mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
54 lines
1.7 KiB
Julia
54 lines
1.7 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
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using JuliaFEM.Preprocess
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using JuliaFEM.Postprocess
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using JuliaFEM.Testing
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@testset "2d poisson problem with known analytical solution" begin
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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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field = Problem(Heat, "unit square, 6x4 triangular mesh", 1)
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field.elements = create_elements(mesh, "UNITSQUARE")
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field.properties.formulation = "2D"
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update!(field, "thermal conductivity", 1.0)
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update!(field, "heat source", -6.0)
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bc = Problem(Dirichlet, "u₀(x,y) = 1 + x² + 2y²", 1, "temperature")
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#bc.properties.order = 2
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#bc.properties.dual_basis = true
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bc.properties.variational = false
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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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end
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update!(bc, "temperature 1", u0)
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solver = LinearSolver(field, bc)
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solver()
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T_fem = Float64[]
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T_acc = Float64[]
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for (nid, X) in field("geometry")
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push!(T_fem, field("temperature", X)[1])
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push!(T_acc, 1.0 + X[1]^2 + 2*X[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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gradT(X) = [2*X[1] 4*X[2]]
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X = [0.5, 0.5]
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gradT1 = gradT(X)
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gradT2 = field("temperature", X, solver.time, Val{:Grad})
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info("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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end
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