3 > &reference_values, const xt::xtensor< double, 3 > &J, const xtl::span< const double > &detJ, const xt::xtensor< double, 3 > &K) const
	Evaluate all basis function derivatives of given order at given points in reference cell. More...

void	transform_reference_basis_derivatives (std::vector< double > &values, std::size_t order, const std::vector< double > &reference_values, const array2d< double > &X, const std::vector< double > &J, const xtl::span< const double > &detJ, const std::vector< double > &K) const
	Push basis function (derivatives) forward to physical element.

int	num_sub_elements () const noexcept
	Get the number of sub elements (for a mixed element) More...

const std::vector< std::shared_ptr< const FiniteElement > > &	sub_elements () const noexcept
	Subelements (if any)

std::size_t	hash () const noexcept
	Return simple hash of the signature string.

std::shared_ptr< const FiniteElement >	extract_sub_element (const std::vector< int > &component) const
	Extract sub finite element for component.

bool	interpolation_ident () const noexcept
	Check if interpolation into the finite element space is an identity operation given the evaluation on an expression at specific points, i.e. the degree-of-freedom are equal to point evaluations. The function will return `true` for Lagrange elements. More...

const xt::xtensor< double, 2 > &	interpolation_points () const
	Points on the reference cell at which an expression need to be evaluated in order to interpolate the expression in the finite element space. For Lagrange elements the points will just be the nodal positions. For other elements the points will typically be the quadrature points used to evaluate moment degrees of freedom. More...

template<typename T >
constexpr void	interpolate (const xt::xtensor< T, 2 > &values, xtl::span< T > dofs) const

bool	needs_permutation_data () const noexcept

template<typename T >
void	apply_dof_transformation (xtl::span< T > data, std::uint32_t cell_permutation, int block_size) const
	Apply permutation to some data. More...

template<typename T >
void	apply_inverse_transpose_dof_transformation (xtl::span< T > data, std::uint32_t cell_permutation, int block_size) const
	Apply inverse transpose permutation to some data. More...

template<typename T >
void	map_pull_back (const xt::xtensor< T, 3 > &u, const xt::xtensor< double, 3 > &J, const xtl::span< const double > &detJ, const xt::xtensor< double, 3 > &K, xt::xtensor< T, 3 > &U) const
	Pull physical data back to the reference element. This passes the inputs directly into Basix's map_pull_back function.

Detailed Description

Finite Element, containing the dof layout on a reference element, and various methods for evaluating and transforming the basis.

Constructor & Destructor Documentation

◆ FiniteElement()

FiniteElement::FiniteElement ( const ufc_finite_element & ufc_element )

explicit

Create finite element from UFC finite element.

Parameters

[in] ufc_element UFC finite element

Member Function Documentation

◆ apply_dof_transformation()

template<typename T >

void dolfinx::fem::FiniteElement::apply_dof_transformation	(	xtl::span< T >	data,
		std::uint32_t	cell_permutation,
		int	block_size
	)		const

inline

Apply permutation to some data.

Parameters

[in,out]	data	The data to be transformed
[in]	cell_permutation	Permutation data for the cell
[in]	block_size	The block_size of the input data

◆ apply_inverse_transpose_dof_transformation()

template<typename T >

void dolfinx::fem::FiniteElement::apply_inverse_transpose_dof_transformation	(	xtl::span< T >	data,
		std::uint32_t	cell_permutation,
		int	block_size
	)		const

inline

Apply inverse transpose permutation to some data.

Parameters

[in,out]	data	The data to be transformed
[in]	cell_permutation	Permutation data for the cell
[in]	block_size	The block_size of the input data

◆ block_size()

int FiniteElement::block_size ( ) const

noexcept

Block size of the finite element function space. For VectorElements and TensorElements, this is the number of DOFs colocated at each DOF point. For other elements, this is always 1.

Returns: Block size of the finite element space

◆ cell_shape()

mesh::CellType FiniteElement::cell_shape ( ) const

noexcept

Cell shape.

Returns: Element cell shape

◆ family()

std::string FiniteElement::family ( ) const

noexcept

The finite element family.

Returns: The string of the finite element family

◆ interpolate()

template<typename T >

constexpr void dolfinx::fem::FiniteElement::interpolate	(	const xt::xtensor< T, 2 > &	values,
		xtl::span< T >	dofs
	)		const

inlineconstexpr

Todo:

Document shape/layout of values

Make the interpolating dofs in/out argument for efficiency as this function is often called from within tight loops

Consider handling block size > 1

Re-work for fields that require a pull-back, e.g. Piols mapped elements

Interpolate a function in the finite element space on a cell. Given the evaluation of the function to be interpolated at points provided by FiniteElement::interpolation_points, it evaluates the degrees of freedom for the interpolant.

Parameters

[in]	values	The values of the function. It has shape (value_size, num_points), where `num_points` is the number of points given by FiniteElement::interpolation_points.
[out]	dofs	The element degrees of freedom (interpolants) of the expression. The call must allocate the space. Is has

◆ interpolation_ident()

bool FiniteElement::interpolation_ident ( ) const

noexcept

Check if interpolation into the finite element space is an identity operation given the evaluation on an expression at specific points, i.e. the degree-of-freedom are equal to point evaluations. The function will return true for Lagrange elements.

Returns: True if interpolation is an identity operation

◆ interpolation_points()

const xt::xtensor< double, 2 > & FiniteElement::interpolation_points ( ) const

Points on the reference cell at which an expression need to be evaluated in order to interpolate the expression in the finite element space. For Lagrange elements the points will just be the nodal positions. For other elements the points will typically be the quadrature points used to evaluate moment degrees of freedom.

Returns: Points on the reference cell. Shape is (num_points, tdim).

◆ needs_permutation_data()

bool FiniteElement::needs_permutation_data ( ) const

noexcept

Todo:: Expand on when permutation data might be required

Check if cell permutation data is required for this element

Returns: True if cell permutation data is required

◆ num_sub_elements()

int FiniteElement::num_sub_elements ( ) const

noexcept

Get the number of sub elements (for a mixed element)

Returns: the Number of sub elements

◆ reference_value_size()

int FiniteElement::reference_value_size ( ) const

noexcept

The value size, e.g. 1 for a scalar function, 2 for a 2D vector for the reference element.

Returns: The value size for the reference element

◆ signature()

std::string FiniteElement::signature ( ) const

noexcept

String identifying the finite element.

Returns: Element signature

◆ space_dimension()

int FiniteElement::space_dimension ( ) const

noexcept

Dimension of the finite element function space.

Returns: Dimension of the finite element space

◆ transform_reference_basis()

void FiniteElement::transform_reference_basis	(	xt::xtensor< double, 3 > &	values,
		const xt::xtensor< double, 3 > &	reference_values,
		const xt::xtensor< double, 3 > &	J,
		const xtl::span< const double > &	detJ,
		const xt::xtensor< double, 3 > &	K
	)		const

Evaluate all basis function derivatives of given order at given points in reference cell.

Push basis functions forward to physical element

◆ value_rank()

int FiniteElement::value_rank ( ) const

noexcept

Rank of the value space.

Returns: The value rank

◆ value_size()

int FiniteElement::value_size ( ) const

noexcept

The value size, e.g. 1 for a scalar function, 2 for a 2D vector.

Returns: The value size

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

/__w/dolfinx/dolfinx/cpp/dolfinx/fem/FiniteElement.h
/__w/dolfinx/dolfinx/cpp/dolfinx/fem/FiniteElement.cpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ FiniteElement()

Member Function Documentation

◆ apply_dof_transformation()

◆ apply_inverse_transpose_dof_transformation()

◆ block_size()

◆ cell_shape()

◆ family()

◆ interpolate()

◆ interpolation_ident()

◆ interpolation_points()

◆ needs_permutation_data()

◆ num_sub_elements()

◆ reference_value_size()

◆ signature()

◆ space_dimension()

◆ transform_reference_basis()

◆ value_rank()

◆ value_size()