Basix: FEniCS runtime basis evaluation library. More...

Namespaces
	cell
	Information about reference cells.

	doftransforms
	Functions to transform DOFs in high degree Lagrange spaces.

	element
	Interfaces for creating finite elements.

	indexing
	Indexing.

	lattice
	Lattices of points.

	maps
	Information about finite element maps.

	math
	Mathematical functions.

	moments
	Functions to create integral moment DOFs.

	polynomials
	Polynomials.

	polyset
	Polynomial expansion sets.

	precompute
	Matrix and permutation precomputation.

	quadrature
	Quadrature rules.

Classes
class	FiniteElement
	A finite element. More...

Functions
FiniteElement	create_custom_element (cell::type cell_type, const std::vector< std::size_t > &value_shape, const xt::xtensor< double, 2 > &wcoeffs, const std::array< std::vector< xt::xtensor< double, 2 >>, 4 > &x, const std::array< std::vector< xt::xtensor< double, 3 >>, 4 > &M, maps::type map_type, bool discontinuous, int highest_complete_degree, int highest_degree)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::lagrange_variant lvariant, bool discontinuous)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::lagrange_variant lvariant, element::dpc_variant dvariant, bool discontinuous)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::dpc_variant dvariant, bool discontinuous)

FiniteElement	create_element (element::family family, cell::type cell, int degree, bool discontinuous)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::lagrange_variant lvariant)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::lagrange_variant lvariant, element::dpc_variant dvariant)

FiniteElement	create_element (element::family family, cell::type cell, int degree, element::dpc_variant dvariant)

FiniteElement	create_element (element::family family, cell::type cell, int degree)

std::string	version ()

xt::xtensor< double, 2 >	compute_interpolation_operator (const FiniteElement &element_from, const FiniteElement &element_to)

Detailed Description

Basix: FEniCS runtime basis evaluation library.

Function Documentation

◆ compute_interpolation_operator()

xt::xtensor< double, 2 > basix::compute_interpolation_operator	(	const FiniteElement &	element_from,
		const FiniteElement &	element_to
	)

Computes a matrix that represents the interpolation between two elements.

If the two elements have the same value size, this function returns the interpolation between them.

If element_from has value size 1 and element_to has value size > 1, then this function returns a matrix to interpolate from a blocked element_from (ie multiple copies of element_from) into element_to.

If element_to has value size 1 and element_from has value size > 1, then this function returns a matrix that interpolates the components of element_from into copies of element_to.

Note: If the elements have different value sizes and both are greater than 1, this function throws a runtime error

In order to interpolate functions between finite element spaces on arbitrary cells, the functions must be pulled back to the reference element (this pull back includes applying DOF transformations). The matrix that this function returns can then be applied, then the result pushed forward to the cell. If element_from and element_to have the same map type, then only the DOF transformations need to be applied, as the pull back and push forward cancel each other out.

Parameters

[in]	element_from	The element to interpolate from
[in]	element_to	The element to interpolate to

Returns: Matrix operator that maps the 'from' degrees-of-freedom to the 'to' degrees-of-freedom

◆ create_custom_element()

basix::FiniteElement basix::create_custom_element	(	cell::type	cell_type,
		const std::vector< std::size_t > &	value_shape,
		const xt::xtensor< double, 2 > &	wcoeffs,
		const std::array< std::vector< xt::xtensor< double, 2 >>, 4 > &	x,
		const std::array< std::vector< xt::xtensor< double, 3 >>, 4 > &	M,
		maps::type	map_type,
		bool	discontinuous,
		int	highest_complete_degree,
		int	highest_degree
	)

Create a custom finite element

Parameters

[in]	cell_type	The cell type
[in]	value_shape	The value shape of the element
[in]	wcoeffs	Matrices for the kth value index containing the expansion coefficients defining a polynomial basis spanning the polynomial space for this element
[in]	x	Interpolation points. Shape is (tdim, entity index, point index, dim)
[in]	M	The interpolation matrices. Indices are (tdim, entity index, dof, vs, point_index)
[in]	map_type	The type of map to be used to map values from the reference to a cell
[in]	discontinuous	Indicates whether or not this is the discontinuous version of the element
[in]	highest_complete_degree	The highest degree n such that a Lagrange (or vector Lagrange) element of degree n is a subspace of this element
[in]	highest_degree	The degree of a polynomial in this element's polyset

Returns: A custom finite element

◆ create_element() [1/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree
	)

Create a continuous element

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element

Returns: A finite element

◆ create_element() [2/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		bool	discontinuous
	)

Create an element

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	discontinuous	Indicates whether the element is discontinuous between cells points of the element. The discontinuous element will have the same DOFs, but they will all be associated with the interior of the cell.

Returns: A finite element

◆ create_element() [3/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::dpc_variant	dvariant
	)

Create a continuous element using a given DPC variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	dvariant	The variant of DPC to use

Returns: A finite element

◆ create_element() [4/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::dpc_variant	dvariant,
		bool	discontinuous
	)

Create an element using a given DPC variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	dvariant	The variant of DPC to use
[in]	discontinuous	Indicates whether the element is discontinuous between cells points of the element. The discontinuous element will have the same DOFs, but they will all be associated with the interior of the cell.

Returns: A finite element

◆ create_element() [5/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::lagrange_variant	lvariant
	)

Create a continuous element using a given Lagrange variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	lvariant	The variant of Lagrange to use

Returns: A finite element

◆ create_element() [6/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::lagrange_variant	lvariant,
		bool	discontinuous
	)

Create an element using a given Lagrange variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	lvariant	The variant of Lagrange to use
[in]	discontinuous	Indicates whether the element is discontinuous between cells points of the element. The discontinuous element will have the same DOFs, but they will all be associated with the interior of the cell.

Returns: A finite element

◆ create_element() [7/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::lagrange_variant	lvariant,
		element::dpc_variant	dvariant
	)

Create a continuous element using a given Lagrange variant and a given DPC variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	lvariant	The variant of Lagrange to use
[in]	dvariant	The variant of DPC to use

Returns: A finite element

◆ create_element() [8/8]

basix::FiniteElement basix::create_element	(	element::family	family,
		cell::type	cell,
		int	degree,
		element::lagrange_variant	lvariant,
		element::dpc_variant	dvariant,
		bool	discontinuous
	)

Create an element using a given Lagrange variant and a given DPC variant

Parameters

[in]	family	The element family
[in]	cell	The reference cell type that the element is defined on
[in]	degree	The degree of the element
[in]	lvariant	The variant of Lagrange to use
[in]	dvariant	The variant of DPC to use
[in]	discontinuous	Indicates whether the element is discontinuous between cells points of the element. The discontinuous element will have the same DOFs, but they will all be associated with the interior of the cell.

Returns: A finite element

◆ version()

std::string basix::version ( )

Return the Basix version number

Returns: version string

Basix 0.4.1

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Namespaces

Classes

Functions

Detailed Description

Function Documentation

◆ compute_interpolation_operator()

◆ create_custom_element()

◆ create_element() [1/8]

◆ create_element() [2/8]

◆ create_element() [3/8]

◆ create_element() [4/8]

◆ create_element() [5/8]

◆ create_element() [6/8]

◆ create_element() [7/8]

◆ create_element() [8/8]

◆ version()