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introduced interpolation Lagrange{RefQuadrilateral, 3} #731

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May 26, 2023
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introduced interpolation Lagrange{RefQuadrilateral, 3} #731

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a469b2e
introduced interpolation Lagrange{2,RefCube,3}
JanM12 May 10, 2023
dda353d
this got lost
fredrikekre May 26, 2023
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53 changes: 53 additions & 0 deletions src/interpolations.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -13,6 +13,7 @@ The following interpolations are implemented:
* `Lagrange{RefLine,2}`
* `Lagrange{RefQuadrilateral,1}`
* `Lagrange{RefQuadrilateral,2}`
* `Lagrange{RefQuadrilateral,3}`
* `Lagrange{RefTriangle,1}`
* `Lagrange{RefTriangle,2}`
* `Lagrange{RefTriangle,3}`
Expand Down Expand Up @@ -491,6 +492,58 @@ function shape_value(ip::Lagrange{RefQuadrilateral, 2}, ξ::Vec{2}, i::Int)
throw(ArgumentError("no shape function $i for interpolation $ip"))
end

#####################################
# Lagrange RefQuadrilateral order 3 #
#####################################
getnbasefunctions(::Lagrange{RefQuadrilateral, 3}) = 16

facedof_indices(::Lagrange{RefQuadrilateral, 3}) = ((1,2, 5,6), (2,3, 7,8), (3,4, 9,10), (4,1, 11,12))
facedof_interior_indices(::Lagrange{RefQuadrilateral, 3}) = ((5,6), (7,8), (9,10), (11,12))
celldof_interior_indices(::Lagrange{RefQuadrilateral, 3}) = (13,14,15,16)

function reference_coordinates(::Lagrange{RefQuadrilateral, 3})
return [Vec{2, Float64}((-1.0, -1.0)),
Vec{2, Float64}(( 1.0, -1.0)),
Vec{2, Float64}(( 1.0, 1.0)),
Vec{2, Float64}((-1.0, 1.0)),
Vec{2, Float64}((-1/3, -1.0)),
Vec{2, Float64}(( 1/3, -1.0)),
Vec{2, Float64}(( 1.0, -1/3)),
Vec{2, Float64}(( 1.0, 1/3)),
Vec{2, Float64}(( 1/3, 1.0)),
Vec{2, Float64}((-1/3, 1.0)),
Vec{2, Float64}((-1.0, 1/3)),
Vec{2, Float64}((-1.0, -1/3)),
Vec{2, Float64}((-1/3, -1/3)),
Vec{2, Float64}(( 1/3, -1/3)),
Vec{2, Float64}((-1/3, 1/3)),
Vec{2, Float64}(( 1/3, 1/3))]
end

function shape_value(ip::Lagrange{RefQuadrilateral, 3}, ξ::Vec{2}, i::Int)
# See https://defelement.com/elements/examples/quadrilateral-Q-3.html
# Transform domain from [-1, 1] × [-1, 1] to [0, 1] × [0, 1]
ξ_x = ξ[1]*0.5 + 0.5
ξ_y = ξ[2]*0.5 + 0.5
i == 1 && return (81*ξ_x^3*ξ_y^3)/4 - (81*ξ_x^3*ξ_y^2)/2 + (99*ξ_x^3*ξ_y)/4 - (9*ξ_x^3)/2 - (81*ξ_x^2*ξ_y^3)/2 + (81*ξ_x^2*ξ_y^2) - (99*ξ_x^2*ξ_y)/2 + (9*ξ_x^2) + (99*ξ_x*ξ_y^3)/4 - (99*ξ_x*ξ_y^2)/2 + (121*ξ_x*ξ_y)/4 - (11*ξ_x)/2 - (9*ξ_y^3)/2 + 9*ξ_y^2 - (11*ξ_y)/2 + 1
i == 2 && return (ξ_x*( - 81*ξ_x^2*ξ_y^3 + 162*ξ_x^2*ξ_y^2 - 99*ξ_x^2*ξ_y + 18*ξ_x^2 + 81*ξ_x*ξ_y^3 - 162*ξ_x*ξ_y^2 + 99*ξ_x*ξ_y - 18*ξ_x - 18*ξ_y^3 + 36*ξ_y^2 - 22*ξ_y + 4))/4
i == 4 && return (ξ_y*( - 81*ξ_x^3*ξ_y^2 + 81*ξ_x^3*ξ_y - 18*ξ_x^3 + 162*ξ_x^2*ξ_y^2 - 162*ξ_x^2*ξ_y + 36*ξ_x^2 - 99*ξ_x*ξ_y^2 + 99*ξ_x*ξ_y - 22*ξ_x + 18*ξ_y^2 - 18*ξ_y + 4))/4
i == 3 && return (ξ_x*ξ_y*(81*ξ_x^2*ξ_y^2 - 81*ξ_x^2*ξ_y + 18*ξ_x^2 - 81*ξ_x*ξ_y^2 + 81*ξ_x*ξ_y - 18*ξ_x + 18*ξ_y^2 - 18*ξ_y + 4))/4
i == 5 && return (9*ξ_x*( - 27*ξ_x^2*ξ_y^3 + 54*ξ_x^2*ξ_y^2 - 33*ξ_x^2*ξ_y + 6*ξ_x^2 + 45*ξ_x*ξ_y^3 - 90*ξ_x*ξ_y^2 + 55*ξ_x*ξ_y - 10*ξ_x - 18*ξ_y^3 + 36*ξ_y^2 - 22*ξ_y + 4))/4
i == 6 && return (9*ξ_x*(27*ξ_x^2*ξ_y^3 - 54*ξ_x^2*ξ_y^2 + 33*ξ_x^2*ξ_y - 6*ξ_x^2 - 36*ξ_x*ξ_y^3 + 72*ξ_x*ξ_y^2 - 44*ξ_x*ξ_y + 8*ξ_x + 9*ξ_y^3 - 18*ξ_y^2 + 11*ξ_y - 2))/4
i == 12 && return (9*ξ_y*( - 27*ξ_x^3*ξ_y^2 + 45*ξ_x^3*ξ_y - 18*ξ_x^3 + 54*ξ_x^2*ξ_y^2 - 90*ξ_x^2*ξ_y + 36*ξ_x^2 - 33*ξ_x*ξ_y^2 + 55*ξ_x*ξ_y - 22*ξ_x + 6*ξ_y^2 - 10*ξ_y + 4))/4
i == 11 && return (9*ξ_y*(27*ξ_x^3*ξ_y^2 - 36*ξ_x^3*ξ_y + 9*ξ_x^3 - 54*ξ_x^2*ξ_y^2 + 72*ξ_x^2*ξ_y - 18*ξ_x^2 + 33*ξ_x*ξ_y^2 - 44*ξ_x*ξ_y + 11*ξ_x - 6*ξ_y^2 + 8*ξ_y - 2))/4
i == 7 && return (9*ξ_x*ξ_y*(27*ξ_x^2*ξ_y^2 - 45*ξ_x^2*ξ_y + 18*ξ_x^2 - 27*ξ_x*ξ_y^2 + 45*ξ_x*ξ_y - 18*ξ_x + 6*ξ_y^2 - 10*ξ_y + 4))/4
i == 8 && return (9*ξ_x*ξ_y*( - 27*ξ_x^2*ξ_y^2 + 36*ξ_x^2*ξ_y - 9*ξ_x^2 + 27*ξ_x*ξ_y^2 - 36*ξ_x*ξ_y + 9*ξ_x - 6*ξ_y^2 + 8*ξ_y - 2))/4
i == 10 && return (9*ξ_x*ξ_y*(27*ξ_x^2*ξ_y^2 - 27*ξ_x^2*ξ_y + 6*ξ_x^2 - 45*ξ_x*ξ_y^2 + 45*ξ_x*ξ_y - 10*ξ_x + 18*ξ_y^2 - 18*ξ_y + 4))/4
i == 9 && return (9*ξ_x*ξ_y*( - 27*ξ_x^2*ξ_y^2 + 27*ξ_x^2*ξ_y - 6*ξ_x^2 + 36*ξ_x*ξ_y^2 - 36*ξ_x*ξ_y + 8*ξ_x - 9*ξ_y^2 + 9*ξ_y - 2))/4
i == 13 && return (81*ξ_x*ξ_y*(9*ξ_x^2*ξ_y^2 - 15*ξ_x^2*ξ_y + 6*ξ_x^2 - 15*ξ_x*ξ_y^2 + 25*ξ_x*ξ_y - 10*ξ_x + 6*ξ_y^2 - 10*ξ_y + 4))/4
i == 14 && return (81*ξ_x*ξ_y*( - 9*ξ_x^2*ξ_y^2 + 15*ξ_x^2*ξ_y - 6*ξ_x^2 + 12*ξ_x*ξ_y^2 - 20*ξ_x*ξ_y + 8*ξ_x - 3*ξ_y^2 + 5*ξ_y - 2))/4
i == 15 && return (81*ξ_x*ξ_y*( - 9*ξ_x^2*ξ_y^2 + 12*ξ_x^2*ξ_y - 3*ξ_x^2 + 15*ξ_x*ξ_y^2 - 20*ξ_x*ξ_y + 5*ξ_x - 6*ξ_y^2 + 8*ξ_y - 2))/4
i == 16 && return (81*ξ_x*ξ_y*(9*ξ_x^2*ξ_y^2 - 12*ξ_x^2*ξ_y + 3*ξ_x^2 - 12*ξ_x*ξ_y^2 + 16*ξ_x*ξ_y - 4*ξ_x + 3*ξ_y^2 - 4*ξ_y + 1))/4
throw(ArgumentError("no shape function $i for interpolation $ip"))
end

################################
# Lagrange RefTriangle order 1 #
################################
Expand Down
4 changes: 3 additions & 1 deletion test/test_interpolations.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,6 +5,7 @@
Lagrange{RefLine, 2}(),
Lagrange{RefQuadrilateral, 1}(),
Lagrange{RefQuadrilateral, 2}(),
Lagrange{RefQuadrilateral, 3}(),
Lagrange{RefTriangle, 1}(),
Lagrange{RefTriangle, 2}(),
Lagrange{RefTriangle, 3}(),
Expand Down Expand Up @@ -102,7 +103,8 @@
if k == dof
@test N_dof ≈ 1.0
else
@test N_dof ≈ 0.0 atol=4eps(Float64) #broken=typeof(interpolation)==Lagrange{2, RefTetrahedron, 5}&&dof==4&&k==18
factor = interpolation isa Lagrange{RefQuadrilateral, 3} ? 200 : 4
@test N_dof ≈ 0.0 atol = factor * eps(Float64)
end
end
end
Expand Down