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FESpace

To generate a finite element space only a finite element type and a grid is needed, dofmaps are generated automatically on their first demand.

ExtendableFEMBase.FESpace — Type
struct FESpace{Tv, Ti, FEType<:AbstractFiniteElement,AT<:AssemblyType}
	name::String                          # full name of finite element space (used in messages)
	broken::Bool                          # if true, broken dofmaps are generated
	ndofs::Int                            # total number of dofs
	coffset::Int                          # offset for component dofs
	xgrid::ExtendableGrid[Tv,Ti}          # link to xgrid 
	dofgrid::ExtendableGrid{Tv,Ti}	      # link to (sub) grid used for dof numbering (expected to be equal to or child grid of xgrid)
	dofmaps::Dict{Type{<:AbstractGridComponent},Any} # backpack with dofmaps
end

A struct that has a finite element type as parameter and carries dofmaps (CellDofs, FaceDofs, BFaceDofs) plus additional grid information and access to arrays holding coefficients if needed.

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ExtendableFEMBase.FESpace — Method
function FESpace{FEType<:AbstractFiniteElement,AT<:AssemblyType}(
	xgrid::ExtendableGrid{Tv,Ti};
	name = "",
	broken::Bool = false)

Constructor for FESpace of the given FEType, AT = ONCELLS/ONFACES/ONEDGES generates a finite elements space on the cells/faces/edges of the provided xgrid (if omitted ONCELLS is used as default). The broken switch allows to generate a broken finite element space (that is piecewise H1/Hdiv/HCurl). If no name is provided it is generated automatically from FEType. If no AT is provided, the space is generated ON_CELLS.

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Base.eltype — Method
eltype(
    _::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT}
) -> Type{FEType} where FEType<:AbstractFiniteElement

Custom eltype function for FESpace returns the finite element type parameter of the finite element space.

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Base.get! — Method
get!(FES::FESpace, DM::Type{<:DofMap}) -> Any

To be called by getindex. This triggers lazy creation of non-existing dofmaps

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Base.getindex — Method
Base.getindex(FES::FESpace,DM::Type{<:DofMap})

Generic method for obtaining dofmap. This method is mutating in the sense that non-existing dofmaps are created on demand. Due to the fact that components are stored as Any the return value triggers type instability.

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Base.show — Method
show(
    io::IO,
    FES::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT}
)

Custom show function for FESpace that prints some information and all available dofmaps.

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ExtendableFEMBase.assemblytype — Method
assemblytype(
    _::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT}
) -> Any

returns the assembly type parameter of the finite element space, i.e. on which entities of the grid the finite element is defined.

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ExtendableFEMBase.count_ndofs — Method
count_ndofs(
    xgrid,
    FEType,
    broken::Bool
) -> Tuple{Int64, Int64}

counts the total number of degrees of freedom for the FEType for the whole grid

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ExtendableFEMBase.get_basis — Method
get_basis(
    AT::Type{<:ExtendableGrids.AssemblyType},
    FEType::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> ExtendableFEMBase.var"#closure#123"

returns the closure function of form

closure(refbasis, xref)

that computes the evaluations of the basis functions on the reference geometry

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ExtendableFEMBase.get_basissubset — Method
get_basissubset(
    _::Type{<:ExtendableGrids.AssemblyType},
    FE::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT},
    _::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Union{ExtendableFEMBase.var"#21#22", ExtendableFEMBase.var"#closure#268"{_A, _B, _C, Int64, Int64} where {_A, _B, _C}}

returns a closure function of the form

closure(subset_ids::Array{Int, 1}, cell)

which returns the ids of the local basis functions needed on the cell. Usually, subset_ids = 1:ndofs (meaning that all basis functions on the reference cells are used),

See e.g. the 3D implementation of BDM1 or H1P3 where different basis functions are chosen depending on the face orientations (which in 3D is not just a sign)

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ExtendableFEMBase.get_coefficients — Method
get_coefficients(
    _::Type{<:ExtendableGrids.AssemblyType},
    FE::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT},
    _::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> ExtendableFEMBase.var"#closure#195"

returns the coefficients for local evaluations of finite element functions ( see e.g. h1v_br.jl for a use-case)

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ExtendableFEMBase.get_ndofs — Method
get_ndofs(
    AT::Type{<:ExtendableGrids.AssemblyType},
    FEType::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Int64

returns the number of degrees of freedom for the given AssemblyType, FEType and geometry

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ExtendableFEMBase.get_ndofs_all — Method
get_ndofs_all(
    AT::Type{<:ExtendableGrids.AssemblyType},
    FEType::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Int64

returns the total number of degrees of freedom for the given AssemblyType, FEType and geometry

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ExtendableFEMBase.get_polynomialorder — Method
get_polynomialorder(
    AT::Type{<:ExtendableGrids.AssemblyType},
    FE::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Int64

returns the expected polynomial order of the basis functions (used to determine default quadrature orders)

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ExtendableFEMBase.interior_dofs_offset — Method
interior_dofs_offset(
    AT::Type{<:ExtendableGrids.AssemblyType},
    FE::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Int64

returns the offset for the interior degrees of freedom (all vertex, face and edge dofs are assumed to come first and before that number)

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ExtendableFEMBase.isdefined — Method
isdefined(
    FEType::Type{<:AbstractFiniteElement},
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> Bool

tells if FEType is defined on this ElementGeometry

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DofMaps

ExtendableFEMBase.DofMap — Type
abstract type DofMap <: ExtendableGrids.AbstractGridAdjacency

Dofmaps are stored as an ExtendableGrids.AbstractGridAdjacency in the finite element space and collect information with respect to different AssemblyTypes. They are generated automatically on demand and the dofmaps associated to each subtype can be accessed via FESpace[DofMap].

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ExtendableFEMBase.ParsedDofMap — Method
ParsedDofMap(
    pattern::String,
    ncomponents,
    EG::Type{<:ExtendableGrids.AbstractElementGeometry}
) -> ExtendableFEMBase.ParsedDofMap

parses a dofmap string (defined in each finite element definition file) and generated a ParsedDofMap for a certain number of components and the given geometry

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ExtendableFEMBase.Dofmap4AssemblyType — Method
Dofmap4AssemblyType(
    FES::FESpace,
    AT::Type{<:ExtendableGrids.AssemblyType}
) -> Any

yields the coressponding dofmap of the FESpace for a given AssemblyType (assumed with respect to the (parent)grid of the FESpace)

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ExtendableFEMBase.EffAT4AssemblyType — Method
EffAT4AssemblyType(
    _::Type{ON_CELLS},
    _::Type{ON_CELLS}
) -> Type{ON_CELLS}

Effective AssemblyType (on the subgrid) for two AssemblyTypes where the first one is related to where the finite element functions live and the second one to where something should be assembled both with respect to the common parent grid (e.g. face-based finite elements live on a subgrid of all faces, where the faces are the cells in this subgrid, and they cannot be evaluated over the cells of the parentgrid, but on the faces of the parengrid, which are the cells in the subgrid)

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ExtendableFEMBase.boundarydofs — Method
boundarydofs(FES; dofmap, regions) -> Any

returns an array with the number of all dofs associated to a boundary dofmap (default: BFaceDofs) and certain boundary regions (default: all regions)

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ExtendableFEMBase.get_ndofs — Method
get_ndofs(
    P::ExtendableFEMBase.ParsedDofMap,
    _::Type{ExtendableFEMBase.DofTypeNode}
) -> Int64

total number of dofs of the DofType

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ExtendableFEMBase.get_ndofs4c — Method
get_ndofs4c(
    P::ExtendableFEMBase.ParsedDofMap,
    _::Type{ExtendableFEMBase.DofTypeNode}
) -> Int64

total number of dofs of the DofType for a single component

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ExtendableFEMBase.init_broken_dofmap! — Method
init_broken_dofmap!(
    FES::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT},
    DM::Union{Type{BFaceDofs}, Type{FaceDofs}}
) -> ExtendableGrids.VariableTargetAdjacency

generates the BFaceDofs or FaceDofs DofMap for a broken FESpace based on the pattern of the FEType

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ExtendableFEMBase.init_dofmap_from_pattern! — Method
init_dofmap_from_pattern!(
    FES::FESpace{Tv, Ti, FEType<:AbstractFiniteElement, APT},
    DM::Type{<:DofMap}
) -> Any

generates the DofMap for the FESpace based on the pattern of the FEType

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ExtendableFEMBase.parse_pattern — Method
parse_pattern(
    pattern::String
) -> Vector{ExtendableFEMBase.DofMapPatternSegment}

splits a pattern string into pairs of single chars and Ints and generated a sequence of DofMapPatternSegments

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The following DofMap subtypes are available and are used as keys to access the dofmap via FESpace[DofMap] (which is equivalent to FESpace.dofmaps[DofMap]).

DofMapExplanation
CellDofsdegrees of freedom for on each cell
FaceDofsdegrees of freedom for each face
EdgeDofsdegrees of freedom for each edge (in 3D)
BFaceDofsdegrees of freedom for each boundary face
BEdgeDofsdegrees of freedom for each boundary edge (in 3D)