mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-19 19:53:51 +00:00
Jukka Aho
ca7e2904cf
* Fix deprecation warnings from tests * Refactor tests so that ´@testset` is usually called in master file `runtests.jl`, not inside test file. Later on we can convert tests to examples. * Syntax of tests now follow more closely syntax used currently in JuliaFEM. We have had earlier studies with different kind of syntaxes, now we have kind of explicit way to do things.
154 lines
4.8 KiB
Julia
154 lines
4.8 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, SparseArrays, LinearAlgebra, Test
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""" Calculate mortar projection matrix P = D^-1*M from mortar assembly. """
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function calculate_mortar_projection_matrix(problem::Problem{Mortar}, ndim::Int)
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C1 = sparse(problem.assembly.C1, ndim, ndim)
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C2 = sparse(problem.assembly.C2, ndim, ndim)
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@debug("problem.assembly", problem.assembly.K, problem.assembly.D,
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problem.assembly.Kg, problem.assembly.fg, problem.assembly.f,
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problem.assembly.g)
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@assert isempty(problem.assembly.K)
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@assert isempty(problem.assembly.D)
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@assert isempty(problem.assembly.Kg)
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@assert isempty(problem.assembly.fg)
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@assert isempty(problem.assembly.f)
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@assert C1 == C2
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@assert problem.properties.adjust == false
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S = get_nonzero_rows(C2)
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M = setdiff(get_nonzero_columns(C2), S)
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# Construct matrix P = D^-1*M
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D_ = C2[S,S]
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M_ = -C2[S,M]
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P = lu(D_) \ Matrix(M_)
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return S, M, P
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end
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# two linear element clipping, calculation of projection matrix P for
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# standard and dual basis
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X = Dict(
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1 => [0.0, 0.0, 0.0],
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2 => [1.0, 0.0, 0.0],
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3 => [0.0, 1.0, 0.0],
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4 => [-0.25, 0.50, 0.00],
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5 => [0.50, -0.25, 0.00],
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6 => [0.75, 0.75, 0.00])
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slave = Element(Tri3, (1, 2, 3))
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master = Element(Tri3, (4, 5, 6))
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update!((slave, master), "geometry", X)
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update!(slave, "master elements", [master])
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problem = Problem(Mortar, "two elements", 1, "temperature")
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problem.properties.dual_basis = false
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initialize!(problem, 0.0)
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assemble!(problem, 0.0)
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# forget to add elements to problem
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add_elements!(problem, slave, master)
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initialize!(problem, 0.0)
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assemble!(problem, 0.0)
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C1 = sparse(problem.assembly.C1)
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C2 = sparse(problem.assembly.C2)
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D = sparse(problem.assembly.D)
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@test length(D) == 0
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@test C1 == C2
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S, M, P = calculate_mortar_projection_matrix(problem, 6)
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@test S == [1, 2, 3]
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@test M == [4, 5, 6]
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# visually inspected to be ok result
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P_expected = 1/15*[9 9 -3; -7 13 9; 13 -7 9]
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@test isapprox(P, P_expected)
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um = [7.5, 15.0, 22.5]
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@test isapprox(P*um, [9.0, 23.0, 13.0])
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empty!(problem.assembly)
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problem.properties.dual_basis = true
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assemble!(problem, 0.0)
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C1 = sparse(problem.assembly.C1)
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C2 = sparse(problem.assembly.C2)
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D = sparse(problem.assembly.D)
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@test length(D) == 0
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@test C1 == C2
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S, M, P = calculate_mortar_projection_matrix(problem, 6)
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@test S == [1, 2, 3]
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@test M == [4, 5, 6]
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@test isapprox(P, P_expected)
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um = [7.5, 15.0, 22.5]
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@test isapprox(P*um, [9.0, 23.0, 13.0])
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# two quadratic element clipping, calculation of projection matrix P
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# for standard basis
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X = Dict(
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1 => [0.0, 0.0, 0.0],
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2 => [1.0, 0.0, 0.0],
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3 => [0.0, 1.0, 0.0],
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7 => [-0.25, 0.50, 0.00],
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8 => [0.50, -0.25, 0.00],
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9 => [0.75, 0.75, 0.00])
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# middle nodes
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X[4] = 1/2*(X[1] + X[2])
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X[5] = 1/2*(X[2] + X[3])
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X[6] = 1/2*(X[3] + X[1])
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X[10] = 1/2*(X[7] + X[8])
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X[11] = 1/2*(X[8] + X[9])
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X[12] = 1/2*(X[9] + X[7])
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slave = Element(Tri6, (1, 2, 3, 4, 5, 6))
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master = Element(Tri6, (7, 8, 9, 10, 11, 12))
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update!((slave, master), "geometry", X)
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update!(slave, "master elements", [master])
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problem = Problem(Mortar, "two elements", 1, "temperature")
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problem.properties.dual_basis = false
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problem.properties.alpha = 0.2
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add_elements!(problem, slave, master)
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initialize!(problem, 0.0)
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assemble!(problem, 0.0)
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C1 = sparse(problem.assembly.C1)
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C2 = sparse(problem.assembly.C2)
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D = sparse(problem.assembly.D)
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@test length(D) == 0
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@test C1 == C2
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S, M, P = calculate_mortar_projection_matrix(problem, 12)
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@test S == [1, 2, 3, 4, 5, 6]
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@test M == [7, 8, 9, 10, 11, 12]
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@debug("Projection matrix P", Matrix(P))
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# visually inspected to be ok result
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P_expected = 1/675*[81 81 189 972 -324 -324; 609 429 81 -1092 1404 -756; 429 609 81 -1092 -756 1404; -39 231 -81 132 396 36; -81 -81 81 108 324 324; 231 -39 -81 132 36 396]
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@test isapprox(P, P_expected)
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um = 15/2*[1, 2, 3]
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um = [um[1], um[2], um[3], 0.5*(um[1]+um[2]), 0.5*(um[2]+um[3]), 0.5*(um[3]+um[1])]
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us = P*um
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@test isapprox(us, [9.0, 23.0, 13.0, 16.0, 18.0, 11.0])
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# two quadratic element clipping, calculation of projection matrix P for
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# dual lagrange basis
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problem.properties.dual_basis = true
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problem.properties.alpha = 0.2
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empty!(problem.assembly)
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initialize!(problem, 0.0)
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assemble!(problem, 0.0)
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C1 = sparse(problem.assembly.C1)
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C2 = sparse(problem.assembly.C2)
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D = sparse(problem.assembly.D)
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@test length(D) == 0
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@test C1 == C2
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S, M, P = calculate_mortar_projection_matrix(problem, 12)
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P_expected = 1/675*[81 81 189 972 -324 -324; 609 429 81 -1092 1404 -756; 429 609 81 -1092 -756 1404; -39 231 -81 132 396 36; -81 -81 81 108 324 324; 231 -39 -81 132 36 396]
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@test isapprox(P, P_expected)
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um = 15/2*[1, 2, 3]
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um = [um[1], um[2], um[3], 0.5*(um[1]+um[2]), 0.5*(um[2]+um[3]), 0.5*(um[3]+um[1])]
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us = P*um
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@test isapprox(us, [9.0, 23.0, 13.0, 16.0, 18.0, 11.0])
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