Force inversion with nonlinear diffusion problem, where the conductiv…

…ity is a function of temperature. Gradient computation is checked with FD gradient and passes, and the tests include both limited memory BFGS as well as reduced Newton's method with matrix-free Hessian. closes idaholab#25

modules/optimization/Makefile

@@ -32,7 +32,7 @@ EXTERNAL_PETSC_SOLVER       := no
 FLUID_PROPERTIES            := no
 FUNCTIONAL_EXPANSION_TOOLS  := no
 HEAT_CONDUCTION             := yes
-LEVEL_SET                   := no
+LEVEL_SET                   := yes
 MISC                        := no
 NAVIER_STOKES               := no
 PHASE_FIELD                 := no

modules/optimization/test/tests/auxkernels/matl_scaled_gradient_vector/gradientVector.imurthy

@@ -0,0 +1,143 @@
+[Mesh]
+  type = GeneratedMesh
+  dim = 2
+  nx = 10
+  ny = 10
+  xmin = 0
+  xmax = 3.141
+  ymin = 0
+  ymax = 3.141
+[]
+
+
+
+[Variables]
+  [u]
+  []
+  [v]
+  []
+[]
+
+[ICs]
+  [./u_ic]
+    type = FunctionIC
+    variable = 'u'
+    function = parsed_function
+  [../]
+  [./v_ic]
+    type = FunctionIC
+    variable = 'v'
+    function = 'x'
+  [../]
+[]
+
+[Functions]
+  [./parsed_function]
+    type = ParsedFunction
+    value = 'sin(x)-cos(y/2)'
+  [../]
+  [./parsed_grad_function]
+    type = ParsedVectorFunction
+    value_x = 'cos(x)'
+    value_y = 'sin(y/2)/2'
+  [../]
+  [./parsed_gradx_function]
+    type = ParsedFunction
+    value = 'cos(x)'
+  [../]
+[]
+
+[AuxVariables]
+  [./funcGrad_u]
+    order = CONSTANT
+    family = MONOMIAL_VEC
+  [../]
+  [./auxGrad_u]
+    order = CONSTANT
+    family = MONOMIAL_VEC
+  [../]
+  [./auxGrad_v]
+    order = CONSTANT
+    family = MONOMIAL_VEC
+  [../]
+  [./funcGrad_u_x]
+    order = CONSTANT
+    family = MONOMIAL
+  [../]
+  [./auxGrad_u_x]
+    order = CONSTANT
+    family = MONOMIAL
+  [../]
+  [./auxGrad_v_x]
+    order = CONSTANT
+    family = MONOMIAL
+  [../]
+[]
+
+[AuxKernels]
+  [vec]
+    type = VectorFunctionAux
+    variable = funcGrad_u
+    function = parsed_grad_function
+  [../]
+  [grad_u]
+    type = MaterialScaledGradientVector
+    gradient_variable = u
+    variable = auxGrad_u
+  []
+  [grad_v]
+    type = MaterialScaledGradientVector
+    gradient_variable = v
+    variable = auxGrad_v
+    material_scaling = 'trig_material'
+  []
+  [funcGrad_u_x]
+    type = VectorVariableComponentAux
+    variable = funcGrad_u_x
+    vector_variable = funcGrad_u
+    component = 'x'
+  []
+  [auxGrad_u_x]
+    type = VectorVariableComponentAux
+    variable = auxGrad_u_x
+    vector_variable = auxGrad_u
+    component = 'x'
+  []
+  [auxGrad_v_x]
+    type = VectorVariableComponentAux
+    variable = auxGrad_v_x
+    vector_variable = auxGrad_v
+    component = 'x'
+  []
+[]
+
+[Materials]
+  [steel]
+    type = GenericFunctionMaterial
+    prop_names = 'trig_material'
+    prop_values = 'parsed_gradx_function'
+  []
+[]
+
+[VectorPostprocessors]
+ [results]
+   type =  LineValueSampler
+   start_point = '0 1 0'
+   end_point = '3.141 1 0'
+   variable = 'funcGrad_u_x auxGrad_u_x auxGrad_v_x'
+   num_points = 20
+   sort_by =  x
+ []
+[]
+
+[Problem]
+  solve = false
+[]
+[Executioner]
+  type = Steady
+[]
+
+[Outputs]
+  # console = true
+  csv = true
+[]

modules/optimization/test/tests/optimizationreporter/objective_gradient_minimize/nonlinear/adjoint.i

@@ -0,0 +1,135 @@
+[Executioner]
+  type = Steady
+  solve_type = NEWTON
+  line_search = none
+  nl_abs_tol = 1e-12
+  nl_rel_tol = 1e-12
+  nl_max_its = 100
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'lu'
+[]
+
+
+[Mesh]
+[]
+[Variables]
+  [adjointT]
+  []
+[]
+[AuxVariables]
+  [forwardT]
+  []
+  [dDdTgradT]
+    order  = CONSTANT
+    family = MONOMIAL_VEC
+  []
+[]
+
+
+[Kernels]
+  [heat_conduction]
+    type = ADHeatConduction
+    thermal_conductivity = 'linearized_conductivity'
+    variable = adjointT
+  []
+  [advection]
+    type = LevelSetAdvection
+    velocity = dDdTgradT
+    variable = adjointT
+  []
+[]
+[AuxKernels]
+  [dDdTgradT]
+    type = MaterialScaledGradientVector
+    gradient_variable = forwardT
+    variable = dDdTgradT
+    material_scaling = 'dDdT'
+  []
+[]
+[Materials]
+  [LinearizedConductivity]
+    type = ADParsedMaterial
+    f_name = 'linearized_conductivity'
+    function = '10+500*forwardT'
+    args = 'forwardT'
+  []
+  [dDdT]
+    type = ParsedMaterial
+    f_name = 'dDdT'
+    function = '500'
+    args = 'forwardT'
+  []
+[]
+
+
+[DiracKernels]
+  [pt]
+    type = ReporterPointSource
+    variable = adjointT
+    x_coord_name = misfit/measurement_xcoord
+    y_coord_name = misfit/measurement_ycoord
+    z_coord_name = misfit/measurement_zcoord
+    value_name   = misfit/misfit_values
+  []
+[]
+[Reporters]
+  [misfit]
+    type = OptimizationData
+  []
+[]
+
+
+[BCs]
+  [left]
+    type = NeumannBC
+    variable = adjointT
+    boundary = left
+    value = 0
+  []
+  [right]
+    type = NeumannBC
+    variable = adjointT
+    boundary = right
+    value = 0
+  []
+  [bottom]
+    type = DirichletBC
+    variable = adjointT
+    boundary = bottom
+    value = 0
+  []
+  [top]
+    type = DirichletBC
+    variable = adjointT
+    boundary = top
+    value = 0
+  []
+[]
+
+
+[VectorPostprocessors]
+  [gradient_vpp]
+    type = VectorOfPostprocessors
+    postprocessors = 'heatSourceGradient'
+  []
+[]
+[Postprocessors]
+  [heatSourceGradient]
+    type = VariableFunctionElementIntegral
+    function = volumetric_heat_func_deriv
+    variable = adjointT
+  []
+[]
+[Functions]
+  [volumetric_heat_func_deriv]
+    type = ParsedFunction
+    value = dq
+    vars = 'dq'
+    vals = 1
+  []
+[]
+
+
+[Outputs]
+  console = false
+[]