Fields

Fields serve as loose wrappers around AbstractArray subtypes such that the size of array slices are known at compile time. Although this introduces a type-instability, the idea is to do this at the top most level (mainly at setup time of a FEM simulation). By introducing this type instability, we can gain information about the field type that is used in methods downstream to construct StaticArrays of views of field types.

All fields are subtypes of the abstract type AbstractField

julia> using FiniteElementContainers
julia> AbstractFieldERROR: UndefVarError: `AbstractField` not defined

Example - H1Field a.k.a. NodalField

We can set up a H1Field in one of two ways. The simplest constructor form can be used as follows

julia> using FiniteElementContainers
julia> field = H1Field(rand(2, 10), (:field_1, :field_2))2×10 H1Field{Float64, 2, Vector{Float64}, (field_1 = 1, field_2 = 2)}:
 0.451377  0.969066   0.438278  0.178982  …  0.779407  0.683729  0.33337
 0.459782  0.0885674  0.917637  0.403944     0.223429  0.487543  0.613777

This is stored in a vectorized way as can be seen above

julia> field.vals20-element Vector{Float64}:
 0.45137713579117145
 0.4597819921140073
 0.9690656663703828
 0.08856743621400542
 0.43827820404704787
 0.9176368122858228
 0.17898154546554157
 0.4039438406946191
 0.3383351119927308
 0.7380317859671546
 0.8577319865177147
 0.7440719386916873
 0.9833626053302903
 0.5001236876783919
 0.7794065793963474
 0.2234290593213245
 0.6837288310673095
 0.48754314672294063
 0.333370277805486
 0.6137771095784643

Fields can be indexed like regular arrays, e.g.

julia> field[1, 1]0.45137713579117145

julia> field[1, :]10-element Vector{Float64}:
 0.45137713579117145
 0.9690656663703828
 0.43827820404704787
 0.17898154546554157
 0.3383351119927308
 0.8577319865177147
 0.9833626053302903
 0.7794065793963474
 0.6837288310673095
 0.333370277805486

etc.

But they can also be indexed by the symbols provided during construction

julia> field[:field_1]10-element Vector{Float64}:
 0.45137713579117145
 0.9690656663703828
 0.43827820404704787
 0.17898154546554157
 0.3383351119927308
 0.8577319865177147
 0.9833626053302903
 0.7794065793963474
 0.6837288310673095
 0.333370277805486

Abstract type

The base type for fields is the AbstractField abstract type.

abstract type AbstractField{T, N, NF, Vals, SymIDMap} <: AbstractArray{T, N}

Any new field added to FiniteElementContainers should be a subtype of this type.

Methods for AbstractField

fill!(
    field::FiniteElementContainers.AbstractField{T, N, NF, V, S},
    v
) -> Any

names(
    _::FiniteElementContainers.AbstractField{T, N, NF, Vals, SymIDMap}
) -> Any

_sym_id_map(
    _::FiniteElementContainers.AbstractField{T, N, NF, Vals, SymIDMap},
    sym::Symbol
) -> Any

num_fields(
    _::FiniteElementContainers.AbstractField{T, N, NF, Vals, SymIDMap}
) -> Any

get_backend(
    field::FiniteElementContainers.AbstractField
) -> Any

Implementations

The existing direct subtypes of AbstractField are the following

Connectivity

The connectivity type is a simple alias for L2ElementField defined below

struct L2ElementField{T, NN, Vals, SymIDMap} <: FiniteElementContainers.AbstractField{T, 2, NN, Vals, SymIDMap}

connectivity(
    conn::Connectivity,
    e::Int64
) -> SubArray{_A, 1, P, I, true} where {_A, P<:(Connectivity), I<:Tuple{Base.Slice{T} where T<:Base.OneTo, Int64}}

connectivity(conn::Connectivity) -> Any

H1 field

struct H1Field{T, NF, Vals<:AbstractArray{T, 1}, SymIDMap} <: FiniteElementContainers.AbstractField{T, 2, NF, Vals<:AbstractArray{T, 1}, SymIDMap}

H1Field(vals::AbstractMatrix, syms) -> H1Field

num_nodes(field::H1Field{T, NF, Vals, SymIDMap}) -> Any

L2Element field

struct L2ElementField{T, NN, Vals<:AbstractArray{T, 1}, SymIDMap} <: FiniteElementContainers.AbstractField{T, 2, NN, Vals<:AbstractArray{T, 1}, SymIDMap}

L2ElementField(vals::AbstractMatrix, syms) -> L2ElementField

num_elements(
    field::L2ElementField{T, NN, Vals, SymIDMap}
) -> Any

num_nodes_per_element(field::L2ElementField) -> Any

L2Quadrature field

struct L2QuadratureField{T, NF, NQ, Vals<:AbstractArray{T, 1}, SymIDMap} <: FiniteElementContainers.AbstractField{T, 3, NF, Vals<:AbstractArray{T, 1}, SymIDMap}

There are plans to add HcurlField and HdivField types as well