Interfaces for creating finite elements. More...

Typedefs
template<typename T , std::size_t d>
using	mdspan_t = impl::mdspan_t< T, d >
	Typedef for mdspan.

Enumerations
enum class	lagrange_variant { unset = 0 , equispaced = 1 , gll_warped = 2 , gll_isaac = 3 , gll_centroid = 4 , chebyshev_warped = 5 , chebyshev_isaac = 6 , chebyshev_centroid = 7 , gl_warped = 8 , gl_isaac = 9 , gl_centroid = 10 , legendre = 11 , bernstein = 12 }
	Variants of a Lagrange space that can be created.

enum class	dpc_variant { unset = 0 , simplex_equispaced = 1 , simplex_gll = 2 , horizontal_equispaced = 3 , horizontal_gll = 4 , diagonal_equispaced = 5 , diagonal_gll = 6 , legendre = 7 }

enum class	family { custom = 0 , P = 1 , RT = 2 , N1E = 3 , BDM = 4 , N2E = 5 , CR = 6 , Regge = 7 , DPC = 8 , bubble = 9 , serendipity = 10 , HHJ = 11 , Hermite = 12 , iso = 13 }
	Available element families.

Functions
template<std::floating_point T>
FiniteElement< T >	create_bdm (cell::type celltype, int degree, lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_bubble (cell::type celltype, int degree, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_cr (cell::type celltype, int degree, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_hermite (cell::type celltype, int degree, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_hhj (cell::type celltype, int degree, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_lagrange (cell::type celltype, int degree, lagrange_variant variant, bool discontinuous, std::vector< int > dof_ordering={})
	Create a Lagrange(-like) element on cell with given degree. More...

template<std::floating_point T>
FiniteElement< T >	create_iso (cell::type celltype, int degree, lagrange_variant variant, bool discontinuous)
	Create an iso macro element on cell with given degree. More...

template<std::floating_point T>
FiniteElement< T >	create_rtc (cell::type celltype, int degree, element::lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_nce (cell::type celltype, int degree, element::lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_nedelec (cell::type celltype, int degree, lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_nedelec2 (cell::type celltype, int degree, lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_rt (cell::type celltype, int degree, element::lagrange_variant lvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_regge (cell::type celltype, int degree, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_serendipity (cell::type celltype, int degree, element::lagrange_variant lvariant, element::dpc_variant dvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_dpc (cell::type celltype, int degree, element::dpc_variant variant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_serendipity_div (cell::type celltype, int degree, element::lagrange_variant lvariant, element::dpc_variant dvariant, bool discontinuous)

template<std::floating_point T>
FiniteElement< T >	create_serendipity_curl (cell::type celltype, int degree, element::lagrange_variant lvariant, element::dpc_variant dvariant, bool discontinuous)

template<std::floating_point T>
std::tuple< std::array< std::vector< std::vector< T > >, 4 >, std::array< std::vector< std::array< std::size_t, 2 > >, 4 >, std::array< std::vector< std::vector< T > >, 4 >, std::array< std::vector< std::array< std::size_t, 4 > >, 4 > >	make_discontinuous (const std::array< std::vector< mdspan_t< const T, 2 >>, 4 > &x, const std::array< std::vector< mdspan_t< const T, 4 >>, 4 > &M, std::size_t tdim, std::size_t value_size)

Detailed Description

Interfaces for creating finite elements.

Enumeration Type Documentation

◆ dpc_variant

enum basix::element::dpc_variant

strong

Variants of a DPC (discontinuous polynomial cubical) space that can be created. DPC spaces span the same set of polynomials as Lagrange spaces on simplices but are defined on tensor product cells.

Function Documentation

◆ create_bdm()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_bdm	(	cell::type	celltype,
		int	degree,
		lagrange_variant	lvariant,
		bool	discontinuous
	)

Create BDM element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_bubble()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_bubble	(	cell::type	celltype,
		int	degree,
		bool	discontinuous
	)

Create a bubble element on cell with given degree

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_cr()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_cr	(	cell::type	celltype,
		int	degree,
		bool	discontinuous
	)

Crouzeix-Raviart element

Note: degree must be 1 for Crouzeix-Raviart

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_hermite()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_hermite	(	cell::type	celltype,
		int	degree,
		bool	discontinuous
	)

Create a Hermite element on cell with given degree

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_hhj()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_hhj	(	cell::type	celltype,
		int	degree,
		bool	discontinuous
	)

Create Hellan-Herrmann-Johnson element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_lagrange()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_lagrange	(	cell::type	celltype,
		int	degree,
		lagrange_variant	variant,
		bool	discontinuous,
		std::vector< int >	dof_ordering = `{}`
	)

Create a Lagrange(-like) element on cell with given degree.

Parameters

[in]	celltype	The element cell type
[in]	degree	The degree of the element
[in]	variant	The variant of the element to be created
[in]	discontinuous	True if the is discontinuous
[in]	dof_ordering	DOF reordering

Returns: A finite element

◆ create_iso()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_iso	(	cell::type	celltype,
		int	degree,
		lagrange_variant	variant,
		bool	discontinuous
	)

Create an iso macro element on cell with given degree.

Parameters

[in]	celltype	The element cell type
[in]	degree	The degree of the element
[in]	variant	The variant of the element to be created
[in]	discontinuous	True if the is discontinuous

Returns: A finite element

◆ create_rtc()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_rtc	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		bool	discontinuous
	)

Create RTC H(div) element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_nce()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_nce	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		bool	discontinuous
	)

Create NC H(curl) element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_nedelec()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_nedelec	(	cell::type	celltype,
		int	degree,
		lagrange_variant	lvariant,
		bool	discontinuous
	)

Create Nedelec element (first kind)

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_nedelec2()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_nedelec2	(	cell::type	celltype,
		int	degree,
		lagrange_variant	lvariant,
		bool	discontinuous
	)

Create Nedelec element (second kind)

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_rt()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_rt	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		bool	discontinuous
	)

Create Raviart-Thomas element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The Lagrange variant to use when defining the element to take integral moments against
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_regge()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_regge	(	cell::type	celltype,
		int	degree,
		bool	discontinuous
	)

Create Regge element

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_serendipity()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_serendipity	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		element::dpc_variant	dvariant,
		bool	discontinuous
	)

Create a serendipity element on cell with given degree

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The variant of the Lagrange element to be used for integral moments on the edges of the cell
[in]	dvariant	The variant of the DPC element to be used for integral moments on the interior of the cell (for quads and hexes). For elements on an interval element::dpc_variant::unset can be passed in
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_dpc()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_dpc	(	cell::type	celltype,
		int	degree,
		element::dpc_variant	variant,
		bool	discontinuous
	)

Create a DPC (discontinuous polynomial cubical) element on cell with given degree.

Note: DPC elements must be discontinuous

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	variant	The variant of the element to be created
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_serendipity_div()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_serendipity_div	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		element::dpc_variant	dvariant,
		bool	discontinuous
	)

Create a serendipity H(div) element on cell with given degree

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The variant of the Lagrange element to be used for integral moments
[in]	dvariant	The variant of the DPC element to be used for integral moments
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ create_serendipity_curl()

template<std::floating_point T>

template FiniteElement< double > basix::element::create_serendipity_curl	(	cell::type	celltype,
		int	degree,
		element::lagrange_variant	lvariant,
		element::dpc_variant	dvariant,
		bool	discontinuous
	)

Create a serendipity H(curl) element on cell with given degree

Parameters

[in]	celltype	The cell type
[in]	degree	The degree of the element
[in]	lvariant	The variant of the Lagrange element to be used for integral moments
[in]	dvariant	The variant of the DPC element to be used for integral moments
[in]	discontinuous	Controls whether the element is continuous or discontinuous

Returns: A finite element

◆ make_discontinuous()

template<std::floating_point T>

std::tuple< std::array< std::vector< std::vector< T > >, 4 >, std::array< std::vector< std::array< std::size_t, 2 > >, 4 >, std::array< std::vector< std::vector< T > >, 4 >, std::array< std::vector< std::array< std::size_t, 4 > >, 4 > > basix::element::make_discontinuous	(	const std::array< std::vector< mdspan_t< const T, 2 >>, 4 > &	x,
		const std::array< std::vector< mdspan_t< const T, 4 >>, 4 > &	M,
		std::size_t	tdim,
		std::size_t	value_size
	)

Create a version of the interpolation points, interpolation matrices and entity transformation that represent a discontinuous version of the element. This discontinuous version will have the same DOFs but they will all be associated with the interior of the reference cell.

Parameters

[in]	x	Interpolation points. Indices are (tdim, entity index, point index, dim)
[in]	M	The interpolation matrices. Indices are (tdim, entity index, dof, vs, point_index, derivative)
[in]	tdim	The topological dimension of the cell the element is defined on
[in]	value_size	The value size of the element

Returns: (xdata, xshape, Mdata, Mshape), where the x and M data are for a discontinuous version of the element (with the same shapes as x and M)

Basix 0.9.0.0

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Typedefs

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ dpc_variant

Function Documentation

◆ create_bdm()

◆ create_bubble()

◆ create_cr()

◆ create_hermite()

◆ create_hhj()

◆ create_lagrange()

◆ create_iso()

◆ create_rtc()

◆ create_nce()

◆ create_nedelec()

◆ create_nedelec2()

◆ create_rt()

◆ create_regge()

◆ create_serendipity()

◆ create_dpc()

◆ create_serendipity_div()

◆ create_serendipity_curl()

◆ make_discontinuous()