Dof Handler

Type definitions

Dof handlers are subtypes of AbstractDofhandler{sdim}, i.e. they are parametrized by the spatial dimension. Internally a helper struct InterpolationInfo is utilized to enforce type stability during dof distribution, because the interpolations are not available as concrete types.

Ferrite.InterpolationInfo — Type

InterpolationInfo

Gathers all the information needed to distribute dofs for a given interpolation. Note that this cache is of the same type no matter the interpolation: the purpose is to make dof-distribution type-stable.

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Ferrite.PathOrientationInfo — Type

PathOrientationInfo

Orientation information for 1D entities.

The orientation for 1D entities is defined by the indices of the grid nodes associated to the vertices. To give an example, the oriented path

1 ---> 2

is called regular, indicated by regular=true, while the oriented path

2 ---> 1

is called inverted, indicated by regular=false.

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Ferrite.SurfaceOrientationInfo — Type

SurfaceOrientationInfo

Orientation information for 2D entities. Such an entity can be possibly flipped (i.e. the defining vertex order is reverse to the spanning vertex order) and the vertices can be rotated against each other. Take for example the faces

1---2 2---3
| A | | B |
4---3 1---4

which are rotated against each other by 90° (shift index is 1) or the faces

1---2 2---1
| A | | B |
4---3 3---4

which are flipped against each other. Any combination of these can happen. The combination to map this local face to the defining face is encoded with this data structure via $rotate \circ flip$ where the rotation is indiced by the shift index. !!!NOTE TODO implement me.

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Internal API

The main entry point for dof distribution is __close!.

Ferrite.__close! — Function

__close!(dh::DofHandler)

Internal entry point for dof distribution.

Dofs are distributed as follows: For the DofHandler each SubDofHandler is visited in the order they were added. For each field in the SubDofHandler create dofs for the cell. This means that dofs on a particular cell will be numbered in groups for each field, so first the dofs for field 1 are distributed, then field 2, etc. For each cell dofs are first distributed on its vertices, then on the interior of edges (if applicable), then on the interior of faces (if applicable), and finally on the cell interior. The entity ordering follows the geometrical ordering found in vertices, faces and edges.

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Ferrite.get_grid — Function

get_grid(dh::AbstractDofHandler)

Access some grid representation for the dof handler.

Note

This API function is currently not well-defined. It acts as the interface between distributed assembly and assembly on a single process, because most parts of the functionality can be handled by only acting on the locally owned cell set.

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Ferrite.find_field — Function

find_field(dh::DofHandler, field_name::Symbol)::NTuple{2,Int}

Return the index of the field with name field_name in a DofHandler. The index is a NTuple{2,Int}, where the 1st entry is the index of the SubDofHandler within which the field was found and the 2nd entry is the index of the field within the SubDofHandler.

Note

Always finds the 1st occurrence of a field within DofHandler.

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find_field(sdh::SubDofHandler, field_name::Symbol)::Int

Return the index of the field with name field_name in a SubDofHandler. Throw an error if the field is not found.

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Ferrite._find_field — Function

_find_field(sdh::SubDofHandler, field_name::Symbol)::Int

Return the index of the field with name field_name in the SubDofHandler sdh. Return nothing if the field is not found.

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Ferrite._close_subdofhandler! — Function

_close_subdofhandler!(dh::DofHandler{sdim}, sdh::SubDofHandler, sdh_index::Int, nextdof::Int, vertexdicts, edgedicts, facedicts) where {sdim}

Main entry point to distribute dofs for a single SubDofHandler on its subdomain.

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Ferrite._distribute_dofs_for_cell! — Function

_distribute_dofs_for_cell!(dh::DofHandler{sdim}, cell::AbstractCell, ip_info::InterpolationInfo, nextdof::Int, vertexdict, edgedict, facedict) where {sdim}

Main entry point to distribute dofs for a single cell.

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Ferrite.permute_and_push! — Function

permute_and_push!

For interpolations with more than one interior dof per edge it may be necessary to adjust the dofs. Since dofs are (initially) enumerated according to the local edge direction there can be a direction mismatch with the neighboring element. For example, in the following nodal interpolation example, with three interior dofs on each edge, the initial pass have distributed dofs 4, 5, 6 according to the local edge directions:

+-----------+
|     A     |
+--4--5--6->+    local edge on element A

 ---------->     global edge

+<-6--5--4--+    local edge on element B
|     B     |
+-----------+

For most scalar-valued interpolations we can simply compensate for this by reversing the numbering on all edges that do not match the global edge direction, i.e. for the edge on element B in the example.

In addition, we also have to preserve the ordering at each dof location.

For more details we refer to Scroggs et al. [13] as we follow the methodology described therein.

References

[13] Scroggs et al. ACM Trans. Math. Softw. 48 (2022).

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!!!NOTE TODO implement me.

For more details we refer to [1] as we follow the methodology described therein.

[1] Scroggs, M. W., Dokken, J. S., Richardson, C. N., & Wells, G. N. (2022). Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes. ACM Transactions on Mathematical Software (TOMS), 48(2), 1-23.

!!!TODO citation via software.

!!!TODO Investigate if we can somehow pass the interpolation into this function in a typestable way.

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