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Quadrature

Usually quadrature is a hidden layer as quadrature rules are chosen automatically based on the polynomial degree of the ansatz functions and the specified quadorder of the user data.

Hence, quadrature rules are only needed if the user wants write his own low-level assembly.

Quadrature rules consist of points (coordinates of evaluation points with respect to reference geometry) and weights. There are constructors for several AbstractElementGeometries (from ExtendableGrids) and different order (some have generic formulas for arbitrary order), see below for a detailed list.

ExtendableFEMBase.QuadratureRule — Type
abstract type QuadratureRule{T<:Real, ET<:ExtendableGrids.AbstractElementGeometry}

A struct that contains the name of the quadrature rule, the reference points and the weights for the parameter-determined element geometry.

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ExtendableFEMBase.QuadratureRule — Method
function QuadratureRule{T,ET}(order::Int) where {T<:Real, ET <: AbstractElementGeometry0D}

Constructs 0D quadrature rule of specified order (always point evaluation).

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ExtendableFEMBase.QuadratureRule — Method
function QuadratureRule{T,ET}(order::Int) where {T<:Real, ET <: Parallelepiped3D}

Constructs quadrature rule on Parallelepiped3D of specified order.

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ExtendableFEMBase.QuadratureRule — Method
function QuadratureRule{T,ET}(order::Int) where {T<:Real, ET <: Parallelogram2D}

Constructs quadrature rule on Parallelogram2D of specified order.

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ExtendableFEMBase.QuadratureRule — Method
function QuadratureRule{T,ET}(order::Int) where {T<:Real, ET <: Tetrahedron3D}

Constructs quadrature rule on Tetrahedron3D of specified order.

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Base.eltype — Method
eltype(
    _::QuadratureRule{T<:Real, ET<:ExtendableGrids.AbstractElementGeometry}
) -> Any

Custom eltype function for QuadratureRule{T,ET}.

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Base.show — Method
show(io::IO, Q::QuadratureRule)

Custom show function for QuadratureRule{T,ET} that prints some information.

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ExtendableFEMBase.integrate! — Method
integrate!(
    integral4items::AbstractArray{T},
    grid::ExtendableGrids.ExtendableGrid{Tv, Ti},
    AT::Type{<:ExtendableGrids.AssemblyType},
    integrand;
    offset,
    bonus_quadorder,
    quadorder,
    time,
    items,
    force_quadrature_rule,
    kwargs...
)

Integration that writes result on every item into integral4items.

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ExtendableFEMBase.integrate — Method
integrate(
    grid::ExtendableGrids.ExtendableGrid,
    AT::Type{<:ExtendableGrids.AssemblyType},
    integrand!,
    resultdim::Int64;
    T,
    kwargs...
) -> Union{Float64, Vector{Float64}}

Integration that returns total integral.

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ExtendableFEMBase.ref_integrate! — Method
ref_integrate!(
    integral::AbstractArray,
    EG::Type{<:ExtendableGrids.AbstractElementGeometry},
    order::Int64,
    integrand::Function
)

Integration for reference basis functions on reference domains (merely for testing stuff).

Note: area of reference geometry is not multiplied

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Accumulating Vector (not relevant for users, but for completeness)

Internally a global integration uses an accumulating vector and calls the cell-wise integration.

ExtendableFEMBase.AccumulatingVector — Type
struct AccumulatingVector{T} <: AbstractArray{T, 2}

vector that is acting as an AbstractArray{T, 2} and automatically accumulates all values from the second dimension

AV[k,j] += s for any j results in AV.entries[k] += s

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