finat.ufl package

Submodules

finat.ufl.brokenelement module

Element.

class finat.ufl.brokenelement.BrokenElement(element)

Bases: FiniteElementBase

The discontinuous version of an existing Finite Element space.

Init.

property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

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reconstruct(**kwargs)

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shortstr()

Format as string for pretty printing.

property sobolev_space

Return the underlying Sobolev space.

finat.ufl.elementlist module

Element.

This module provides an extensive list of predefined finite element families. Users or, more likely, form compilers, may register new elements by calling the function register_element.

finat.ufl.elementlist.canonical_element_description(family, cell, order, form_degree)

Given basic element information, return corresponding element information on canonical form.

Input: family, cell, (polynomial) order, form_degree Output: family (canonical), short_name (for printing), order, value shape, reference value shape, sobolev_space.

This is used by the FiniteElement constructor to ved input data against the element list and aliases defined in ufl.

finat.ufl.elementlist.feec_element(family, n, r, k)

Finite element exterior calculus notation.

n = topological dimension of domain r = polynomial order k = form_degree

finat.ufl.elementlist.feec_element_l2(family, n, r, k)

Finite element exterior calculus notation.

n = topological dimension of domain r = polynomial order k = form_degree

finat.ufl.elementlist.register_alias(alias, to)

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finat.ufl.elementlist.register_element(family, short_name, value_rank, sobolev_space, mapping, degree_range, cellnames)

Register new finite element family.

finat.ufl.elementlist.show_elements()

Shows all registered elements.

finat.ufl.enrichedelement module

This module defines the UFL finite element classes.

class finat.ufl.enrichedelement.EnrichedElement(*elements)

Bases: EnrichedElementBase

The vector sum of several finite element spaces.

\[\begin{split}\\textrm{EnrichedElement}(V, Q) = \\{v + q | v \\in V, q \\in Q\\}.\end{split}\]

Dual basis is a concatenation of subelements dual bases; primal basis is a concatenation of subelements primal bases; resulting element is not nodal even when subelements are. Structured basis may be exploited in form compilers.

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is_cellwise_constant()

Return whether the basis functions of this element is spatially constant over each cell.

shortstr()

Format as string for pretty printing.

class finat.ufl.enrichedelement.EnrichedElementBase(*elements)

Bases: FiniteElementBase

The vector sum of several finite element spaces.

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property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

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reconstruct(**kwargs)

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property sobolev_space

Return the underlying Sobolev space.

variant()

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class finat.ufl.enrichedelement.NodalEnrichedElement(*elements)

Bases: EnrichedElementBase

The vector sum of several finite element spaces.

\[\begin{split}\\textrm{EnrichedElement}(V, Q) = \\{v + q | v \\in V, q \\in Q\\}.\end{split}\]

Primal basis is reorthogonalized to dual basis which is a concatenation of subelements dual bases; resulting element is nodal.

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is_cellwise_constant()

Return whether the basis functions of this element is spatially constant over each cell.

shortstr()

Format as string for pretty printing.

finat.ufl.finiteelement module

This module defines the UFL finite element classes.

class finat.ufl.finiteelement.FiniteElement(family, cell=None, degree=None, form_degree=None, quad_scheme=None, variant=None)

Bases: FiniteElementBase

The basic finite element class for all simple finite elements.

Create finite element.

Args:

family: The finite element family cell: The geometric cell degree: The polynomial degree (optional) form_degree: The form degree (FEEC notation, used when field is

viewed as k-form)

quad_scheme: The quadrature scheme (optional) variant: Hint for the local basis function variant (optional)

property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

Return the mapping type for this element .

reconstruct(family=None, cell=None, degree=None, quad_scheme=None, variant=None)

Construct a new FiniteElement object with some properties replaced with new values.

shortstr()

Format as string for pretty printing.

property sobolev_space

Return the underlying Sobolev space.

variant()

Return the variant used to initialise the element.

finat.ufl.finiteelementbase module

This module defines the UFL finite element classes.

class finat.ufl.finiteelementbase.FiniteElementBase(family, cell, degree, quad_scheme, value_shape, reference_value_shape)

Bases: AbstractFiniteElement

Base class for all finite elements.

Initialize basic finite element data.

property cell

Return cell of finite element.

degree(component=None)

Return polynomial degree of finite element.

property embedded_subdegree

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property embedded_superdegree

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extract_component(i)

Recursively extract component index relative to a (simple) element.

and that element for given value component index.

extract_reference_component(i)

Recursively extract reference component index relative to a (simple) element.

and that element for given reference value component index.

extract_subelement_component(i)

Extract direct subelement index and subelement relative component index for a given component index.

extract_subelement_reference_component(i)

Extract direct subelement index and subelement relative.

reference component index for a given reference component index.

family()

Return finite element family.

is_cellwise_constant(component=None)

Return whether the basis functions of this element is spatially constant over each cell.

abstract mapping()

Return the mapping type for this element.

property num_sub_elements

Return number of sub-elements.

property pullback

Get the pull back.

quadrature_scheme()

Return quadrature scheme of finite element.

property reference_value_shape

Return the shape of the value space on the reference cell.

property reference_value_size

Return the integer product of the reference value shape.

abstract property sobolev_space

Return the underlying Sobolev space.

property sub_elements

Return list of sub-elements.

symmetry()

Return the symmetry dict.

This is a mapping \(c_0 \\to c_1\) meaning that component \(c_0\) is represented by component \(c_1\). A component is a tuple of one or more ints.

property value_shape

Return the shape of the value space on the global domain.

property value_size

Return the integer product of the value shape.

variant()

Return the variant used to initialise the element.

finat.ufl.hdivcurl module

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class finat.ufl.hdivcurl.CallableSobolevSpace(name, parents=None)

Bases: SobolevSpace

A Sobolev space that can be called to create HDiv and HCurl elements.

Instantiate a SobolevSpace object.

Args:

name: The name of this space, parents: A set of Sobolev spaces of which this space is a subspace.

class finat.ufl.hdivcurl.HCurlElement(element)

Bases: FiniteElementBase

A curl-conforming version of an outer product element, assuming this makes mathematical sense.

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property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

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reconstruct(**kwargs)

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shortstr()

Format as string for pretty printing.

property sobolev_space

Return the underlying Sobolev space.

variant()

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class finat.ufl.hdivcurl.HDivElement(element)

Bases: FiniteElementBase

A div-conforming version of an outer product element, assuming this makes mathematical sense.

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property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

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reconstruct(**kwargs)

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shortstr()

Format as string for pretty printing.

property sobolev_space

Return the underlying Sobolev space.

variant()

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class finat.ufl.hdivcurl.WithMapping(wrapee, mapping)

Bases: FiniteElementBase

Specify an alternative mapping for the wrappee.

For example, to use identity mapping instead of Piola map with an element E, write remapped = WithMapping(E, “identity”)

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property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

mapping()

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reconstruct(**kwargs)

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property reference_value_shape

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shortstr()

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property sobolev_space

Return the underlying Sobolev space.

property value_shape

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variant()

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finat.ufl.mixedelement module

This module defines the UFL finite element classes.

class finat.ufl.mixedelement.MixedElement(*elements, **kwargs)

Bases: FiniteElementBase

A finite element composed of a nested hierarchy of mixed or simple elements.

Create mixed finite element from given list of elements.

degree(component=None)

Return polynomial degree of finite element.

property embedded_subdegree

Return embedded subdegree.

property embedded_superdegree

Return embedded superdegree.

extract_component(i)

Recursively extract component index relative to a (simple) element.

and that element for given value component index.

extract_reference_component(i)

Recursively extract reference_component index relative to a (simple) element.

and that element for given value reference_component index.

extract_subelement_component(i)

Extract direct subelement index and subelement relative.

component index for a given component index.

extract_subelement_reference_component(i)

Extract direct subelement index and subelement relative.

reference_component index for a given reference_component index.

is_cellwise_constant(component=None)

Return whether the basis functions of this element is spatially constant over each cell.

mapping()

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property num_sub_elements

Return number of sub elements.

property pullback

Get the pull back.

reconstruct(**kwargs)

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reconstruct_from_elements(*elements)

Reconstruct a mixed element from new subelements.

shortstr()

Format as string for pretty printing.

property sobolev_space

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property sub_elements

Return list of sub elements.

symmetry()

Return the symmetry dict, which is a mapping \(c_0 \\to c_1\).

meaning that component \(c_0\) is represented by component \(c_1\). A component is a tuple of one or more ints.

variant()

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class finat.ufl.mixedelement.TensorElement(family, cell=None, degree=None, shape=None, symmetry=None, quad_scheme=None, variant=None)

Bases: MixedElement

A special case of a mixed finite element where all elements are equal.

Create tensor element (repeated mixed element with optional symmetries).

extract_subelement_component(i)

Extract direct subelement index and subelement relative.

component index for a given component index.

flattened_sub_element_mapping()

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mapping()

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property pullback

Get pull back.

reconstruct(**kwargs)

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shortstr()

Format as string for pretty printing.

symmetry()

Return the symmetry dict, which is a mapping \(c_0 \\to c_1\).

meaning that component \(c_0\) is represented by component \(c_1\). A component is a tuple of one or more ints.

variant()

Return the variant used to initialise the element.

class finat.ufl.mixedelement.VectorElement(family, cell=None, degree=None, dim=None, form_degree=None, quad_scheme=None, variant=None)

Bases: MixedElement

A special case of a mixed finite element where all elements are equal.

Create vector element (repeated mixed element).

mapping()

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reconstruct(**kwargs)

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shortstr()

Format as string for pretty printing.

variant()

Return the variant used to initialise the element.

finat.ufl.restrictedelement module

This module defines the UFL finite element classes.

class finat.ufl.restrictedelement.RestrictedElement(element, restriction_domain)

Bases: FiniteElementBase

Represents the restriction of a finite element to a type of cell entity.

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is_cellwise_constant()

Return whether the basis functions of this element is spatially constant over each cell.

mapping()

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num_restricted_sub_elements()

Return number of restricted sub elements.

property num_sub_elements

Return number of sub elements.

reconstruct(**kwargs)

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restricted_sub_elements()

Return list of restricted sub elements.

restriction_domain()

Return the domain onto which the element is restricted.

shortstr()

Format as string for pretty printing.

property sobolev_space

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sub_element()

Return the element which is restricted.

property sub_elements

Return list of sub elements.

symmetry()

Return the symmetry dict, which is a mapping \(c_0 \\to c_1\).

meaning that component \(c_0\) is represented by component \(c_1\). A component is a tuple of one or more ints.

variant()

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finat.ufl.tensorproductelement module

This module defines the UFL finite element classes.

class finat.ufl.tensorproductelement.TensorProductElement(*elements, **kwargs)

Bases: FiniteElementBase

The tensor product of \(d\) element spaces.

\[V = V_1 \otimes V_2 \otimes ... \otimes V_d\]

Given bases \(\{\phi_{j_i}\}\) of the spaces \(V_i\) for \(i = 1, ...., d\), \(\{ \phi_{j_1} \otimes \phi_{j_2} \otimes \cdots \otimes \phi_{j_d} \}\) forms a basis for \(V\).

Create TensorProductElement from a given list of elements.

property embedded_subdegree

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property embedded_superdegree

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mapping()

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property num_sub_elements

Return number of subelements.

reconstruct(**kwargs)

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shortstr()

Short pretty-print.

property sobolev_space

Return the underlying Sobolev space of the TensorProductElement.

property sub_elements

Return subelements (factors).

variant()

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Module contents

Legacy UFL features.