mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-30 08:02:50 +00:00
Jukka Aho
107 lines
3.2 KiB
Julia
107 lines
3.2 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
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abstract CG <: Element
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"""
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Create new element with element_name to family element_family
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Examples
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--------
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>>> @create_element(Seg2, CG, "2 node linear segment")
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"""
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macro create_element(element_name, element_family, element_description)
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# Logging.debug("Creating element ", element_name, ": ", element_description, "\n")
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eltype = esc(element_name)
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elfam = esc(element_family)
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quote
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global get_element_description
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type $eltype <: $elfam
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connectivity :: Array{Int, 1}
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fields :: Dict{Any, Any}
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end
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$eltype(connectivity) = $eltype(connectivity, Dict{Any, Any}())
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get_element_description(el::Type{$eltype}) = $element_description
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end
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end
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"""
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Given polynomial P and coordinates of reference element, calculate
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Lagrange basis function and partial derivatives.
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"""
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function calculate_lagrange_basis(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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# Logging.debug("Calculating inverse of A")
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invA = inv(A)'
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basis(xi) = invA*P(xi)
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dbasisdxi = ForwardDiff.jacobian(basis)
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basis, dbasisdxi
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end
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"""
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Assign Lagrange basis for element.
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"""
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macro create_lagrange_basis(element_name, X, P)
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# Logging.debug("Creating Lagrange basis for element ", element_name, ". ")
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eltype = esc(element_name)
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quote
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global get_number_of_basis_functions, get_element_dimension
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global get_basis, get_dbasisdxi
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dim = size($X, 1)
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nbasis = size($X, 2)
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# Logging.debug("Number of basis functions: ", nbasis, ". ")
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# Logging.debug("Element dimension: ", dim)
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get_number_of_basis_functions(el::Type{$(esc(element_name))}) = nbasis
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get_number_of_basis_functions(el::$(esc(element_name))) = nbasis
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get_element_dimension(el::$(esc(element_name))) = dim
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basis, dbasisdxi = calculate_lagrange_basis($P, $X)
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get_basis(el::$eltype, xi) = basis(xi)
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get_dbasisdxi(el::$eltype, xi) = dbasisdxi(xi)
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# Logging.debug("Element ", $element_name, " created.")
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end
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end
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# 0d Lagrange element
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@create_element(Point1, CG, "1 node point element")
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# 1d Lagrange elements
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@create_element(Seg2, CG, "2 node linear line element")
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@create_lagrange_basis(Seg2, [-1.0 1.0], (xi) -> [1.0, xi[1]])
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@create_element(Seg3, CG, "3 node quadratic line element")
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@create_lagrange_basis(Seg3, [-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_element(Quad4, CG, "4 node bilinear quadrangle element")
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@create_lagrange_basis(Quad4,
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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_element(Tet10, CG, "10 node quadratic tetrahedron")
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@create_lagrange_basis(Tet10,
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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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