basix.ufl

Functions to directly wrap Basix elements in UFL.

Functions

_compute_signature(element)	Compute a signature of a custom element.
_ufl_pullback_from_enum(m)	Convert an enum to a UFL pull back.
_ufl_sobolev_space_from_enum(s)	Convert a Basix Sobolev space enum to a UFL Sobolev space.
blocked_element(sub_element, shape[, symmetry])	Create a UFL compatible blocked element.
custom_element(cell_type, ...[, ...])	Create a UFL compatible custom Basix element.
element(family, cell, degree[, ...])	Create a UFL compatible element using Basix.
enriched_element(elements[, map_type])	Create an UFL compatible enriched element from a list of elements.
mixed_element(elements)	Create a UFL compatible mixed element from a list of elements.
quadrature_element(cell[, value_shape, ...])	Create a quadrature element.
real_element(cell, value_shape)	Create a real element.
wrap_element(element)	Wrap a Basix element as a Basix UFL element.

Classes

_BasixElement(element)	A wrapper allowing Basix elements to be used directly with UFL.
_BlockedElement(sub_element, shape[, symmetry])	Element with a block size that contains multiple copies of a sub element.
_ComponentElement(element, component)	An element representing one component of a _BasixElement.
_ElementBase(repr, cellname, ...[, degree, ...])	A base wrapper to allow elements to be used with UFL.
_MixedElement(sub_elements)	A mixed element that combines two or more elements.
_QuadratureElement(cell, points, weights, ...)	A quadrature element.
_RealElement(cell, value_shape)	A real element.

basix.ufl.blocked_element(sub_element: _ElementBase, shape: tuple[int, ...], symmetry: bool | None = None) → _ElementBase

Create a UFL compatible blocked element.

Parameters:

• sub_element – Element used for each block.

• shape – Value shape of the element. For scalar-valued families, this can be used to create vector and tensor elements.

• symmetry – Set to True if the tensor is symmetric. Valid for rank 2 elements only.

Returns:

A blocked finite element.

basix.ufl.custom_element(cell_type: CellType, reference_value_shape: list[int] | tuple[int, ...], wcoeffs: ndarray[Any, dtype[floating]], x: list[list[ndarray[Any, dtype[floating]]]], M: list[list[ndarray[Any, dtype[floating]]]], interpolation_nderivs: int, map_type: MapType, sobolev_space: SobolevSpace, discontinuous: bool, embedded_subdegree: int, embedded_superdegree: int, polyset_type: PolysetType = PolysetType.standard, dtype: dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any] = None) → _ElementBase

Create a UFL compatible custom Basix element.

Parameters:

• cell_type – The cell type

• reference_value_shape – The reference value shape of the element

• wcoeffs – Matrices for the kth value index containing the expansion coefficients defining a polynomial basis spanning the polynomial space for this element. Shape is (dim(finite element polyset), dim(Legenre polynomials)).

• x – Interpolation points. Indices are (tdim, entity index, point index, dim).

• M – The interpolation matrices. Indices are (tdim, entity index, dof, vs, point_index, derivative).

• interpolation_nderivs – The number of derivatives that need to be used during interpolation.

• map_type – The type of map to be used to map values from the reference to a cell.

• sobolev_space – Underlying Sobolev space for the element.

• discontinuous – Indicates whether or not this is the discontinuous version of the element.

• embedded_subdegree – The highest degree n such that a Lagrange (or vector Lagrange) element of degree n is a subspace of this element.

• embedded_superdegree – The highest degree of a polynomial in this element’s polyset.

• polyset_type – Polyset type for the element.

• dtype – Floating point data type.

Returns:

A custom finite element.

basix.ufl.element(family: ElementFamily | str, cell: CellType | str, degree: int, lagrange_variant: LagrangeVariant = LagrangeVariant.unset, dpc_variant: DPCVariant = DPCVariant.unset, discontinuous: bool = False, shape: tuple[int, ...] | None = None, symmetry: bool | None = None, dtype: dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any] = None) → _ElementBase

Create a UFL compatible element using Basix.

Parameters:

• family – Element family/type.

• cell – Element cell type.

• degree – Degree of the finite element.

• lagrange_variant – Variant of Lagrange to be used.

• dpc_variant – Variant of DPC to be used.

• discontinuous – If True, the discontinuous version of the element is created.

• shape – Value shape of the element. For scalar-valued families, this can be used to create vector and tensor elements.

• symmetry – Set to True if the tensor is symmetric. Valid for rank 2 elements only.

• dtype – Floating point data type.

Returns:

A finite element.

basix.ufl.enriched_element(elements: list[_ElementBase], map_type: MapType | None = None) → _ElementBase

Create an UFL compatible enriched element from a list of elements.

Parameters:

• elements – The list of elements

• map_type – The map type for the enriched element.

Returns:

An enriched finite element.

basix.ufl.mixed_element(elements: list[_ElementBase]) → _ElementBase

Create a UFL compatible mixed element from a list of elements.

Parameters:

elements – The list of elements

Returns:

A mixed finite element.

basix.ufl.quadrature_element(cell: str | CellType, value_shape: tuple[int, ...] = (), scheme: str | None = None, degree: int | None = None, points: ndarray[Any, dtype[floating]] | None = None, weights: ndarray[Any, dtype[floating]] | None = None, pullback: AbstractPullback = IdentityPullback(), symmetry: bool | None = None) → _ElementBase

Create a quadrature element.

When creating this element, either the quadrature scheme and degree must be input or the quadrature points and weights must be.

Parameters:

• cell – Cell to create the element on.

• value_shape – Value shape of the element.

• scheme – Quadrature scheme.

• degree – Quadrature degree.

• points – Quadrature points.

• weights – Quadrature weights.

• pullback – Map name.

• symmetry – Set to True if the tensor is symmetric. Valid for rank 2 elements only.

Returns:

A ‘quadrature’ finite element.

basix.ufl.real_element(cell: CellType | str, value_shape: tuple[int, ...]) → _ElementBase

Create a real element.

Parameters:

• cell – Cell to create the element on.

• value_shape – Value shape of the element.

Returns:

A ‘real’ finite element.

basix.ufl.wrap_element(element: FiniteElement) → _ElementBase

Wrap a Basix element as a Basix UFL element.