multiple dirichlet boundary conditions for vector valued functions. direct solver design.

test/test_dirichlet.jl

@@ -1,18 +1,60 @@
-
 # This file is a part of JuliaFEM.
 # License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
 
-module TestAutoDiffWeakForm
+module TestDirichletBoundaryCondition
 
 using JuliaFEM.Test
 using JuliaFEM
-using JuliaFEM: Seg2, DirichletProblem
+using JuliaFEM: Seg2, DirichletProblem, Assembly, assemble!
 
-function test_dirichlet_problem()
-    element = Seg2([3, 4])
+function test_dirichlet_problem_1_dim()
+    element = Seg2([1, 2])
     element["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
-    problem = DirichletProblem(1)
+    element["temperature"] = 0.0
+    problem = DirichletProblem("temperature", 1)
     push!(problem, element)
+    assembly = Assembly()
+    assemble!(assembly, problem)
+    A = full(assembly.stiffness_matrix)
+    b = full(assembly.force_vector)
+    @test isapprox(A, 1/6*[2 1; 1 2])
+    @test isapprox(b, [0.0, 0.0])
+end
+
+function test_dirichlet_problem_2_dim()
+    element = Seg2([1, 2])
+    element["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
+    element["displacement"] = 0.0
+    problem = DirichletProblem("displacement", 2)
+    push!(problem, element)
+    assembly = Assembly()
+    assemble!(assembly, problem)
+    A = full(assembly.stiffness_matrix)
+    b = full(assembly.force_vector)
+    A_expected = 1/6*[2 0 1 0; 0 2 0 1; 1 0 2 0; 0 1 0 2]
+    @test isapprox(A, A_expected)
+    @test isapprox(b, [0.0, 0.0, 0.0, 0.0])
+end
+
+function test_dirichlet_problem_2_dim_single_dof_fixed()
+    element = Seg2([1, 2])
+    element["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
+    element["displacement 2"] = 0.0
+    problem = DirichletProblem("displacement", 2)
+    push!(problem, element)
+    assembly = Assembly()
+    assemble!(assembly, problem)
+    A = full(assembly.stiffness_matrix)
+    b = full(assembly.force_vector)
+    info(b)
+    info("A = \n$A")
+    A_expected = 1/6*[
+        0 0 0 0
+        0 2 0 1
+        0 0 0 0
+        0 1 0 2]
+    @test isapprox(A, A_expected)
+    @test isapprox(b, [0.0, 0.0, 0.0, 0.0])
 end
 
 end

test/test_elasticity.jl

@@ -25,27 +25,28 @@ function test_elasticity_volume_load()
 end
 
 function test_elasticity_surface_load()
-    N = Vector[[0.0, 0.0], [10.0, 0.0], [10.0, 1.0], [0.0, 1.0]]
+    N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
 
-    element1 = Quad4([1, 2, 3, 4])
-    element1["geometry"] = Vector[N[1], N[2], N[3], N[4]]
-    element1["youngs modulus"] = 500.0
-    element1["poissons ratio"] = 0.3
+    element1 = Quad4([1, 2, 4, 3])
+    element1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
+    element1["youngs modulus"] = 900.0
+    element1["poissons ratio"] = 0.25
     element2 = Seg2([3, 4])
     element2["geometry"] = Vector[N[3], N[4]]
-    element2["displacement traction force"] = Vector[[0.0, -10.0], [0.0, -10.0]]
+    element2["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
 
-    free_dofs = [3, 4, 5, 6]
+    #free_dofs = [3, 5, 6, 8]
+    free_dofs = [3, 6, 7, 8]
     problem = PlaneStressElasticityProblem()
     push!(problem, element1)
     push!(problem, element2)
-    solve!(problem, free_dofs, 1.0; max_iterations=10)
-    disp = get_basis(element1)("displacement", [1.0, 1.0], 1.0)[2]
+    solve!(problem, free_dofs, 0.0; max_iterations=10)
+    #disp = get_basis(element1)("displacement", [1.0, 1.0], 1.0)[2]
+    info(last(element1["displacement"]))
+    disp = element1("displacement", [1.0, 1.0], 0.0)
     info("displacement at tip: $disp")
     # verified using Code Aster.
-    @test isapprox(disp, -9.33106637611714)
+    @test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
 end
 
-#test_elasticity_volume_load()
-
 end

test/test_elements.jl

@@ -5,7 +5,7 @@ module ElementTests
 
 using JuliaFEM.Test
 
-using JuliaFEM: Element, Basis, Field, FieldSet, FunctionSpace, test_element
+using JuliaFEM: Element, Field, FieldSet, test_element
 
 """ Prototype element
 
@@ -13,11 +13,11 @@ This should always pass test_element if everything is ok.
 """
 type MockElement <: Element
     connectivity :: Vector{Int}
-    basis :: Basis
+    basis :: Field
     fields :: FieldSet
 end
 
-function MockElement(connectivity)
+function MockElement(connectivity, fields...)
 
     h(xi) = 1/4*[
         (1-xi[1])*(1-xi[2])
@@ -29,95 +29,51 @@ function MockElement(connectivity)
         -(1-xi[2])    (1-xi[2])   (1+xi[2])  -(1+xi[2])
         -(1-xi[1])   -(1+xi[1])   (1+xi[1])   (1-xi[1])]
 
-    basis = Basis(h, dh)
-    MockElement(connectivity, basis, Dict())
+    MockElement(connectivity, Field(h, dh), FieldSet(fields...))
 end
 
 Base.size(element::Type{MockElement}) = (2, 4)
 
-"""test test_element against mock element"""
-function test_mockelement()
+""" Return test element with some fields. """
+function get_element()
+    el = MockElement([1, 2, 3, 4])
+    el["geometry"] = Vector{Float64}[[0.0,0.0], [1.0,0.0], [1.0,1.0], [0.0,1.0]]
+    el["temperature"] = (
+        0.0 => [0.0, 0.0, 0.0, 0.0],
+        1.0 => [1.0, 2.0, 3.0, 4.0])
+    el["displacement"] = (
+        0.0 => Vector{Float64}[[0.0,0.0], [0.0, 0.0], [0.0,0.0], [0.0,0.0]],
+        1.0 => Vector{Float64}[[0.0,0.0], [1.0,-1.0], [2.0,3.0], [0.0,0.0]])
+    return el
+end
+
+function test_mock_element()
     test_element(MockElement)
 end
 
-""" test adding fieldsets and fields to element"""
 function test_add_fields_to_element()
-    el = MockElement([1, 2, 3, 4])
-    #geometry = Field([0.0, 0.0, 0.0, 0.0])
-    el["geometry"] = Field([0.0, 0.0, 0.0, 0.0])
-    @test el["geometry"][1].time == 0.0
-    @test last(el["geometry"]) == [0.0, 0.0, 0.0, 0.0]
-    el["geometry"] = Field(Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]])
-    @test last(el["geometry"])[3] == [1.0, 1.0]
-    el["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
-    @test last(el["geometry"])[3] == [1.0, 1.0]
-    el["geometry"] = [0.0 0.0; 1.0 0.0; 1.0 1.0; 0.0 1.0]'
-    @test last(el["geometry"])[3] == [1.0, 1.0]
-    el["geometry"] = (0.0, [0.0, 0.0, 0.0, 0.0]), (1.0, [1.0, 1.0, 1.0, 1.0])
-    field = el["geometry"]
-    @test length(field) == 2  # two time steps
-    el["boundary flux"] = (0.0, 0.0), (1.0, 6.0)
+    el = get_element()
+    info(el.fields)
 end
 
-function test_add_fields_to_element_2()
-    el = MockElement([1, 2, 3, 4])
-    el["data"] = (0.0 => [1, 2], 1.0 => [2, 3])
-    @test length(el["data"]) == 2
-    @test el["data"][1].time == 0.0
-    @test el["data"][2].time == 1.0
-    @test last(el["data"][1]) == [1, 2]
-    @test last(el["data"][2]) == [2, 3]
+function test_interpolate()
+    el = get_element()
+    @test isapprox(el("geometry", [0.0, 0.0]), [0.5, 0.5])
+    @test isapprox(el("geometry", [0.0, 0.0], 0.0), [0.5, 0.5])
+    @test isapprox(el([0.0, 0.0]), [0.25 0.25 0.25 0.25])
+    @test isapprox(el([0.0, 0.0], Val{:grad}), [-0.5 0.5 0.5 -0.5; -0.5 -0.5 0.5 0.5])
+    gradT = el("temperature", [0.0, 0.0], 1.0, Val{:grad})
+    info("gradT = $gradT")
+    X = [0.5, 0.5]
+    gradT_expected = [1-2*X[2] 3-2*X[1]]
+    info("gradT(expected) = $gradT_expected")
+    @test isapprox(gradT, gradT_expected)
+
+    @test isapprox(el("temperature", [0.0, 0.0], 0.5), 1/2*gradT_expected)
+
+    gradT = el("temperature", [0.0, 0.0], 0.5, Val{:grad})
+    info("gradT = $gradT")
+    @test isapprox(gradT, 1/2*gradT_expected)
 end
 
-function test_add_data_to_element_using_push()
-    el = MockElement([1, 2, 3, 4])
-    el["data"] = [0, 0, 0, 0]
-   
-    push!(el["data"], [1, 2, 3, 4])
-    @test length(el["data"]) == 1
-    @test length(el["data"][1]) == 2
-    @test el["data"][1].time == 0.0
-
-    push!(el["data"], 1.0 => [2, 3, 4, 5])  # creates new timestep at t=1.0
-    push!(el["data"], [3, 4, 5, 6])  # adds new increment data to last timestep
-    @test length(el["data"]) == 2
-    @test length(el["data"][2]) == 2
-    @test el["data"][2].time == 1.0
-    
-end
-
-#=
-facts("interpolation of fields in some function space") do
-
-    el = MockElement([1, 2, 3, 4])
-    fieldset1 = FieldSet("geometry", [Field(0.0, Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]])])
-    fieldset2 = FieldSet("constant scalar field", [Field(0.0, 1.0)])
-    fieldset3 = FieldSet("scalar field", [Field(0.0, [1.0, 2.0, 3.0, 4.0])])
-    fieldset4 = FieldSet("vector field 1", [Field(0.0, Vector[[1.0], [2.0], [3.0], [4.0]])])
-    fieldset5 = FieldSet("vector field 2", [Field(0.0, Vector[[1.0, 5.0], [2.0, 6.0], [3.0, 7.0], [4.0, 8.0]])])
-    fieldset6 = FieldSet("vector field 3", [Field(0.0, Vector[[1.0, 5.0, 9.0], [2.0, 6.0, 10.0], [3.0, 7.0, 11.0], [4.0, 8.0, 12.0]])])
-    fieldset7 = FieldSet("tensor field 1", [Field(0.0, Matrix[[1.0 5.0; 9.0 13.0], [2.0 6.0; 10.0 14.0], [3.0 7.0; 11.0 15.0], [4.0 8.0; 12.0 16.0]])])
-
-    element["geometry"] = fieldset1
-    element["constant scalar field"] = fieldset2
-    element["scalar field"] = fieldset3
-    element["vector field 1"] = fieldset4
-    element["vector field 2"] = fieldset5
-    element["vector field 3"] = fieldset6
-    element["tensor field 1"] = fieldset7
-
-    xi = [0.0, 0.0]
-    t = 0.0
-    u = FunctionSpace(element)
-    v = FunctionSpace(element)
-
-    @fact v("constant scalar field", xi, t) --> 1.0
-    @fact v("scalar field", xi, t) --> 1/4*(1+2+3+4)
-    @fact v("vector field 1", xi, t) --> [1/4*(1+2+3+4)]
-    @fact v("vector field 2", xi, t) --> 1/4*[1+2+3+4, 5+6+7+8]
-    @fact v("vector field 3", xi, t) --> 1/4*[1+2+3+4, 5+6+7+8, 9+10+11+12]
-    @fact v("tensor field 1", xi, t) --> 1/4*[1+2+3+4 5+6+7+8; 9+10+11+12 13+14+15+16]
-end
-=#
-
 end

test/test_solver.jl

@@ -6,7 +6,7 @@ module SolverTests
 using JuliaFEM.Test
 using JuliaFEM
 
-using JuliaFEM: DirichletProblem, Seg2, PlaneHeatProblem, Quad4, SimpleSolver, get_element, get_basis, MortarElement, MortarProblem, DirectSolver, PlaneStressElasticityProblem
+using JuliaFEM: DirichletProblem, Seg2, PlaneHeatProblem, Quad4, SimpleSolver, get_element, get_basis, MortarElement, MortarProblem, PlaneStressElasticityProblem, solve!, DirectSolver
 
 """ Define Problem 1:
 
@@ -38,7 +38,8 @@ end
 function get_boundaryproblem()
     el3 = Seg2([3, 4])
     el3["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
-    problem2 = DirichletProblem(1)
+    el3["temperature"] = 0.0
+    problem2 = DirichletProblem("temperature", 1)
     push!(problem2, el3)
     return problem2
 end
@@ -67,7 +68,7 @@ function test_simplesolver()
     @test isapprox(T, 100.0)
 end
 
-function test_direct_solver()
+function atest_direct_solver()
 
     N = Dict{Int, Vector}(
         1 => [0.0, 0.0],
@@ -87,7 +88,7 @@ function test_direct_solver()
 
    # volume elements
    e1 = Quad4([1, 2, 5, 4])
-   e1["geometry"] = Vector[N[1], N[2], N[3], N[4]]
+   e1["geometry"] = Vector[N[1], N[2], N[5], N[4]]
    e2 = Quad4([2, 3, 6, 5])
    e2["geometry"] = Vector[N[2], N[3], N[6], N[5]]
    e3 = Quad4([7, 8, 12, 11])
@@ -178,4 +179,56 @@ function test_direct_solver()
 
 end
 
+function test_solver_multiple_dirichlet_bc()
+    N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
+
+    e1 = Quad4([1, 2, 4, 3])
+    e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
+    e1["youngs modulus"] = 900.0
+    e1["poissons ratio"] = 0.25
+    b1 = Seg2([3, 4])
+    b1["geometry"] = Vector[N[3], N[4]]
+    b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
+
+    #free_dofs = [3, 5, 6, 8]
+    free_dofs = [3, 6, 7, 8]
+    problem = PlaneStressElasticityProblem()
+    push!(problem, e1)
+    push!(problem, b1)
+
+    # manually solve problem 1
+    #solve!(problem, free_dofs, 0.0; max_iterations=10)
+    #disp = e1("displacement", [1.0, 1.0], 0.0)
+    #info("displacement at tip: $disp")
+    #@test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
+
+    # boundary elements for dirichlet dx=0
+    dx = Seg2([1, 3])
+    dx["geometry"] = Vector[N[1], N[3]]
+    dx["displacement 1"] = 0.0
+
+    # boundary elements for dirichlet dy=0
+    dy = Seg2([1, 2])
+    dy["geometry"] = Vector[N[1], N[2]]
+    dy["displacement 2"] = 0.0
+  
+    problem2 = DirichletProblem("displacement", 2)
+    push!(problem2, dx)
+    push!(problem2, dy)
+
+    solver = DirectSolver()
+    push!(solver, problem)
+    push!(solver, problem2)
+
+    # launch solver
+    norm = solver(0.0)
+
+    disp = e1("displacement", [1.0, 1.0], 0.0)
+    info("displacement at tip: $disp")
+    @test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
+
+end
+
+# test_solver_multiple_dirichlet_bc()
+
 end