Tri3 -> Topology + Basis

[ahojukka5]

Currently, we define elements using style

element = Element(Tri3, [1, 2, 3])

and it is somewhat implicitly assumed that the basis for the element is a nodal basis, e.g. N(xi, eta) = (xi, eta, 1-xi-eta) in this particular case. We should extend this definition by explicitly giving a basis, which defaults to nodal basis. So we can have Tri3{CG}, Tri3{Morley}, Tri3{DKT} and so on. We could implement this several ways, here's couple options:

abstract type AbstractBasis end
struct CG <: AbstractBasis end
struct Morley <: AbstractBasis end
abstract type AbstractTopology end
struct Tet10{T<:AbstractBasis} <: AbstractTopology end
abstract type AbstractElement end

struct Element{T<:AbstractTopology} <: AbstractElement
    # rest of stuff ...
    topology :: T
end

Element(Tet10{CG}())

# output

Element{Tet10{CG}}(Tet10{CG}())

Other way is

struct Tet4 <: AbstractTopology end

struct Element2{T<:AbstractTopology, B<:AbstractBasis} <: AbstractElement
    # rest of stuff ...
    topology :: T
    basis :: B
end

Element2(Tet4(), CG())

# output

Element2{Tet4,CG}(Tet4(), CG())

I don't know which one is better or is there maybe third and better way to think this. Anyway we can do this change so that element = Element(Tri3, [1, 2, 3]) is still working and having CG basis as default one:

function Element2(::Type{T}, connectivity) where {T <: AbstractTopology}
    return Element2(T(), CG())
end

Element2(Tet4, [1, 2, 3, 4])

# output

Element2{Tet4,CG}(Tet4(), CG())