mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-18 11:20:12 +00:00
Jukka Aho
72 lines
2.3 KiB
Julia
72 lines
2.3 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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using JuliaFEM: Basis, Field, get_field, diff
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using FactCheck
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facts("test fields and interpolation") do
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# simple interpolation in domain [-1, 1]
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N = Basis((ξ) -> [0.5*(1.0-ξ[1]), 0.5*(1.0+ξ[1])])
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u = Field(0.0, [0.0, 1.0])
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@fact N([0.0])*u --> 0.5
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@fact (N*u)([0.0]) --> 0.5
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# multiply of field with constant
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u1 = Field(0.0, [0.0, 1.0])
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u2 = 3.0*u1
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@fact u1.time --> 0.0
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@fact u2.time --> 0.0
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@fact u2.values --> [0.0, 3.0]
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# addition of fields together
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u1 = Field(0.0, [0.0, 1.0])
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u2 = Field(0.0, [1.0, 2.0])
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u3 = u1 + u2
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@fact u3.values --> [1.0, 3.0]
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# interpolation between two fields in time domain
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u1 = Field(0.0, [0.0, 1.0])
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u2 = Field(0.0, [1.0, 2.0])
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t = Basis((t) -> [1-t, t])
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u = Field[u1, u2]
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u2 = (t*u)(0.5)
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@fact u2.values --> [0.5, 1.5]
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# interpolation in set of fields is defined for every time value
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u1 = Field(0.0, [0.0, 0.0])
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u2 = Field(1.0, [1.0, 2.0])
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u3 = Field(2.0, [0.5, 1.5])
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u = Field[u1, u2, u3]
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@fact u(-1.0).values --> [0.0, 0.0] # "out of range -" -> first known value
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@fact u(0.0).values --> [0.0, 0.0]
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@fact u(1.0).values --> [1.0, 2.0]
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@fact u(2.0).values --> [0.5, 1.5]
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@fact u(3.0).values --> [0.5, 1.5] # "out of range +" -> last known value
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@fact u(0.5).values --> [0.5, 1.0]
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@fact u(1.5).values --> [0.75, 1.75]
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# use Inf to get very first or last value of field
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@fact u(-Inf).values --> [0.0, 0.0]
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@fact u(+Inf).values --> [0.75, 1.75]
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# multidimensional interpolation with and without derivatives
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X = Field(0.0, Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]])
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h = Basis((xi) ->
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[(1-xi[1])*(1-xi[2])/4
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(1+xi[1])*(1-xi[2])/4
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(1+xi[1])*(1+xi[2])/4
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(1-xi[1])*(1+xi[2])/4])
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# midpoint of field
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@fact (h*X)([0.0, 0.0]) --> [0.5, 0.5]
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@fact h([0.0, 0.0])*X --> [0.5, 0.5]
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# derivatives of field at midpoint
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@fact diff(h)([0.0, 0.0])*X --> [0.5 0.0; 0.0 0.5]
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@fact (diff(h)*X)([0.0, 0.0]) --> [0.5 0.0; 0.0 0.5]
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# multiplying scalar field with a vector -> vector
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b = Basis((xi) -> [1/2*(1-xi[1]), 1/2*(1+xi[1])])
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f = Field(0.0, 100.0)
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@fact b(0.0) * f --> [50.0, 50.0]
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end
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