mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 09:54:55 +00:00
Jukka Aho
126 lines
3.4 KiB
Julia
126 lines
3.4 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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# Lagrange (Continous Galerkin) finite elements shape functions generated using macro.
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"""
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Given polynomial P and coordinates of reference element, calculate
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Lagrange basis functions
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"""
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function calculate_lagrange_basis_coefficients(P, X)
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dim, nbasis = size(X)
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A = zeros(nbasis, nbasis)
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for i=1:nbasis
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A[i,:] = P(X[:, i])
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end
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return inv(A)
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end
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function refcoords(X::Matrix)
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return Vector{Float64}[X[:,i] for i=1:size(X,2)]
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end
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"""
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Create new Lagrange element
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Examples
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--------
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>>> @create_lagrange_element(Seg2, "2 node linear segment", X, P)
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"""
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macro create_lagrange_element(element_name, element_description, X, P)
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eltype = esc(element_name)
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quote
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global get_basis, length, size
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#=
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get_reference_element_coordinates,
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get_reference_element_midpoint
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=#
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type $eltype <: AbstractElement
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end
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A = calculate_lagrange_basis_coefficients($P, $X)
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#basis(xi) = C*$P(xi)
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function get_basis(element::Element{$eltype}, ip, time)
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return transpose($P(ip))*A
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end
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function size(element::Element{$eltype})
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return size($X)
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end
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function length(element::Element{$eltype})
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return size($X, 2)
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end
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#=
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XX = refcoords($X)
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function get_reference_element_coordinates(::Type{$eltype})
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return XX
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end
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XXX = vec(mean($X, 2))
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function get_reference_element_midpoint(::Type{$eltype})
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return XXX
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end
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function $eltype(args...)
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return Element{$eltype}(args...)
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end
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=#
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end
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end
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# 1d Lagrange elements
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@create_lagrange_element(Seg2, "2 node linear line element",
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[-1.0 1.0], (xi) -> [1.0, xi[1]])
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@create_lagrange_element(Seg3, "3 node quadratic line element",
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[-1.0 1.0 0.0], (xi) -> [1.0, xi[1], xi[1]^2])
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# 2d Lagrange elements
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@create_lagrange_element(Tri3, "3 node bilinear triangle element",
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[0.0 1.0 0.0
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0.0 0.0 1.0],
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(xi) -> [1.0, xi[1], xi[2]])
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@create_lagrange_element(Tri6, "6 node quadratic triangle element",
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[0.0 1.0 0.0 0.5 0.5 0.0
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0.0 0.0 1.0 0.0 0.5 0.5],
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(xi) -> [1.0, xi[1], xi[2], xi[1]^2, xi[2]^2, xi[1]*xi[2]])
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@create_lagrange_element(Quad4, "4 node bilinear quadrangle element",
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[-1.0 1.0 1.0 -1.0
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-1.0 -1.0 1.0 1.0],
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(xi) -> [1.0, xi[1], xi[2], xi[1]*xi[2]])
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# 3d Lagrange elements
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@create_lagrange_element(Hex8, "8 node hexahedra",
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[-1.0 1.0 1.0 -1.0 -1.0 1.0 1.0 -1.0
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-1.0 -1.0 1.0 1.0 -1.0 -1.0 1.0 1.0
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-1.0 -1.0 -1.0 -1.0 1.0 1.0 1.0 1.0],
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(xi) -> [1.0, xi[1], xi[2], xi[1]*xi[2], xi[3], xi[1]*xi[3], xi[2]*xi[3], xi[1]*xi[2]*xi[3]])
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@create_lagrange_element(Tet4, "4 node tetrahedron",
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[0.0 1.0 0.0 0.0
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0.0 0.0 1.0 0.0
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0.0 0.0 0.0 1.0],
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(xi) -> [1.0, xi[1], xi[2], xi[3]])
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@create_lagrange_element(Tet10, "10 node quadratic tetrahedron",
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[0.0 1.0 0.0 0.0 0.5 0.5 0.0 0.0 0.5 0.0
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0.0 0.0 1.0 0.0 0.0 0.5 0.5 0.0 0.0 0.5
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0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.5 0.5 0.5],
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(xi) -> [ 1.0, xi[1], xi[2], xi[3], xi[1]^2,
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xi[2]^2, xi[3]^2, xi[1]*xi[2], xi[2]*xi[3], xi[3]*xi[1]])
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function get_reference_element_midpoint{E}(element::Element{E})
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get_reference_element_midpoint(E)
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end
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