2016-07-07 18:04:09 +03:00
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# 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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2016-07-10 04:26:21 +03:00
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2018-09-06 12:08:16 +03:00
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using JuliaFEM, Test
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# 2d poisson problem with known analytical solution
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# from FENiCS tutorial, u(x,y) = 1 + x² + 2y² on [0x1]×[0,1]
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# and u₀(x,y) = 1 + x² + 2y², f(x,y) = -6
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mesh_file = @__DIR__()*"/testdata/primitives.med"
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mesh = aster_read_mesh(mesh_file, "UNITSQUARE_6X4")
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square = Problem(PlaneHeat, "unit square, 6x4 triangular mesh", 1)
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square_elements = create_elements(mesh, "UNITSQUARE")
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update!(square_elements, "thermal conductivity", 1.0)
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update!(square_elements, "heat source", -6.0)
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add_elements!(square, square_elements)
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bc = Problem(Dirichlet, "u₀(x,y) = 1 + x² + 2y²", 1, "temperature")
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bc_elements = create_elements(mesh, "FACE1", "FACE2", "FACE3", "FACE4")
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function u0(element, ip, time)
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x, y = element("geometry", ip, time)
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return 1 + x^2 + 2*y^2
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2016-07-07 18:04:09 +03:00
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end
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2018-09-06 12:08:16 +03:00
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update!(bc_elements, "temperature 1", u0)
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add_elements!(bc, bc_elements)
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analysis = Analysis(Linear)
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add_problems!(analysis, square, bc)
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run!(analysis)
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T_fem = Float64[]
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T_acc = Float64[]
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for (nid, Xi) in square("geometry", 0.0)
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push!(T_fem, square("temperature", Xi, 0.0)[1])
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push!(T_acc, 1.0 + Xi[1]^2 + 2*Xi[2]^2)
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end
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@test maximum(abs.(T_fem-T_acc)) < 1.0e-12
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# gradient of field is
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X = [0.5, 0.5]
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gradT1 = [2*X[1] 4*X[2]]
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gradT2 = square("temperature", X, 0.0, Val{:Grad})
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@debug("gradT1 = $gradT1, gradT2 = $gradT2")
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# [1.1666666666666625 1.5000000000000018] quite big difference ..?
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@test isapprox(gradT1, gradT2; rtol=25.0e-2)
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