Adding example with transient adjoint calculation idaholab#42

modules/optimization/examples/simpleTransient/adjoint.i

@@ -0,0 +1,104 @@
+[Mesh]
+  [gmg]
+    type = GeneratedMeshGenerator
+    dim = 2
+    nx = 10
+    ny = 10
+    xmin = -1
+    xmax = 1
+    ymin = -1
+    ymax = 1
+  []
+[]
+
+[Variables]
+  [u]
+  []
+[]
+
+[Kernels]
+  [dt]
+    type = TimeDerivative
+    variable = u
+  []
+  [diff]
+    type = Diffusion
+    variable = u
+  []
+[]
+
+[BCs]
+  [dirichlet]
+    type = DirichletBC
+    variable = u
+    boundary = 'left right top bottom'
+    value = 0
+  []
+[]
+
+[Reporters]
+  [measured_data]
+    type = OptimizationData
+    measurement_file = mms_data.csv
+    file_xcoord = x
+    file_ycoord = y
+    file_zcoord = z
+    file_time = t
+    file_value = u
+  []
+[]
+
+[DiracKernels]
+  [misfit]
+    type = VectorPointSource
+    variable = u
+    value = measured_data/misfit_values
+    coord_x = measured_data/measurement_xcoord
+    coord_y = measured_data/measurement_ycoord
+    coord_z = measured_data/measurement_zcoord
+    time = measured_data/measurement_time
+    reverse_time_end = 1
+  []
+[]
+
+[VectorPostprocessors]
+  [src_values]
+    type = CSVReader
+    csv_file = source_params.csv
+    header = true
+  []
+[]
+
+[Functions]
+  [source]
+    type = VectorNearestPointFunction
+    coord_x = src_values/coordx
+    coord_y = src_values/coordy
+    time = src_values/time
+    value = src_values/values
+  []
+[]
+
+[VectorPostprocessors]
+  [adjoint]
+    type = ElementOptimizationSourceFunctionInnerProduct
+    variable = u
+    function = source
+    reverse_time_end = 1
+  []
+[]
+
+[Executioner]
+  type = Transient
+
+  num_steps = 100
+  end_time = 1
+
+  solve_type = NEWTON
+  petsc_options_iname = '-pc_type -pc_hypre_type'
+  petsc_options_value = 'hypre boomeramg'
+[]
+
+[Outputs]
+  console = false
+[]