added tests

test/test_elasticity.jl

@@ -0,0 +1,26 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+# unit tests for heat equations
+
+using FactCheck
+using JuliaFEM: Quad4, Field, FieldSet, CPS4, get_basis, solve!, PlaneStressElasticityProblem
+
+
+facts("test plane elasticity on single element, volume load") do
+    element = Quad4([1, 2, 3, 4])
+    element["geometry"] = FieldSet(Field(Vector[[0.0, 0.0], [10.0, 0.0], [10.0, 1.0], [0.0, 1.0]]))
+    element["youngs modulus"] = FieldSet(Field(500.0))
+    element["poissons ratio"] = FieldSet(Field(0.3))
+    element["displacement load"] = FieldSet(Field(0.0, Vector[[0.0, -10.0], [0.0, -10.0], [0.0, -10.0], [0.0, -10.0]]))
+    equation = CPS4(element)
+    free_dofs = [3, 4, 5, 6]
+    problem = PlaneStressElasticityProblem([equation])
+    solve!(problem, free_dofs; max_iterations=10)
+    #solve!(equation, "displacement", free_dofs; max_iterations=10)
+    disp = get_basis(element)("displacement", [1.0, 1.0])[2]
+    Logging.info("displacement at tip: $disp")
+    # verified using Code Aster.
+    @fact disp --> roughly(-8.77303119819776E+00)
+end
+

test/test_elements.jl

@@ -34,12 +34,14 @@ end
 
 facts("test adding fieldsets and fields to element") do
     el = MockElement([1, 2, 3, 4])
+ 
     fieldset = JuliaFEM.FieldSet("geometry")
     field1 = JuliaFEM.Field(0.0, [0.0, 0.0, 0.0, 0.0])
     push!(fieldset, field1)
     field2 = JuliaFEM.Field(1.0, [1.0, 1.0, 1.0, 1.0])
     push!(fieldset, field2)
-    push!(el, fieldset)
+
+    el["geometry"] = fieldset
     fields = el["geometry"]
     @fact length(fields) --> 2
     @fact fields[1] --> field1
@@ -57,13 +59,13 @@ facts("interpolation of fields in some function space") do
     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]])])
 
-    push!(element, fieldset1)
-    push!(element, fieldset2)
-    push!(element, fieldset3)
-    push!(element, fieldset4)
-    push!(element, fieldset5)
-    push!(element, fieldset6)
-    push!(element, fieldset7)
+    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

test/test_global_assembly.jl

@@ -0,0 +1,32 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using JuliaFEM: Quad4, Seg2, FieldSet, Field, PlaneHeatProblem
+using JuliaFEM: initialize_global_assembly, calculate_global_assembly!
+using FactCheck
+
+facts("assemble a simple two element problem and solve") do 
+    el1 = Quad4([1, 2, 3, 4])
+    el1["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
+    el1["temperature thermal conductivity"] = 6.0
+    el1["temperature load"] = [12.0, 12.0, 12.0, 12.0]
+    el1["density"] = 10
+
+    el2 = Seg2([1, 2])
+    el2["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0]]
+
+    # Boundary load, linear ramp 0 -> 600 at time 0 -> 1
+    el2["temperature flux"] = FieldSet(Field[Field(0.0, 0.0), Field(1.0, 600.0)])
+
+    problem = PlaneHeatProblem()
+    push!(problem, el1)
+    push!(problem, el2)
+
+    global_assembly = initialize_global_assembly(problem)
+    calculate_global_assembly!(global_assembly, problem)
+    free_dofs = [1, 2]
+    A = lufact(global_assembly.stiffness_matrix[free_dofs, free_dofs])
+    b = full(global_assembly.force_vector)[free_dofs]
+    u = A \ b
+    @fact u --> roughly([101.0, 101.0])
+end

test/test_heat.jl

@@ -0,0 +1,43 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+# unit tests for heat equations
+
+using FactCheck
+using JuliaFEM: Seg2, Quad4, Field, FieldSet, DC2D4, initialize_local_assembly, calculate_local_assembly!, DC2D2
+
+facts("tests on [0x1]x[0x1] domain") do
+
+    # volume element
+    element = Quad4([1, 2, 3, 4])
+    element["geometry"] = FieldSet(Field(Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]))
+    element["temperature thermal conductivity"] = FieldSet(Field(0.0, 6.0))
+    element["temperature load"] = FieldSet(Field(0.0, [12.0, 12.0, 12.0, 12.0]))
+    element["density"] = FieldSet(Field(0.0, 36.0))
+
+    # boundary element 
+    boundary_element = Seg2([1, 2])
+    boundary_element["geometry"] = FieldSet(Field(Vector[[0.0, 0.0], [1.0, 0.0]]))
+    # linear ramp from 1 to 6 in time 0 to 1
+    boundary_element["temperature flux"] = FieldSet(Field[Field(0.0, 0.0), Field(1.0, 6.0)])
+
+    # Set constant source f=12 with k=6. Accurate solution is
+    # T=1 on free boundary, u(x,y) = -1/6*(1/2*f*x^2 - f*x)
+    equation = DC2D4(element)
+    la = initialize_local_assembly()
+    calculate_local_assembly!(la, equation, "temperature")
+    fdofs = [1, 2]
+    A = la.stiffness_matrix
+    b = la.force_vector
+    @fact A[fdofs, fdofs] \ b[fdofs] --> roughly([1.0, 1.0])
+
+    # Set constant flux g=6 on boundary. Accurate solution is
+    # u(x,y) = x which equals T=1 on boundary.
+    boundary_equation = DC2D2(boundary_element);
+
+    calculate_local_assembly!(la, boundary_equation, "temperature")
+    b = la.force_vector
+    @fact A[fdofs, fdofs] \ b[fdofs] --> roughly([1.0, 1.0])
+
+end
+

test/test_interpolation.jl

@@ -4,28 +4,17 @@
 using JuliaFEM: get_basis, grad, FieldSet, Field, Quad4
 using FactCheck
 
-element = Quad4([1, 2, 3, 4])
-
-geometry_field = Field(0.0, Vector[])  # Create empty field at time t=0.0
-push!(geometry_field, [ 0.0, 0.0])  # push some values for field
-push!(geometry_field, [ 1.0, 0.0])
-push!(geometry_field, [ 1.0, 1.0])
-push!(geometry_field, [ 0.0, 1.0])
-geometry_fieldset = FieldSet("geometry")  # create fieldset "geometry"
-push!(geometry_fieldset, geometry_field)  # add field to fieldset
-push!(element, geometry_fieldset) # add fieldset to element
-
-temperature_fieldset = FieldSet("temperature")
-push!(temperature_fieldset, Field(0.0, [0.0, 0.0, 0.0, 0.0]))
-push!(temperature_fieldset, Field(1.0, [1.0, 2.0, 3.0, 4.0]))
-push!(element, temperature_fieldset)
-
-displacement_fieldset = FieldSet("displacement")
-push!(displacement_fieldset, Field(0.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0]]))
-push!(displacement_fieldset, Field(1.0, Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]]))
-push!(element, displacement_fieldset)
 
 facts("basic continuum interpolations") do
+
+    element = Quad4([1, 2, 3, 4])
+
+    element["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
+    element["temperature"] = ([0.0, 0.0, 0.0, 0.0], [1.0, 2.0, 3.0, 4.0])
+    element["displacement"] = (
+        Vector[[0.0, 0.0], [0.0, 0.0], [0.00, 0.0], [0.0, 0.0]],
+        Vector[[0.0, 0.0], [0.0, 0.0], [0.25, 0.0], [0.0, 0.0]])
+
     # from my old home works
     basis = get_basis(element)
     dbasis = grad(basis)

test/test_solver.jl

@@ -0,0 +1,71 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+# test SimpleSolver
+
+using FactCheck
+using JuliaFEM: DirichletProblem, Seg2, PlaneHeatProblem, Quad4, SimpleSolver, get_element, get_basis
+
+""" Define Problem 1:
+
+- Field function: Laplace equation Δu=0 in Ω={u∈R²|(x,y)∈[0,1]×[0,1]}
+- Neumann boundary on Γ₁={0<=x<=1, y=0}, ∂u/∂n=600 on Γ₁
+"""
+function get_heatproblem()
+    el1 = Quad4([1, 2, 3, 4])
+    # these might look like normal values but believe me, they
+    # are fields with temporal and spatial dimension
+    el1["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]
+    el1["temperature thermal conductivity"] = 6.0
+    el1["density"] = 36.0
+
+    el2 = Seg2([1, 2])
+    el2["geometry"] = Vector[[0.0, 0.0], [1.0, 0.0]]
+    # Boundary load, linear ramp 0 -> 600 at time 0 -> 1
+    # yet another simplification, if field is given as a tuple,
+    # multiple fields are created. there is 1 second time step between
+    # each field. So the following is basically same as
+    # fieldset = FieldSet("temperature flux")
+    # field1 = Field(0.0, 0.0)
+    # field2 = Field(1.0, 600.0)
+    # push!(fieldset, field1)
+    # push!(fieldset, field2)
+    # element["temperature flux"] = fieldset
+    el2["temperature flux"] = (0.0, 600.0)
+
+    problem1 = PlaneHeatProblem()
+    push!(problem1, el1)
+    push!(problem1, el2)
+    return problem1
+end
+
+""" Define Problem 2:
+ - Dirichlet boundary Γ₂={0<=x<=1, y=1}, u=0 on Γ₂
+"""
+function get_boundaryproblem()
+    el3 = Seg2([3, 4])
+    el3["geometry"] = Vector[[1.0, 1.0], [0.0, 1.0]]
+    problem2 = DirichletProblem(1)
+    push!(problem2, el3)
+    return problem2
+end
+
+facts("test simplesolver") do
+    problem1 = get_heatproblem()
+    problem2 = get_boundaryproblem()
+    # Create a solver for a set of problems
+    solver = SimpleSolver()
+    push!(solver, problem1)
+    push!(solver, problem2)
+    # Solve problem at time t=1.0 and update fields
+    call(solver, 1.0)
+    # Postprocess.
+    # Interpolate temperature field along boundary of Γ₁ at time t=1.0
+    xi = [0.0, -1.0]
+    el2 = get_element(problem1.equations[2])
+    basis = get_basis(el2)
+    X = basis("geometry", xi, 1.0)
+    T = basis("temperature", xi, 1.0)
+    Logging.info("Temperature at point X = $X is T = $T")
+    @fact T --> roughly(100.0)
+end