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https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-10-02 06:13:59 +00:00
defining basis. still needs some rethinking...
This commit is contained in:
Jukka Aho
+157
-31
@@ -5,9 +5,163 @@ module BasisTests
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using JuliaFEM.Test
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using JuliaFEM: get_basis, grad, FieldSet, Field, Quad4
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using JuliaFEM
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using JuliaFEM: Basis, ElementGradientBasis, ElementFieldGradientBasis, Field
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function get_basis()
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basis(xi) = 1/4*[
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(1-xi[1])*(1-xi[2])
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(1+xi[1])*(1-xi[2])
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(1+xi[1])*(1+xi[2])
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(1-xi[1])*(1+xi[2])]'
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dbasis(xi) = 1/4*[
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-(1-xi[2]) (1-xi[2]) (1+xi[2]) -(1+xi[2])
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-(1-xi[1]) -(1+xi[1]) (1+xi[1]) (1-xi[1])]
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return basis, dbasis
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end
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function test_basic_interpolation()
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basis, dbasis = get_basis()
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b = Basis(basis, dbasis)
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@test b([0.0, 0.0]) == 1/4*[1 1 1 1]
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@test b([0.0, 0.0], 1.0) == 1/4*[1 1 1 1]
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end
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function test_basic_interpolation_of_field()
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# in unit square: T(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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temperature = Field(
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(0.0, [0.0, 0.0, 0.0, 0.0]),
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(1.0, [1.0, 2.0, 3.0, 4.0]))
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basis, dbasis = get_basis()
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b = Basis(basis, dbasis, temperature)
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T(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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@test b([0.0, 0.0], 0.0) == T([0.5, 0.5], 0.0)
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@test b([0.0, 0.0], 0.6) == T([0.5, 0.5], 0.6)
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@test b([0.0, 0.0], 1.0) == T([0.5, 0.5], 1.0)
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end
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function test_linear_time_extrapolation_of_field()
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temperature = Field(
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(0.0, [0.0, 0.0, 0.0, 0.0]),
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(1.0, [1.0, 2.0, 3.0, 4.0]))
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basis, dbasis = get_basis()
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b = Basis(basis, dbasis, temperature, :linear)
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T(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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@test b([0.0, 0.0], -1.0) == T([0.5, 0.5], -1.0)
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@test b([0.0, 0.0], 3.0) == T([0.5, 0.5], 3.0)
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end
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function test_constant_time_extrapolation_of_field()
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temperature = Field(
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(0.0, [0.0, 0.0, 0.0, 0.0]),
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(1.0, [1.0, 2.0, 3.0, 4.0]))
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basis, dbasis = get_basis()
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b = Basis(basis, dbasis, temperature, :constant)
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T(X,t) = t*(1 + X[1] + 3*X[2] - 2*X[1]*X[2])
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@test b([0.0, 0.0], -1.0) == T([0.5, 0.5], 0.0)
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@test b([0.0, 0.0], 3.0) == T([0.5, 0.5], 1.0)
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end
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function test_time_extrapolation_of_field_with_single_timestep()
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temperature = Field([1.0, 2.0, 3.0, 4.0])
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basis, dbasis = get_basis()
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b = Basis(basis, dbasis, temperature)
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@test b([0.0, 0.0], 1.0) == mean([1.0, 2.0, 3.0, 4.0])
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end
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function test_gradient_interpolation_empty_gradient()
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X = [0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]'
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geometry = Field(X)
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# P(X) = [1.0, X[1], X[2], X[1]*X[2]]
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# basis2, dbasis2 = JuliaFEM.calculate_lagrange_basis(P, X)
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basis, dbasis = get_basis()
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N = Basis(basis, dbasis)
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dN = ElementGradientBasis(N, geometry)
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@test dN([0.0, 0.0]) == 1/2*[-1 1 1 -1; -1 -1 1 1]
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# @test dN([0.0, 0.0]) == dbasis2([0.5, 0.5])
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end
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function test_gradient_interpolation_of_scalar_field()
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# in unit square: grad(T)(X) = [1-2X[2], 3-2*X[1]]
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geometry = Field([0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]')
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temperature = Field([1, 2, 3, 4])
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basis, dbasis = get_basis()
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N = Basis(basis, dbasis)
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dN = ElementGradientBasis(N, geometry)
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dT = ElementFieldGradientBasis(dN, temperature)
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dT_expected(X) = [1-2*X[2] 3-2*X[1]]
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@test dT([0.0, 0.0]) == dT_expected([0.5, 0.5])
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end
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function test_interpolation_of_vector_field()
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# in unit square, u(X,t) = [1/4*t*X[1]*X[2], 0, 0]
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geometry = Field([0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]')
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displacement = Field(
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(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]),
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(1.0, Vector[[0.0, 0.0], [0.0, 0.0], [1/4, 0.0], [0.0, 0.0]]))
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basis, dbasis = get_basis()
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X = Basis(basis, dbasis, geometry)
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u = Basis(basis, dbasis, displacement)
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u_expected(X,t) = [1/4*t*X[1]*X[2], 0]
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# x = X + u
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x = X([0.0, 0.0], 1.0) + u([0.0, 0.0], 1.0)
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@test isapprox(x, [9/16, 1/2])
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@test isapprox(u([0.0, 0.0], 1.0), u_expected([0.5, 0.5], 1.0))
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end
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function test_interpolation_of_gradient_of_vector_field()
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# in unit square, u(X) = t*[X[1]*X[2]/4, X[1]*(X[1]+X[2])/2]
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# => u_i,j = t*[X[2]/4 X[1]/4; X[1]/2+(X[1]+X[2])/2 X[1]/2]
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geometry = Field([0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]')
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displacement = Field(
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(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.00, 0.0], [0.0, 0.0]]),
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(1.0, Vector[[0.0, 0.0], [0.0, 0.5], [0.25, 1.0], [0.0, 0.0]]))
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basis, dbasis = get_basis()
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N = Basis(basis, dbasis)
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dN = ElementGradientBasis(N, geometry)
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dU = ElementFieldGradientBasis(dN, displacement)
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dU_expected(X, t) = t*[X[2]/4 X[1]/4; X[1]/2+(X[1]+X[2])/2 X[1]/2]
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@test isapprox(dU([0.0, 0.0], 1.0), dU_expected([0.5, 0.5], 1.0))
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end
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# TODO: how on earth make this work without some serious spaghetti code
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function test_time_derivative_gradient_interpolation_of_field()
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# in unit square, u(X) = t*[X[1]*X[2]/4, X[1]*(X[1]+X[2])/2]
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# => u_i,j = t*[X[2]/4 X[1]/4; X[1]/2+(X[1]+X[2])/2 X[1]/2]
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# => d(u_i,j)/dt = [X[2]/4 X[1]/4; X[1]/2+(X[1]+X[2])/2 X[1]/2]
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geometry = Field([0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]')
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displacement = Field(
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(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.00, 0.0], [0.0, 0.0]]),
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(1.0, Vector[[0.0, 0.0], [0.0, 0.5], [0.25, 1.0], [0.0, 0.0]]))
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basis, dbasis = get_basis()
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N = Basis(basis, dbasis)
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# wanted
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#u = Basis(basis, dbasis, displacement)
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#L = grad(diff(u))
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#D = 1/2*(L + L')
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#@text isapprox(D([0.0, 0.0], 1.0), ...)
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xi = [0.0, 0.0]
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time = 1.0
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grad = ElementGradientBasis(N, geometry)(xi, time)
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increment = displacement(time, Val{:derivative}, :linear, :linear)
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diffgradu = sum([grad[:,i]*increment[i]' for i=1:length(increment)])'
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diffgradu_expected(X, t) = [X[2]/4 X[1]/4; X[1]/2+(X[1]+X[2])/2 X[1]/2]
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@test diffgradu == diffgradu_expected([0.5, 0.5], 1.0)
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end
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#=
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"""basic continuum interpolations"""
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function test_basic_interpolations()
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@@ -42,10 +196,9 @@ function test_basic_interpolations()
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@test isapprox(U, [1.24235 0.13804; 0.13804 1.02149])
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end
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=#
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function test_interpolation_in_temporal_basis()
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info("testing interpolation on temporal basis")
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temporalbasis = TemporalBasis((t) -> [1-t, t], (t) -> [-1, 1])
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@test temporalbasis(0.2) == [0.8, 0.2]
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i1 = Increment([0.0])
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i2 = Increment([1.0])
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i3 = Increment([2.0])
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@@ -90,31 +243,4 @@ function test_interpolation_in_temporal_basis()
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@test isa(velocity, Increment) == true
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end
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function test_interpolation_in_spatial_basis()
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info("testing interpolation on spatial basis")
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basis(xi) = 1/4*[
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(1-xi[1])*(1-xi[2])
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(1+xi[1])*(1-xi[2])
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(1+xi[1])*(1+xi[2])
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(1-xi[1])*(1+xi[2])]'
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dbasis(xi) = 1/4*[
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-(1-xi[2]) (1-xi[2]) (1+xi[2]) -(1+xi[2])
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-(1-xi[1]) -(1+xi[1]) (1+xi[1]) (1-xi[1])]
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spatialbasis = SpatialBasis(basis, dbasis)
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@test spatialbasis.basis([0.0, 0.0]) == 1/4*[1 1 1 1]
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fs = FieldSet()
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fs["geometry"] = Vector{Float64}[[0.0,0.0], [1.0,0.0], [1.0,1.0], [0.0,1.0]]
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fs["displacement"] = (0.0, zeros(2, 4)), (1.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]])
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X = call(last(fs["geometry"]), spatialbasis, [0.0, 0.0])
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u = call(last(fs["displacement"]), spatialbasis, [0.0, 0.0])
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x = X+u
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@test X ≈ 1/2*[1, 1]
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@test x ≈ [9/16, 1/2]
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gradu = call(last(fs["displacement"]), spatialbasis, [0.0, 0.0], last(fs["geometry"]), Val{:gradient})
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@test gradu ≈ [0.125 0.125; 0.0 0.0]
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end
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end
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+18
-6
@@ -6,8 +6,7 @@ module FieldTests
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using JuliaFEM
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using JuliaFEM: Increment, TimeStep, Field, DefaultDiscreteField, FieldSet
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using JuliaFEM: TemporalBasis, SpatialBasis, ContinuousField, DiscreteField
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using JuliaFEM: DefaultContinuousField
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using JuliaFEM: ContinuousField, DiscreteField, DefaultContinuousField
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using JuliaFEM.Test
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@@ -189,7 +188,9 @@ function test_default_discrete_field_quick_way_two_timesteps_with_vector_value()
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end
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function test_default_discrete_field_quick_way_set_time_vector_also()
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f1 = DefaultDiscreteField( (0.5, [1, 2, 3]), (1.0, [3, 4, 5]) )
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f1 = DefaultDiscreteField(
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(0.5, [1, 2, 3]),
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(1.0, [3, 4, 5]))
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@test isa(f1[1], TimeStep)
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@test isa(f1[2], TimeStep)
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@test isa(f1[1][1], Increment)
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@@ -200,6 +201,20 @@ function test_default_discrete_field_quick_way_set_time_vector_also()
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@test f1[2].time == 1.0
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end
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function test_default_discrete_field_for_loop()
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field = DefaultDiscreteField(
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(0.5, [1, 2, 3]),
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(1.0, [3, 4, 5]),
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(1.5, [4, 5, 6]))
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timesteps = [ts for ts in field]
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@test timesteps[1].time == 0.5
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@test timesteps[2].time == 1.0
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@test timesteps[3].time == 1.5
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@test timesteps[1][end] == [1, 2, 3]
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@test timesteps[2][end] == [3, 4, 5]
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@test timesteps[3][end] == [4, 5, 6]
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end
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function test_default_continuous_field()
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function myfield(xi::Vector, time::Float64)
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@@ -244,13 +259,10 @@ function test_adding_timesteps()
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fs = FieldSet()
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fs["temperature"] = [1, 2, 3, 4]
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T0 = last(fs["temperature"]) # last increment of last field
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@debug("last temperature T0 = $T0")
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T1 = Increment(T0 + 1)
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@debug("typeof T1 = $(typeof(T1))")
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timestep = TimeStep(1.0, Increment[T1]) # new list of increments for timestep
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push!(fs["temperature"], timestep)
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T2 = last(fs["temperature"])
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@debug("last temperature T2 = $T2")
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@test length(fs["temperature"]) == 2
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@test last(fs["temperature"]) == [2, 3, 4, 5]
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@test fs["temperature"][end].time == 1.0
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