mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-23 19:06:15 +00:00
Calculate shape functions using FEMBasis.jl
A lot of code is moved to FEMBasis.jl regarding calculating basis / shape functions of finite elements. * add FEMBasis to REQUIRE * remove obsolete files * remove obsolete test files * make integration point iterable * loosen type definitions * get length of element rather from basis than connectivity * calculate midpoint of reference element * wrong input argument to eval_basis! fixed
This commit is contained in:
Jukka Aho
+25
-589
@@ -1,66 +1,11 @@
|
||||
# This file is a part of JuliaFEM.
|
||||
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
||||
|
||||
global const ELEMENT_DESCRIPTIONS = Dict(
|
||||
"Poi1" => "1 node discrete point element",
|
||||
"Seg2" => "2 node linear segment/line element",
|
||||
"Seg3" => "3 node quadratic segment/line element",
|
||||
"Tri3" => "3 node linear triangle element",
|
||||
"Tri6" => "6 node quadratic triangle element",
|
||||
"Tri7" => "7 node quadratic triangle element (has middle node)",
|
||||
"Quad4" => "4 node linear quadrangle element",
|
||||
"Quad8" => "8 node quadratic quadrangle element (Serendip)",
|
||||
"Quad9" => "9 node quadratic quadrangle element",
|
||||
"Tet4" => "4 node linear tetrahedral element",
|
||||
"Tet10" => "10 node quadratic tetrahedral element",
|
||||
"Pyr5" => "5 node linear pyramid element",
|
||||
"Wedge6" => "6 node linear prismatic element (wedge)",
|
||||
"Wedge15" => "15 node quadratic prismatic element (wedge)",
|
||||
"Hex8" => "8 node linear hexahedral element",
|
||||
"Hex20" => "20 node biquadratic hexahedral element",
|
||||
"Hex27" => "27 node quadratic hexahedral element")
|
||||
using FEMBasis
|
||||
|
||||
global const ELEMENT_SIZES = Dict(
|
||||
"Poi1" => (0, 1),
|
||||
"Seg2" => (1, 2),
|
||||
"Seg3" => (1, 3),
|
||||
"Tri3" => (2, 3),
|
||||
"Tri6" => (2, 6),
|
||||
"Tri7" => (2, 7),
|
||||
"Quad4" => (2, 4),
|
||||
"Quad8" => (2, 8),
|
||||
"Quad9" => (2, 9),
|
||||
"Tet4" => (3, 4),
|
||||
"Tet10" => (3, 10),
|
||||
"Pyr5" => (3,5),
|
||||
"Wedge6" => (3, 6),
|
||||
"Wedge15" => (3, 15),
|
||||
"Hex8" => (3, 8),
|
||||
"Hex20" => (3, 20),
|
||||
"Hex27" => (3, 27))
|
||||
|
||||
""" Return description line of element. """
|
||||
function description{T}(element::Element{T})
|
||||
element_type = last(split("$T", '.'))
|
||||
return get(ELEMENT_DESCRIPTIONS, element_type, "Unknown element description")
|
||||
end
|
||||
|
||||
""" Return size of element, i.e. tuple (n, m) where n is dimension of element
|
||||
(0, 1, 2, 3) and m is number of nodes. """
|
||||
function size{T}(element::Element{T})
|
||||
element_type = last(split("$T", '.'))
|
||||
return ELEMENT_SIZES[element_type]
|
||||
end
|
||||
|
||||
""" Return length of element, i.e. number of nodes. """
|
||||
function length{T}(element::Element{T})
|
||||
return size(element)[end]
|
||||
end
|
||||
|
||||
### 0d element
|
||||
|
||||
|
||||
type Poi1 <: AbstractElement
|
||||
# "Poi1" => (0, 1),
|
||||
"1 node discrete point element",
|
||||
type Poi1 <: AbstractBasis
|
||||
end
|
||||
|
||||
function get_basis(element::Element{Poi1}, ip, time)
|
||||
@@ -83,541 +28,32 @@ function get_integration_points(element::Poi1, order::Int64)
|
||||
return [ (1.0, [] ) ]
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Poi1})
|
||||
function size(::Type{Poi1})
|
||||
return (0, 1)
|
||||
end
|
||||
|
||||
function length(::Type{Poi1})
|
||||
return 1
|
||||
end
|
||||
|
||||
function FEMBasis.get_reference_element_coordinates(::Type{Poi1})
|
||||
Vector{Float64}[[0.0]]
|
||||
end
|
||||
|
||||
### 1d elements
|
||||
|
||||
type Seg2 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Seg2})
|
||||
Vector{Float64}[
|
||||
[-1.0], # N1
|
||||
[ 1.0]] # N2
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Seg2}, xi)
|
||||
[1.0 xi[1]]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Seg2}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[0.0 1.0]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Seg3 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Seg3})
|
||||
Vector{Float64}[
|
||||
[-1.0], # N1
|
||||
[ 1.0], # N2
|
||||
[ 0.0]] # N3
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Seg3}, xi)
|
||||
[1.0 xi[1] xi[1]^2]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Seg3}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[0.0 1.0 2.0*xi[1]]
|
||||
end
|
||||
|
||||
### 2d elements
|
||||
|
||||
type Tri3 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Tri3})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0], # N1
|
||||
[1.0, 0.0], # N2
|
||||
[0.0, 1.0]] # N3
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri3}, xi)
|
||||
[
|
||||
1 xi[1] xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri3}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0.0 1.0 0.0
|
||||
0.0 0.0 1.0
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Tri6 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Tri6})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0], # N1
|
||||
[1.0, 0.0], # N2
|
||||
[0.0, 1.0], # N3
|
||||
[0.5, 0.0], # N4
|
||||
[0.5, 0.5], # N5
|
||||
[0.0, 0.5]] # N6
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri6}, xi)
|
||||
[
|
||||
1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri6}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 0 2*xi[1] xi[2] 0
|
||||
0 0 1 0 xi[1] 2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Tri7 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Tri7})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0], # N1
|
||||
[1.0, 0.0], # N2
|
||||
[0.0, 1.0], # N3
|
||||
[0.5, 0.0], # N4
|
||||
[0.5, 0.5], # N5
|
||||
[0.0, 0.5], # N6
|
||||
[1/3, 1/3]] # N7
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri7}, xi)
|
||||
[
|
||||
1 xi[1] xi[2] xi[1]^2 xi[1]*xi[2] xi[2]^2 xi[1]^2*xi[2]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tri7}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 0 2*xi[1] xi[2] 0 2*xi[1]*xi[2]^2
|
||||
0 0 1 0 xi[1] 2*xi[2] 2*xi[1]^2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Quad4 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Quad4})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0], # N1
|
||||
[ 1.0, -1.0], # N2
|
||||
[ 1.0, 1.0], # N3
|
||||
[-1.0, 1.0]] # N4
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad4}, xi)
|
||||
[
|
||||
1.0 xi[1] xi[2] xi[1]*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad4}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 0 xi[2]
|
||||
0 0 1 xi[1]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Quad8 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Quad8})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0], # N1
|
||||
[ 1.0, -1.0], # N2
|
||||
[ 1.0, 1.0], # N3
|
||||
[-1.0, 1.0], # N4
|
||||
[ 0.0, -1.0], # N5
|
||||
[ 1.0, 0.0], # N6
|
||||
[ 0.0, 1.0], # N7
|
||||
[-1.0, 0.0]] # N8
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad8}, xi)
|
||||
[
|
||||
1 xi[2] xi[1] xi[2]^2 xi[1]*xi[2] xi[1]^2 xi[1]*xi[2]^2 xi[1]^2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad8}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2]
|
||||
0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Quad9 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Quad9})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0], # N1
|
||||
[ 1.0, -1.0], # N2
|
||||
[ 1.0, 1.0], # N3
|
||||
[-1.0, 1.0], # N4
|
||||
[ 0.0, -1.0], # N5
|
||||
[ 1.0, 0.0], # N6
|
||||
[ 0.0, 1.0], # N7
|
||||
[-1.0, 0.0], # N8
|
||||
[ 0.0, 0.0]] # N9
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad9}, xi)
|
||||
[
|
||||
1 xi[2] xi[1] xi[2]^2 xi[1]*xi[2] xi[1]^2 xi[1]*xi[2]^2 xi[1]^2*xi[2] xi[1]^2*xi[2]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Quad9}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 1 0 xi[2] 2*xi[1] xi[2]^2 2*xi[1]*xi[2] 2*xi[1]*xi[2]^2
|
||||
0 1 0 2*xi[2] xi[1] 0 2*xi[1]*xi[2] xi[1]^2 2*xi[1]^2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
### 3d elements
|
||||
|
||||
type Tet4 <: AbstractElement
|
||||
function get_basis{B}(element::Element{B}, ip, time)
|
||||
T = typeof(first(ip))
|
||||
N = zeros(T, 1, length(B))
|
||||
eval_basis!(B, N, tuple(ip...))
|
||||
return N
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Tet4})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, 0.0], # N1
|
||||
[1.0, 0.0, 0.0], # N2
|
||||
[0.0, 1.0, 0.0], # N3
|
||||
[0.0, 0.0, 1.0]] # N4
|
||||
function get_dbasis{B}(element::Element{B}, ip, time)
|
||||
T = typeof(first(ip))
|
||||
dN = zeros(T, size(B)...)
|
||||
eval_dbasis!(B, dN, tuple(ip...))
|
||||
return dN
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tet4}, xi)
|
||||
[
|
||||
1.0 xi[1] xi[2] xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tet4}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0.0 1.0 0.0 0.0
|
||||
0.0 0.0 1.0 0.0
|
||||
0.0 0.0 0.0 1.0
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Tet10 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Tet10})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, 0.0], # N1
|
||||
[1.0, 0.0, 0.0], # N2
|
||||
[0.0, 1.0, 0.0], # N3
|
||||
[0.0, 0.0, 1.0], # N4
|
||||
[0.5, 0.0, 0.0], # N5
|
||||
[0.5, 0.5, 0.0], # N6
|
||||
[0.0, 0.5, 0.0], # N7
|
||||
[0.0, 0.0, 0.5], # N8
|
||||
[0.5, 0.0, 0.5], # N9
|
||||
[0.0, 0.5, 0.5]] # N10
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tet10}, xi)
|
||||
[
|
||||
1.0 xi[3] xi[2] xi[1] xi[3]^2 xi[2]*xi[3] xi[2]^2 xi[1]*xi[3] xi[1]*xi[2] xi[1]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Tet10}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 0 0 xi[3] xi[2] 2*xi[1]
|
||||
0 0 1 0 0 xi[3] 2*xi[2] 0 xi[1] 0
|
||||
0 1 0 0 2*xi[3] xi[2] 0 xi[1] 0 0
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Pyr5 <: AbstractElement
|
||||
end
|
||||
|
||||
|
||||
function get_reference_coordinates(::Type{Pyr5})
|
||||
Vector{Float64}[
|
||||
[-1.0,-1.0,-1.0], # N1
|
||||
[ 1.0,-1.0,-1.0], # N2
|
||||
[ 1.0, 1.0,-1.0], # N3
|
||||
[-1.0, 1.0,-1.0], # N4
|
||||
[ 0.0, 0.0, 1.0]] # N5
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Pyr5}, xi)
|
||||
[
|
||||
1.0/8.0*(1.0-1.0*xi[1])*(1.0-1.0*xi[2])*(1.0-1.0*xi[3])
|
||||
1.0/8.0*(1.0+1.0*xi[1])*(1.0-1.0*xi[2])*(1.0-1.0*xi[3])
|
||||
1.0/8.0*(1.0+1.0*xi[1])*(1.0+1.0*xi[2])*(1.0-1.0*xi[3])
|
||||
1.0/8.0*(1.0-1.0*xi[1])*(1.0+1.0*xi[2])*(1.0-1.0*xi[3])
|
||||
1.0/2.0*(1.0+xi[3])
|
||||
]'
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Pyr5}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
-0.125*(1.0-xi[2])*(1.0-xi[3]) 0.125*(1.0-xi[2])*(1.0-xi[3]) 0.125*(1.0+xi[2])*(1.0-xi[3]) -0.125*(1.0+xi[2])*(1.0-xi[3]) 0.0
|
||||
-0.125*(1.0-xi[1])*(1.0-xi[3]) -0.125*(1.0+xi[1])*(1.0-xi[3]) 0.125*(1.0+xi[1])*(1.0-xi[3]) 0.125*(1.0-xi[1])*(1.0-xi[3]) 0.0
|
||||
-0.125*(1.0-xi[1])*(1.0-xi[2]) -0.125*(1.0+xi[1])*(1.0-xi[2]) -0.125*(1.0+xi[1])*(1.0+xi[2]) -0.125*(1.0-xi[1])*(1.0+xi[2]) 0.5
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Wedge6 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Wedge6})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, -1.0], # N1
|
||||
[1.0, 0.0, -1.0], # N2
|
||||
[0.0, 1.0, -1.0], # N3
|
||||
[0.0, 0.0, 1.0], # N4
|
||||
[1.0, 0.0, 1.0], # N5
|
||||
[0.0, 1.0, 1.0]] # N6
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge6}, x)
|
||||
[
|
||||
1 x[1] x[2] x[3] x[1]*x[3] x[2]*x[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge6}, x, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 0 0 x[3] 0
|
||||
0 0 1 0 0 x[3]
|
||||
0 0 0 1 x[1] x[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Wedge15 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Wedge15})
|
||||
Vector{Float64}[
|
||||
[0.0, 0.0, -1.0], # N1
|
||||
[1.0, 0.0, -1.0], # N2
|
||||
[0.0, 1.0, -1.0], # N3
|
||||
[0.0, 0.0, 1.0], # N4
|
||||
[1.0, 0.0, 1.0], # N5
|
||||
[0.0, 1.0, 1.0], # N6
|
||||
[0.5, 0.0, -1.0], # N7
|
||||
[0.5, 0.5, -1.0], # N8
|
||||
[0.0, 0.5, -1.0], # N9
|
||||
[0.5, 0.0, 1.0], # N10
|
||||
[0.5, 0.5, 1.0], # N11
|
||||
[0.0, 0.5, 1.0], # N12
|
||||
[0.0, 0.0, 0.0], # N13
|
||||
[1.0, 0.0, 0.0], # N14
|
||||
[0.0, 1.0, 0.0]] # N15
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge15}, x)
|
||||
[
|
||||
1 x[1] x[1]^2 x[2] x[1]*x[2] x[2]^2 x[3] x[1]*x[3] x[1]^2*x[3] x[2]*x[3] x[1]*x[2]*x[3] x[2]^2*x[3] x[3]^2 x[1]*x[3]^2 x[2]*x[3]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Wedge15}, x, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 1 2*x[1] 0 x[2] 0 0 x[3] 2*x[1]*x[3] 0 x[2]*x[3] 0 0 x[3]^2 0
|
||||
0 0 0 1 x[1] 2*x[2] 0 0 0 x[3] x[1]*x[3] 2*x[2]*x[3] 0 0 x[3]^2
|
||||
0 0 0 0 0 0 1 x[1] x[1]^2 x[2] x[1]*x[2] x[2]^2 2*x[3] 2*x[1]*x[3] 2*x[2]*x[3]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Hex8 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex8})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0, -1.0], # N1
|
||||
[ 1.0, -1.0, -1.0], # N2
|
||||
[ 1.0, 1.0, -1.0], # N3
|
||||
[-1.0, 1.0, -1.0], # N4
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0]] # N8
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex8}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex8}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3]
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3]
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
#
|
||||
|
||||
type Hex20 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex20})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0, -1.0], # N1
|
||||
[ 1.0, -1.0, -1.0], # N2
|
||||
[ 1.0, 1.0, -1.0], # N3
|
||||
[-1.0, 1.0, -1.0], # N4
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0], # N8
|
||||
[ 0.0, -1.0, -1.0], # N9
|
||||
[ 1.0, 0.0, -1.0], # N10
|
||||
[ 0.0, 1.0, -1.0], # N11
|
||||
[-1.0, 0.0, -1.0], # N12
|
||||
[-1.0, -1.0, 0.0], # N13
|
||||
[ 1.0, -1.0, 0.0], # N14
|
||||
[ 1.0, 1.0, 0.0], # N15
|
||||
[-1.0, 1.0, 0.0], # N16
|
||||
[ 0.0, -1.0, 1.0], # N17
|
||||
[ 1.0, 0.0, 1.0], # N18
|
||||
[ 0.0, 1.0, 1.0], # N19
|
||||
[-1.0, 0.0, 1.0]] # N20
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex20}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3] xi[3]^2 xi[2]^2 xi[1]^2 xi[2]*xi[3]^2 xi[2]^2*xi[3] xi[1]*xi[3]^2 xi[1]*xi[2]^2 xi[1]^2*xi[3] xi[1]^2*xi[2] xi[1]*xi[2]*xi[3]^2 xi[1]*xi[2]^2*xi[3] xi[1]^2*xi[2]*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex20}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3] 0 0 2*xi[1] 0 0 xi[3]^2 xi[2]^2 2*xi[1]*xi[3] 2*xi[1]*xi[2] xi[2]*xi[3]^2 xi[2]^2*xi[3] 2*xi[1]*xi[2]*xi[3]
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3] 0 2*xi[2] 0 xi[3]^2 2*xi[2]*xi[3] 0 2*xi[1]*xi[2] 0 xi[1]^2 xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] xi[1]^2*xi[3]
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2] 2*xi[3] 0 0 2*xi[2]*xi[3] xi[2]^2 2*xi[1]*xi[3] 0 xi[1]^2 0 2*xi[1]*xi[2]*xi[3] xi[1]*xi[2]^2 xi[1]^2*xi[2]
|
||||
]
|
||||
end
|
||||
|
||||
###
|
||||
|
||||
type Hex27 <: AbstractElement
|
||||
end
|
||||
|
||||
function get_reference_coordinates(::Type{Hex27})
|
||||
Vector{Float64}[
|
||||
[-1.0, -1.0, -1.0], # N1
|
||||
[ 1.0, -1.0, -1.0], # N2
|
||||
[ 1.0, 1.0, -1.0], # N3
|
||||
[-1.0, 1.0, -1.0], # N4
|
||||
[-1.0, -1.0, 1.0], # N5
|
||||
[ 1.0, -1.0, 1.0], # N6
|
||||
[ 1.0, 1.0, 1.0], # N7
|
||||
[-1.0, 1.0, 1.0], # N8
|
||||
[ 0.0, -1.0, -1.0], # N9
|
||||
[ 1.0, 0.0, -1.0], # N10
|
||||
[ 0.0, 1.0, -1.0], # N11
|
||||
[-1.0, 0.0, -1.0], # N12
|
||||
[-1.0, -1.0, 0.0], # N13
|
||||
[ 1.0, -1.0, 0.0], # N14
|
||||
[ 1.0, 1.0, 0.0], # N15
|
||||
[-1.0, 1.0, 0.0], # N16
|
||||
[ 0.0, -1.0, 1.0], # N17
|
||||
[ 1.0, 0.0, 1.0], # N18
|
||||
[ 0.0, 1.0, 1.0], # N19
|
||||
[-1.0, 0.0, 1.0], # N20
|
||||
[ 0.0, 0.0, -1.0], # N21
|
||||
[ 0.0, -1.0, 0.0], # N22
|
||||
[ 1.0, 0.0, 0.0], # N23
|
||||
[ 0.0, 1.0, 0.0], # N24
|
||||
[-1.0, 0.0, 0.0], # N25
|
||||
[ 0.0, 0.0, 1.0], # N26
|
||||
[ 0.0, 0.0, 0.0]] # N27
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex27}, xi)
|
||||
[
|
||||
1 xi[3] xi[2] xi[1] xi[2]*xi[3] xi[1]*xi[3] xi[1]*xi[2] xi[1]*xi[2]*xi[3] xi[3]^2 xi[2]^2 xi[1]^2 xi[2]*xi[3]^2 xi[2]^2*xi[3] xi[1]*xi[3]^2 xi[1]*xi[2]^2 xi[1]^2*xi[3] xi[1]^2*xi[2] xi[2]^2*xi[3]^2 xi[1]*xi[2]*xi[3]^2 xi[1]*xi[2]^2*xi[3] xi[1]^2*xi[3]^2 xi[1]^2*xi[2]*xi[3] xi[1]^2*xi[2]^2 xi[1]*xi[2]^2*xi[3]^2 xi[1]^2*xi[2]*xi[3]^2 xi[1]^2*xi[2]^2*xi[3] xi[1]^2*xi[2]^2*xi[3]^2
|
||||
]
|
||||
end
|
||||
|
||||
function get_interpolation_polynomial(::Type{Hex27}, xi, ::Type{Val{:partial_derivatives}})
|
||||
[
|
||||
0 0 0 1 0 xi[3] xi[2] xi[2]*xi[3] 0 0 2*xi[1] 0 0 xi[3]^2 xi[2]^2 2*xi[1]*xi[3] 2*xi[1]*xi[2] 0 xi[2]*xi[3]^2 xi[2]^2*xi[3] 2*xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] 2*xi[1]*xi[2]^2 xi[2]^2*xi[3]^2 2*xi[1]*xi[2]*xi[3]^2 2*xi[1]*xi[2]^2*xi[3] 2*xi[1]*xi[2]^2*xi[3]^2
|
||||
0 0 1 0 xi[3] 0 xi[1] xi[1]*xi[3] 0 2*xi[2] 0 xi[3]^2 2*xi[2]*xi[3] 0 2*xi[1]*xi[2] 0 xi[1]^2 2*xi[2]*xi[3]^2 xi[1]*xi[3]^2 2*xi[1]*xi[2]*xi[3] 0 xi[1]^2*xi[3] 2*xi[1]^2*xi[2] 2*xi[1]*xi[2]*xi[3]^2 xi[1]^2*xi[3]^2 2*xi[1]^2*xi[2]*xi[3] 2*xi[1]^2*xi[2]*xi[3]^2
|
||||
0 1 0 0 xi[2] xi[1] 0 xi[1]*xi[2] 2*xi[3] 0 0 2*xi[2]*xi[3] xi[2]^2 2*xi[1]*xi[3] 0 xi[1]^2 0 2*xi[2]^2*xi[3] 2*xi[1]*xi[2]*xi[3] xi[1]*xi[2]^2 2*xi[1]^2*xi[3] xi[1]^2*xi[2] 0 2*xi[1]*xi[2]^2*xi[3] 2*xi[1]^2*xi[2]*xi[3] xi[1]^2*xi[2]^2 2*xi[1]^2*xi[2]^2*xi[3]
|
||||
]
|
||||
end
|
||||
|
||||
###
|
||||
|
||||
macro create_basis(T)
|
||||
quote
|
||||
T = $T
|
||||
global get_basis, get_dbasis, length, size
|
||||
X = get_reference_coordinates(T)
|
||||
nbasis = length(X)
|
||||
A = zeros(nbasis, nbasis)
|
||||
for i=1:nbasis
|
||||
A[i,:] = get_interpolation_polynomial(T, X[i])
|
||||
end
|
||||
invA = inv(A)
|
||||
function get_basis(element::Element{$T}, ip, time)
|
||||
return get_interpolation_polynomial($T, ip)*invA
|
||||
end
|
||||
function get_dbasis(element::Element{$T}, ip, time)
|
||||
return get_interpolation_polynomial($T, ip, Val{:partial_derivatives})*invA
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
@create_basis Seg2
|
||||
@create_basis Seg3
|
||||
@create_basis Tri3
|
||||
@create_basis Tri6
|
||||
@create_basis Tri7
|
||||
@create_basis Quad4
|
||||
@create_basis Quad8
|
||||
@create_basis Quad9
|
||||
@create_basis Tet4
|
||||
@create_basis Tet10
|
||||
@create_basis Pyr5
|
||||
@create_basis Wedge6
|
||||
@create_basis Wedge15
|
||||
@create_basis Hex8
|
||||
@create_basis Hex20
|
||||
@create_basis Hex27
|
||||
|
||||
function inside(::Union{Type{Seg2}, Type{Seg3}, Type{Quad4}, Type{Quad8},
|
||||
Type{Quad9}, Type{Pyr5}, Type{Hex8}, Type{Hex20},
|
||||
Type{Hex27}}, xi)
|
||||
@@ -628,7 +64,7 @@ function inside(::Union{Type{Tri3}, Type{Tri6}, Type{Tri7}, Type{Tet4}, Type{Tet
|
||||
return all(xi .>= 0.0) && (sum(xi) <= 1.0)
|
||||
end
|
||||
|
||||
function get_reference_coordinates{E}(element::Element{E})
|
||||
get_reference_coordinates(E)
|
||||
function get_reference_coordinates{B}(element::Element{B})
|
||||
return get_reference_element_coordinates(B)
|
||||
end
|
||||
|
||||
|
||||
Reference in New Issue
Block a user