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more integration rules for wedge elements

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Jukka Aho
2016-12-01 11:14:13 +02:00
parent d9daf1776f
commit b3a14c99f4
1 changed files with 76 additions and 2 deletions
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src/integrate.jl
+76 -2
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@@ -240,7 +240,6 @@ end
typealias PrismaticElement Union{Wedge6, Wedge15}
#=
function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
weights = 1/6*[1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
points = Vector{Float64}[
@@ -252,9 +251,9 @@ function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
[0.5, 0.5, 1.0/sqrt(3)]]
return zip(weights, points)
end
=#
# tensor product of triangular element + segment element
#=
function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
weights = 1.0/6.0*[1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
points = Vector{Float64}[
@@ -267,8 +266,10 @@ function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
]
return zip(weights, points)
end
=#
# tensor product of triangular element + segment element
#=
function get_integration_points(element::PrismaticElement, ::Type{Val{3}})
weights = [
5.0/9.0*1.5902069087198858469718450103758e-01,
@@ -299,6 +300,79 @@ function get_integration_points(element::PrismaticElement, ::Type{Val{3}})
]
return zip(weights, points)
end
=#
#=
function get_integration_points(element::PrismaticElement, ::Type{Val{2}})
weights = 1.0/96.0*[-27.0, 25.0, 25.0, 25.0, -27.0, 25.0, 25.0, 25.0]
a = 1.0/sqrt(3.0)
points = Vector{Float64}[
[1/3, 1/3, -a],
[0.6, 0.2, -a],
[0.2, 0.6, -a],
[0.2, 0.2, -a],
[1/3, 1/3, a],
[0.6, 0.2, a],
[0.2, 0.6, a],
[0.2, 0.2, a]]
return zip(weights, points)
end
=#
function get_integration_points(element::PrismaticElement, ::Type{Val{3}})
alpha = sqrt(3/5)
c1 = 5/9
c2 = 8/9
a = (6+sqrt(15))/21
b = (6-sqrt(15))/21
weights = [
c1*9/80,
c1*((155+sqrt(15))/2400),
c1*((155+sqrt(15))/2400),
c1*((155+sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
c2*9/80,
c2*((155+sqrt(15))/2400),
c2*((155+sqrt(15))/2400),
c2*((155+sqrt(15))/2400),
c2*((155-sqrt(15))/2400),
c2*((155-sqrt(15))/2400),
c2*((155-sqrt(15))/2400),
c1*9/80,
c1*((155+sqrt(15))/2400),
c1*((155+sqrt(15))/2400),
c1*((155+sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
c1*((155-sqrt(15))/2400),
]
points = Vector{Float64}[
[1/3, 1/3, -alpha],
[a, a, -alpha],
[1-2a, a, -alpha],
[a, 1-2a, -alpha],
[b, b, -alpha],
[1-2b, b, -alpha],
[b, 1-2b, -alpha],
[1/3, 1/3, 0],
[a, a, 0],
[1-2a, a, 0],
[a, 1-2a, 0],
[b, b, 0],
[1-2b, b, 0],
[b, 1-2b, 0],
[1/3, 1/3, alpha],
[a, a, alpha],
[1-2a, a, alpha],
[a, 1-2a, alpha],
[b, b, alpha],
[1-2b, b, alpha],
[b, 1-2b, alpha],
]
return zip(weights, points)
end
function get_integration_points(element::Union{TriangularElement,
TetrahedralElement, PrismaticElement}, order::Int64)