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Interpolations

Type definitions

Interpolations are subtypes of Interpolation{shape, order}, i.e. they are parametrized by the reference element and its characteristic order.

Fallback methods applicable for all subtypes of Interpolation

Ferrite.getrefshape — Method
Ferrite.getrefshape(::Interpolation)::AbstractRefShape

Return the reference element shape of the interpolation.

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Ferrite.reference_shape_gradient — Method
reference_shape_gradient(ip::Interpolation, ξ::Vec, i::Int)

Evaluate the gradient of the ith shape function of the interpolation ip in reference coordinate ξ.

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Ferrite.boundarydof_indices — Function
boundarydof_indices(::Type{<:BoundaryIndex})

Helper function to generically dispatch on the correct dof sets of a boundary entity.

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Ferrite.reference_shape_values! — Function
reference_shape_values!(values::AbstractArray{T}, ip::Interpolation, ξ::Vec)

Evaluate all shape functions of ip at once at the reference point ξ and store them in values.

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Ferrite.reference_shape_gradients! — Function
reference_shape_gradients!(gradients::AbstractArray, ip::Interpolation, ξ::Vec)

Evaluate all shape function gradients of ip at once at the reference point ξ and store them in gradients.

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Ferrite.reference_shape_gradients_and_values! — Function
reference_shape_gradients_and_values!(gradients::AbstractArray, values::AbstractArray, ip::Interpolation, ξ::Vec)

Evaluate all shape function gradients and values of ip at once at the reference point ξ and store them in values.

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Ferrite.reference_shape_hessians_gradients_and_values! — Function
reference_shape_hessians_gradients_and_values!(hessians::AbstractVector, gradients::AbstractVector, values::AbstractVector, ip::Interpolation, ξ::Vec)

Evaluate all shape function hessians, gradients and values of ip at once at the reference point ξ and store them in hessians, gradients, and values.

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Required methods to implement for all subtypes of Interpolation to define a new finite element

Depending on the dimension of the reference element the following functions have to be implemented

Ferrite.vertexdof_indices — Method
vertexdof_indices(ip::Interpolation)

A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by vertices(::Cell). The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell.

Note

The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.

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Ferrite.dirichlet_vertexdof_indices — Method
dirichlet_vertexdof_indices(ip::Interpolation)

A tuple containing tuples of local dof indices for the respective vertex in local enumeration on a cell defined by vertices(::Cell). The vertex enumeration must match the vertex enumeration of the corresponding geometrical cell. Used internally in ConstraintHandler and defaults to vertexdof_indices(ip::Interpolation) for continuous interpolation.

Note

The dofs appearing in the tuple must be continuous and increasing! The first dof must be the 1, as vertex dofs are enumerated first.

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Ferrite.facedof_indices — Method
facedof_indices(ip::Interpolation)

A tuple containing tuples of all local dof indices for the respective face in local enumeration on a cell defined by faces(::Cell). The face enumeration must match the face enumeration of the corresponding geometrical cell.

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Ferrite.facedof_interior_indices — Method
facedof_interior_indices(ip::Interpolation)

A tuple containing tuples of the local dof indices on the interior of the respective face in local enumeration on a cell defined by faces(::Cell). The face enumeration must match the face enumeration of the corresponding geometrical cell. Note that the vertex and edge dofs are included here.

Note

The dofs appearing in the tuple must be continuous and increasing! The first dof must be the computed via "last edge interior dof index + 1", if face dofs exist.

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Ferrite.edgedof_indices — Method
edgedof_indices(ip::Interpolation)

A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by edges(::Cell). The edge enumeration must match the edge enumeration of the corresponding geometrical cell.

The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.

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Ferrite.dirichlet_edgedof_indices — Method
dirichlet_edgedof_indices(ip::Interpolation)

A tuple containing tuples of local dof indices for the respective edge in local enumeration on a cell defined by edges(::Cell). The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Used internally in ConstraintHandler and defaults to edgedof_indices(ip::Interpolation) for continuous interpolation.

The dofs are guaranteed to be aligned with the local ordering of the entities on the oriented edge. Here the first entries are the vertex dofs, followed by the edge interior dofs.

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Ferrite.edgedof_interior_indices — Method
edgedof_interior_indices(ip::Interpolation)

A tuple containing tuples of the local dof indices on the interior of the respective edge in local enumeration on a cell defined by edges(::Cell). The edge enumeration must match the edge enumeration of the corresponding geometrical cell. Note that the vertex dofs are included here.

Note

The dofs appearing in the tuple must be continuous and increasing! The first dof must be computed via "last vertex dof index + 1", if edge dofs exist.

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Ferrite.volumedof_interior_indices — Method
volumedof_interior_indices(ip::Interpolation)

Tuple containing the dof indices associated with the interior of a volume.

Note

The dofs appearing in the tuple must be continuous and increasing, volumedofs are enumerated last.

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Ferrite.is_discontinuous — Method
is_discontinuous(::Interpolation)
is_discontinuous(::Type{<:Interpolation})

Checks whether the interpolation is discontinuous (i.e. DiscontinuousLagrange)

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Ferrite.adjust_dofs_during_distribution — Method
adjust_dofs_during_distribution(::Interpolation)

This function must return true if the dofs should be adjusted (i.e. permuted) during dof distribution. This is in contrast to i) adjusting the dofs during reinit! in the assembly loop, or ii) not adjusting at all (which is not needed for low order interpolations, generally).

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Ferrite.mapping_type — Function
mapping_type(ip::Interpolation)

Get the type of mapping from the reference cell to the real cell for an interpolation ip. Subtypes of ScalarInterpolation and VectorizedInterpolation return IdentityMapping(), but other non-scalar interpolations may request different mapping types.

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for all entities which exist on that reference element. The dof functions default to having no dofs defined on a specific entity. Hence, not overloading of the dof functions will result in an element with zero dofs. Also, it should always be double checked that everything is consistent as specified in the docstring of the corresponding function, as inconsistent implementations can lead to bugs which are really difficult to track down.