ExtendableFEMBase.jl/src/fedefs/h1_bubble.jl at 59ad089b4163bb44cb436d3b8f827f1e015b3431 · WIAS-PDELib/ExtendableFEMBase.jl · GitHub

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"""
````
abstract type H1BUBBLE{ncomponents} <: AbstractH1FiniteElement where {ncomponents<:Int}
````

Piecewise bubbles (=zero at boundary)

allowed element geometries:
- Edge1D (one quadratic bubble)
- Triangle2D (one cubic bubble)
- Quadrilateral2D (one quartic bubble)
- Tetrahedron3D (one cubic bubble)
"""
abstract type H1BUBBLE{ncomponents} <: AbstractH1FiniteElement where {ncomponents <: Int} end
H1BUBBLE(ncomponents::Int) = H1BUBBLE{ncomponents}

function Base.show(io::Core.IO, ::Type{<:H1BUBBLE{ncomponents}}) where {ncomponents}
    return print(io, "H1BUBBLE{$ncomponents}")
end

get_ncomponents(FEType::Type{<:H1BUBBLE}) = FEType.parameters[1]
get_ndofs(::Type{<:AssemblyType}, FEType::Type{<:H1BUBBLE}, EG::Type{<:AbstractElementGeometry}) = FEType.parameters[1]

get_polynomialorder(::Type{<:H1BUBBLE}, ::Type{<:AbstractElementGeometry1D}) = 2;
get_polynomialorder(::Type{<:H1BUBBLE}, ::Type{<:Triangle2D}) = 3;
get_polynomialorder(::Type{<:H1BUBBLE}, ::Type{<:Quadrilateral2D}) = 4;
get_polynomialorder(::Type{<:H1BUBBLE}, ::Type{<:Tetrahedron3D}) = 4;

get_dofmap_pattern(FEType::Type{<:H1BUBBLE}, ::Type{CellDofs}, EG::Type{<:AbstractElementGeometry}) = "I1"

isdefined(FEType::Type{<:H1BUBBLE}, ::Type{<:AbstractElementGeometry1D}) = true
isdefined(FEType::Type{<:H1BUBBLE}, ::Type{<:Triangle2D}) = true
isdefined(FEType::Type{<:H1BUBBLE}, ::Type{<:Quadrilateral2D}) = true
isdefined(FEType::Type{<:H1BUBBLE}, ::Type{<:Tetrahedron3D}) = true

interior_dofs_offset(::Type{ON_CELLS}, ::Type{H1BUBBLE{ncomponents}}, EG::Type{<:AbstractElementGeometry}) where {ncomponents} = 0

init_interpolator!(FES::FESpace{Tv, Ti, FEType, APT}, ::Type{ON_CELLS}) where {Tv, Ti, FEType <: H1BUBBLE, APT} = MomentInterpolator(FES, ON_CELLS)

function ExtendableGrids.interpolate!(Target::AbstractArray{T, 1}, FE::FESpace{Tv, Ti, FEType, APT}, ::Type{ON_CELLS}, exact_function!; items = [], kwargs...) where {T, Tv, Ti, FEType <: H1BUBBLE, APT}
    get_interpolator(FE, ON_CELLS).evaluate!(Target, exact_function!, items, kwargs...)
end

function get_basis(::Type{<:AssemblyType}, ::Type{H1BUBBLE{ncomponents}}, ::Type{<:AbstractElementGeometry1D}) where {ncomponents}
    return function closure(refbasis, xref)
        for k in 1:ncomponents
            refbasis[k, k] = 6 * xref[1] * (1 - xref[1])
        end
        return
    end
end

function get_basis(::Type{<:AssemblyType}, ::Type{H1BUBBLE{ncomponents}}, ::Type{<:Triangle2D}) where {ncomponents}
    return function closure(refbasis, xref)
        for k in 1:ncomponents
            refbasis[k, k] = 60 * (1 - xref[1] - xref[2]) * xref[1] * xref[2]
        end
        return
    end
end

function get_basis(::Type{<:AssemblyType}, ::Type{H1BUBBLE{ncomponents}}, ::Type{<:Quadrilateral2D}) where {ncomponents}
    return function closure(refbasis, xref)
        for k in 1:ncomponents
            refbasis[k, k] = 36 * (1 - xref[1]) * (1 - xref[2]) * xref[1] * xref[2]
        end
        return
    end
end

function get_basis(::Type{<:AssemblyType}, ::Type{H1BUBBLE{ncomponents}}, ::Type{<:Tetrahedron3D}) where {ncomponents}
    return function closure(refbasis, xref)
        for k in 1:ncomponents
            refbasis[k, k] = 840 * (1 - xref[1] - xref[2] - xref[3]) * xref[1] * xref[2] * xref[3]
        end
        return
    end
end