ffcx.element_interface

Finite element interface.

Functions

`basix_index`(*args)	Get the Basix index of a derivative.
`create_basix_element`(family_type, cell_type, ...)	Create a basix element.
`create_element`(element)	Create an FFCx element from a UFL element.
`create_quadrature`(cellname, degree, rule)	Create a quadrature rule.
`map_facet_points`(points, facet, cellname)	Map points from a reference facet to a physical facet.
`reference_cell_vertices`(cellname)	Get the vertices of a reference cell.

Classes

`BaseElement`()	An abstract element class.
`BasixElement`(element)	An element defined by Basix.
`BlockedElement`(sub_element, block_size[, ...])	An element with a block size that contains multiple copies of a sub element.
`ComponentElement`(element, component)	An element representing one component of a BasixElement.
`MixedElement`(sub_elements)	A mixed element that combines two or more elements.
`QuadratureElement`(ufl_element)	A quadrature element.

class ffcx.element_interface.ABC[source]

Bases: object

Helper class that provides a standard way to create an ABC using inheritance.

class ffcx.element_interface.BaseElement[source]

Bases: abc.ABC

An abstract element class.

abstract property cell_type: Basix cell type used to initialise the element.

abstract property dim: int: Number of DOFs the element has.

abstract property discontinuous: bool: True if the discontinuous version of the element is used.

abstract property dpc_variant: Basix DPC variant used to initialise the element.

abstract property element_family: Basix element family used to initialise the element.

property element_type: Element type.

abstract property entity_closure_dofs: DOF numbers associated with the closure of each entity.

abstract property entity_dofs: DOF numbers associated with each entity.

abstract property family_name: str: Family name of the element.

abstract get_component_element(flat_component: int) → tuple[BaseElement, int, int][source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property is_custom_element: bool: True if the element is a custom Basix element.

abstract property lagrange_variant: Basix Lagrange variant used to initialise the element.

abstract property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

abstract property num_entity_dofs: Number of DOFs associated with each entity.

abstract property num_global_support_dofs

abstract property reference_geometry: Geometry of the reference element.

abstract property reference_topology: Topology of the reference element.

abstract tabulate(nderivs: int, points: numpy.ndarray)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

abstract property value_shape: Tuple[int, ...]: Value shape of the element basis function.

Note

For scalar elements, (1,) is returned. This is different from Basix where the value shape for scalar elements is (,).

abstract property value_size: int

Value size of the element.

Equal to numpy.prod(value_shape).

class ffcx.element_interface.BasixElement(element)[source]

Bases: ffcx.element_interface.BaseElement

An element defined by Basix.

property cell_type: Basix cell type used to initialise the element.

property dim: Number of DOFs the element has.

property discontinuous: True if the discontinuous version of the element is used.

property dpc_variant: Basix DPC variant used to initialise the element.

property element_family: Basix element family used to initialise the element.

property element_type: str: Element type.

property entity_closure_dofs: DOF numbers associated with the closure of each entity.

property entity_dofs: DOF numbers associated with each entity.

property family_name: Family name of the element.

get_component_element(flat_component)[source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property is_custom_element: bool: True if the element is a custom Basix element.

property lagrange_variant: Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

property num_entity_dofs: Number of DOFs associated with each entity.

property num_global_support_dofs

property reference_geometry: Geometry of the reference element.

property reference_topology: Topology of the reference element.

tabulate(nderivs, points)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

property value_shape: Get the value shape of the element.

property value_size

Value size of the element.

Equal to numpy.prod(value_shape).

class ffcx.element_interface.BlockedElement(sub_element, block_size, block_shape=None)[source]

Bases: ffcx.element_interface.BaseElement

An element with a block size that contains multiple copies of a sub element.

property cell_type: Basix cell type used to initialise the element.

property dim: Number of DOFs the element has.

property discontinuous: True if the discontinuous version of the element is used.

property dpc_variant: Basix DPC variant used to initialise the element.

property element_family: Basix element family used to initialise the element.

property element_type: Element type.

property entity_closure_dofs: DOF numbers associated with the closure of each entity.

property entity_dofs: DOF numbers associated with each entity.

property family_name: Family name of the element.

get_component_element(flat_component)[source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property lagrange_variant: Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

property num_entity_dofs: Number of DOFs associated with each entity.

property num_global_support_dofs

property reference_geometry: Geometry of the reference element.

property reference_topology: Topology of the reference element.

tabulate(nderivs, points)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

property value_shape: Value shape of the element basis function.

Note

For scalar elements, (1,) is returned. This is different from Basix where the value shape for scalar elements is (,).

property value_size

Value size of the element.

Equal to numpy.prod(value_shape).

class ffcx.element_interface.ComponentElement(element, component)[source]

Bases: ffcx.element_interface.BaseElement

An element representing one component of a BasixElement.

property cell_type: Basix cell type used to initialise the element.

property dim: Number of DOFs the element has.

property discontinuous: True if the discontinuous version of the element is used.

property dpc_variant: Basix DPC variant used to initialise the element.

property element_family: Basix element family used to initialise the element.

property entity_closure_dofs: DOF numbers associated with the closure of each entity.

property entity_dofs: DOF numbers associated with each entity.

property family_name: str: Family name of the element.

get_component_element(flat_component)[source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property lagrange_variant: Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

property num_entity_dofs: Number of DOFs associated with each entity.

property num_global_support_dofs

property reference_geometry: Geometry of the reference element.

property reference_topology: Topology of the reference element.

tabulate(nderivs, points)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

property value_shape: Value shape of the element basis function.

Note

For scalar elements, (1,) is returned. This is different from Basix where the value shape for scalar elements is (,).

property value_size

Value size of the element.

Equal to numpy.prod(value_shape).

class ffcx.element_interface.MixedElement(sub_elements)[source]

Bases: ffcx.element_interface.BaseElement

A mixed element that combines two or more elements.

property cell_type: Basix cell type used to initialise the element.

property dim: Number of DOFs the element has.

property discontinuous: True if the discontinuous version of the element is used.

property dpc_variant: Basix DPC variant used to initialise the element.

property element_family: Basix element family used to initialise the element.

property element_type: str: Get the element type.

property entity_closure_dofs: DOF numbers associated with the closure of each entity.

property entity_dofs: DOF numbers associated with each entity.

property family_name: Family name of the element.

get_component_element(flat_component)[source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property lagrange_variant: Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

property num_entity_dofs: Number of DOFs associated with each entity.

property num_global_support_dofs

property reference_geometry: Geometry of the reference element.

property reference_topology: Topology of the reference element.

tabulate(nderivs, points)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

property value_shape: Value shape of the element basis function.

Note

For scalar elements, (1,) is returned. This is different from Basix where the value shape for scalar elements is (,).

property value_size

Value size of the element.

Equal to numpy.prod(value_shape).

class ffcx.element_interface.QuadratureElement(ufl_element)[source]

Bases: ffcx.element_interface.BaseElement

A quadrature element.

property cell_type: None: Basix cell type used to initialise the element.

property dim: Number of DOFs the element has.

property discontinuous: True if the discontinuous version of the element is used.

property dpc_variant: Basix DPC variant used to initialise the element.

property element_family: Basix element family used to initialise the element.

property element_type: str: Element type.

property entity_closure_dofs: DOF numbers associated with the closure of each entity.

property entity_dofs: DOF numbers associated with each entity.

property family_name: Family name of the element.

get_component_element(flat_component)[source]

Get element that represents a component of the element, and the offset and stride of the component.

For example, for a MixedElement, this will return the sub-element that represents the given component, the offset of that sub-element, and a stride of 1. For a BlockedElement, this will return the sub-element, an offset equal to the component number, and a stride equal to the block size. For vector-valued element (eg H(curl) and H(div) elements), this returns a ComponentElement (and as offset of 0 and a stride of 1). When tabulate is called on the ComponentElement, only the part of the table for the given component is returned.

Parameters: flat_component – The component
Returns: component element, offset of the component, stride of the component

property lagrange_variant: Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: Number of DOFs associated with the closure of each entity.

property num_entity_dofs: Number of DOFs associated with each entity.

property num_global_support_dofs

property reference_geometry: Geometry of the reference element.

property reference_topology: Topology of the reference element.

tabulate(nderivs, points)[source]

Tabulate the basis functions of the element.

Parameters

nderivs – Number of derivatives to tabulate.
points – Points to tabulate at

Returns

Tabulated basis functions

property value_shape: Value shape of the element basis function.

Note

For scalar elements, (1,) is returned. This is different from Basix where the value shape for scalar elements is (,).

property value_size

Value size of the element.

Equal to numpy.prod(value_shape).

ffcx.element_interface.abstractmethod(funcobj)[source]

A decorator indicating abstract methods.

Requires that the metaclass is ABCMeta or derived from it. A class that has a metaclass derived from ABCMeta cannot be instantiated unless all of its abstract methods are overridden. The abstract methods can be called using any of the normal ‘super’ call mechanisms. abstractmethod() may be used to declare abstract methods for properties and descriptors.

Usage:

class C(metaclass=ABCMeta):
@abstractmethod def my_abstract_method(self, …):

…

ffcx.element_interface.basix_index(*args)[source]: Get the Basix index of a derivative.

ffcx.element_interface.create_basix_element(family_type, cell_type, degree, variant_info, discontinuous)[source]: Create a basix element.

ffcx.element_interface.create_element(element: ufl.finiteelement.finiteelementbase.FiniteElementBase) → ffcx.element_interface.BaseElement[source]

Create an FFCx element from a UFL element.

Parameters: element – A UFL finite element
Returns: A FFCx finite element

ffcx.element_interface.create_quadrature(cellname, degree, rule)[source]: Create a quadrature rule.

ffcx.element_interface.map_facet_points(points, facet, cellname)[source]: Map points from a reference facet to a physical facet.

ffcx.element_interface.reference_cell_vertices(cellname)[source]: Get the vertices of a reference cell.