JuliaFEM.jl/test/test_lagrange.jl

# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md

using JuliaFEM
using JuliaFEM.Testing

ALL_ELEMENTS = [
    Seg2, Seg3,
    Tri3, Tri6, Tri7,
    Quad4, Quad8, Quad9,
    Tet4, Tet10,
    Wedge6,
    Hex8, Hex20, Hex27
]

info("basic data for elements implemented so far:")
for element_type in [Poi1; ALL_ELEMENTS]
    element = Element(element_type, Int[])
    element_length = length(element)
    element_size = size(element)
    element_description = description(element)
    info("Element $element_type, description = $element_description, length = $element_length, size = $element_size")
end


ALL_ELEMENTS_NODES = [
    [1,2], [1,2,3],
    [1,2,3], [1,2,3,4,5,6], [1,2,3,4,5,6,7],
    [1,2,3,4], [1,2,3,4,5,6,7,8], [1,2,3,4,5,6,7,8,9],
    [1,2,3,4], [1,2,3,4,5,6,7,8,9,10],
    [1,2,3,4,5,6],
    [1,2,3,4,5,6,7,8],
    [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,17,18,19,20],
    [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,17,18,19,20,
    21,22,23,24,25,26,27]
]

@testset "Evaluating basis" begin
    for (T, nod) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES)
        el = Element(T,nod)
        nnodes = length(el)
        for (i, X) in enumerate(get_reference_coordinates(T))
            Ni = vec(el(X))
            expected = zeros(nnodes)
            expected[i] = 1.0
            @test isapprox(Ni, expected)
        end
    end
end

function get_volume{T<:AbstractElement}(::Type{T},nodes)
    X = get_reference_coordinates(T)
    element = Element(T,nodes)
    update!(element, "geometry", X)
    V = 0.0
    for ip in get_integration_points(element)
        V += ip.weight*element(ip, 0.0, Val{:detJ})
    end
    return V
end

RESULTS = [2.0, 2.0, 0.5, 0.5, 0.5, 2.0^2, 2.0^2,
           2.0^2, 1/6, 1/6, 1.0, 2.0^3, 2.0^3, 2.0^3,]

@testset "Calculate reference element length/area/volume" begin
    for (T, nod, res) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES,
                             RESULTS)
        @test isapprox(get_volume(T,nod),  res)
    end
end

SIZES = [(1,2), (1,3), (2,3), (2,6), (2,7), (2,4),
         (2,8), (2,9), (3,4), (3,10), (3,6), (3,8),
         (3,20), (3,27)]

@testset "element size" begin
    for (T, nod, res) in zip(ALL_ELEMENTS,ALL_ELEMENTS_NODES, SIZES)
        @test size(Element(T,nod)) == res
    end
end

@testset "element length" begin
    for i in 1:length(ALL_ELEMENTS)
        typ = ALL_ELEMENTS[i]
        vec = ALL_ELEMENTS_NODES[i]
        el = Element(typ,vec)
        @test length(el) == length(vec)
    end
end