CoupledForce / ADCoupledForce

(test/tests/bcs/coupled_dirichlet_bc/coupled_dirichlet_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./coupled_force_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  # BCs on left
  # u: u=1
  # v: v=2
  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 2
  [../]

  # BCs on right
  # u: c*u + u^2 + v^2 = 9
  # v: no flux
  [./right_u]
    type = CoupledDirichletBC
    variable = u
    boundary = 1
    value = 9
    v=v
  [../]
[]

[Preconditioning]
  [./precond]
    type = SMP
    # 'full = true' is required for computeOffDiagJacobian() to get
    # called.  If you comment this out, you should see that this test
    # requires a different number of linear and nonlinear iterations.
    full = true
  [../]
[]

[Executioner]
  type = Steady

  # solve_type = 'PJFNK'
  solve_type = 'NEWTON'

  # Uncomment next line to disable line search.  With line search enabled, you must use full=true with Newton or else it will fail.
  # line_search = 'none'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  nl_rel_tol = 1e-10
  l_tol = 1e-12
  nl_max_its = 10
[]

[Outputs]
  file_base = out
  exodus = true
[]

v

C++ Type:std::vector<VariableName>

Unit:(no unit assumed)

Controllable:No

Description:The coupled variable which provides the force

variable

C++ Type:NonlinearVariableName

Unit:(no unit assumed)

Controllable:No

Description:The name of the variable that this residual object operates on

(test/tests/auxkernels/element_aux_var/l2_element_aux_var_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
  second_order = true
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./l2_lagrange]
    order = FIRST
    family = L2_LAGRANGE
  [../]
  [./l2_hierarchic]
    order = FIRST
    family = L2_HIERARCHIC
  [../]
  [./one]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  # Coupling of nonlinear to Aux
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./force]
    type = CoupledForce
    variable = u
    v = one
  [../]
[]

[AuxKernels]
  [./coupled_l2_lagrange]
    variable = l2_lagrange
    type = CoupledAux
    value = 2
    operator = +
    coupled = u
    execute_on = 'initial timestep_end'
  [../]
  [./coupled_l2_hierarchic]
    variable = l2_hierarchic
    type = CoupledAux
    value = 2
    operator = +
    coupled = u
    execute_on = 'initial timestep_end'
  [../]
  [./constant]
    variable = one
    type = ConstantAux
    value = 1
    execute_on = 'initial timestep_end'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Postprocessors]
 [./int2_u]
   type = ElementL2Norm
   variable = u
   execute_on = 'initial timestep_end'
 [../]
 [./int2_l2_lagrange]
   type = ElementL2Norm
   variable = l2_lagrange
   execute_on = 'initial timestep_end'
 [../]
 [./int2_l2_hierarchic]
   type = ElementL2Norm
   variable = l2_hierarchic
   execute_on = 'initial timestep_end'
 [../]
 [./int_u]
   type = ElementIntegralVariablePostprocessor
   variable = u
   execute_on = 'initial timestep_end'
 [../]
 [./int_l2_lagrange]
   type = ElementIntegralVariablePostprocessor
   variable = l2_lagrange
   execute_on = 'initial timestep_end'
 [../]
 [./int_l2_hierarchic]
   type = ElementIntegralVariablePostprocessor
   variable = l2_hierarchic
   execute_on = 'initial timestep_end'
 [../]
[]

[Outputs]
  [./ex_out]
    type = Exodus
    file_base = l2elemaux
    elemental_as_nodal = true
  [../]
[]

(modules/navier_stokes/test/tests/finite_element/ins/bcs/advection_bc/advection_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 10.0
  nx = 100
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    expression = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    expression = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    expression = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(test/tests/fvkernels/fv_coupled_var/coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 2
[]

[Variables]
  [u][]
  [v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
  [w]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  []
  [s][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [rxn]
    type = Reaction
    variable = u
    rate = 2.0
  []
  [diffs]
    type = Diffusion
    variable = s
  []
  [prod]
    type = CoupledForce
    variable = s
    v = u
  []
[]

[FVKernels]
  [diff]
    type = FVDiffusion
    variable = v
    coeff = coeff
  []
  [rxn]
    type = FVReaction
    variable = v
    rate = 2.0
  []
  [diffw]
    type = FVDiffusion
    variable = w
    coeff = coeff
  []
  [prod]
    type = FVCoupledForce
    variable = w
    v = 'v'
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right]
    type = FVDirichletBC
    variable = v
    boundary = right
    value = 1
  []
  [leftw]
    type = FVDirichletBC
    variable = w
    boundary = left
    value = 0
  []
  [rightw]
    type = FVDirichletBC
    variable = w
    boundary = right
    value = 1
  []
[]

[Materials]
  [diff]
    type = ADGenericFunctorMaterial
    prop_names = 'coeff'
    prop_values = '1'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [lefts]
    type = DirichletBC
    variable = s
    boundary = left
    value = 0
  []
  [rights]
    type = DirichletBC
    variable = s
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(test/tests/transfers/coord_transform/both-transformed/nearest-node/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
  [v_elem]
    order = CONSTANT
    family = MONOMIAL
  []
  [w][]
  [w_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [w]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w
  []
  [w_elem]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w_elem
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppNearestNodeTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [from_sub_elem]
    type = MultiAppNearestNodeTransfer
    from_multi_app = sub
    source_variable = v_elem
    variable = v_elem
    execute_on = 'timestep_begin'
  []
  [to_sub]
    type = MultiAppNearestNodeTransfer
    to_multi_app = sub
    source_variable = w
    variable = w
    execute_on = 'timestep_begin'
  []
  [to_sub_elem]
    type = MultiAppNearestNodeTransfer
    to_multi_app = sub
    source_variable = w_elem
    variable = w_elem
    execute_on = 'timestep_begin'
  []
[]

(modules/external_petsc_solver/test/tests/partition/moose_as_parent.i)

[Mesh]
  [gmg]
    type = DistributedRectilinearMeshGenerator
    dim = 2
    nx = 20
    ny = 21
    partition = square
  []
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v]
  [../]
  [pid]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [pid_aux]
    type = ProcessorIDAux
    variable = pid
    execute_on = 'INITIAL'
  []
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./cf]
    type = CoupledForce
    coef = 10000
    variable = u
    v=v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.2

  solve_type = 'PJFNK'

  fixed_point_max_its = 10
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [./picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[MultiApps]
  [./sub_app]
    type = TransientMultiApp
    input_files = 'petsc_transient_as_sub.i'
    app_type = ExternalPetscSolverApp
    library_path = '../../../../external_petsc_solver/lib'
  [../]
[]

[Transfers]
  [./fromsub]
    type = MultiAppShapeEvaluationTransfer
    from_multi_app = sub_app
    source_variable = u
    variable = v
  [../]
[]

(test/tests/transfers/coord_transform/rz-xyz/2d-rz.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
  coord_type = RZ
  beta_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_rz_cylinder.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100
  [Quadrature]
    # order = fifth
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(test/tests/executioners/nullspace/singular_contaminated.i)

[Mesh]
 type = GeneratedMesh
 dim = 1
 xmin = 0
 xmax = 10
 nx = 8
[]

[Problem]
  null_space_dimension = 1
  transpose_null_space_dimension = 1
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./eig]
    type = MassEigenKernel
    variable = u
    eigen_postprocessor = 1.0002920196258376e+01
    eigen = false
  [../]

  [./force]
    type = CoupledForce
    variable = u
    v = aux_v
  [../]
[]

[AuxVariables]
  [./aux_v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = eigen_mode
    [../]
  [../]
[]

[AuxKernels]
  [./set_source]
    type = FunctionAux
    variable = aux_v
    function = contaminated_second_harmonic
    execute_on = timestep_begin
  [../]
[]

[Functions]
  [./eigen_mode]
    type = ParsedFunction
    expression = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    symbol_names = 'L  mode'
    symbol_values = '10 1'
  [../]

  [./contaminated_second_harmonic]
    type = ParsedFunction
    expression = 'sqrt(2.0 / L) * sin(mode * pi  * x / L) + a * sqrt(2.0 / L) * sin(pi * x / L)'
    symbol_names = 'L  mode a'
    symbol_values = '10 2    1'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1'
    value = 0
  [../]
[]

[VectorPostprocessors]
  [./sample_solution]
    type = LineValueSampler
    variable = u
    start_point = '0 0 0'
    end_point = '10 0 0'
    sort_by = x
    num_points = 9
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./prec]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = SteadyWithNull
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_pc_side -snes_type -ksp_norm_type'
  petsc_options_value = 'hypre boomeramg  left ksponly preconditioned'
  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

(test/tests/outputs/variables/output_vars_nonexistent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD9
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = SECOND
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[AuxVariables]
  [./elemental]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./elemental_restricted]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./nodal]
    order = FIRST
    family = LAGRANGE
  [../]

  [./nodal_restricted]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[AuxKernels]
  [./elemental]
    type = ConstantAux
    variable = elemental
    value = 1
  [../]

  [./elemental_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 1
  [../]

  [./nodal]
    type = ConstantAux
    variable = elemental
    value = 2
  [../]

  [./nodal_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 2
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ImplicitODEx
    variable = x
    y = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ImplicitODEy
    variable = y
    x = x
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 9
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 5
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 2
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  dt = 0.01
  num_steps = 10
[]

[Outputs]
  file_base = out_nonexistent
  exodus = true
  show = 'u elemental nodal x foo1 foo2'
[]

(test/tests/multiapps/picard/steady_custom_picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
    execute_on = 'initial timestep_end'
  []
  [vnorm]
    type = ElementL2Norm
    variable = v
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = SteadyWithPicardCheck
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  disable_fixed_point_residual_norm_check = true
  pp_name = unorm
  pp_step_tol = 1e-4
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = steady_picard_sub.i
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/transfers/multiapp_high_order_variable_transfer/sub_L2_Lagrange.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[AuxVariables]
  [./power_density]
    family = L2_LAGRANGE
    order = FIRST
  [../]
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./heat_conduction]
     type = Diffusion
     variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  [../]
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '0 1 2 3'
    value = 450
  []
[]

[Executioner]
  type = Steady

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [./temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = '0'
    execute_on = 'initial timestep_end'
  [../]
  [./pwr_density]
    type = ElementIntegralVariablePostprocessor
    block = '0'
    variable = power_density
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(modules/functional_expansion_tools/test/tests/errors/multiapp_bad_function_series.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
  [./AnotherFunction]
    type = ConstantFunction
    value = -1
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = AnotherFunction
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/transfers/multiapp_postprocessor_interpolation_transfer/multilevel_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./subsub_average]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./force]
    type = CoupledForce
    variable = u
    v = subsub_average
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Postprocessors]
  [./sub_average]
    type = ElementAverageValue
    variable = u
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 0.3

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0 0.5 0.5 0'
    input_files = multilevel_subsub.i
  [../]
[]

[Transfers]
  [./subsub_average]
    type = MultiAppPostprocessorInterpolationTransfer
    from_multi_app = sub
    variable = subsub_average
    postprocessor = subsub_average
  [../]
[]

(test/tests/restart/restart_transient_from_transient/restart_trans_with_2subs_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
  xmax = 0.3
  ymax = 0.3
[]

[AuxVariables]
  [power_density]
  []
[]

[Variables]
  [temp]
  []
[]

[Kernels]
  [heat_conduction]
     type = Diffusion
     variable = temp
  []
  [heat_ie]
    type = TimeDerivative
    variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  []
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '1 3'
    value = 100
  []
  [bc2]
    type = NeumannBC
    variable = temp
    boundary = '0 2'
    value = 10.0
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  start_time = 0
  end_time = 3
  dt = 1.0

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = '0'
    execute_on = 'initial timestep_end'
  []
  [pwr_density]
    type = ElementIntegralVariablePostprocessor
    block = '0'
    variable = power_density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/time_steppers/fixed_point_iteration_adaptive_dt/main.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    execute_on = 'TIMESTEP_END'
  []
  [fp_its]
    type = NumFixedPointIterations
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 10
  fixed_point_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  verbose = true

  [TimeStepper]
    type = FixedPointIterationAdaptiveDT
    dt_initial = 0.1
    target_iterations = 6
    target_window = 0
    increase_factor = 2.0
    decrease_factor = 0.5
  []
[]

[Outputs]
  file_base = 'increase_dt'
  [csv]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = sub.i
    sub_cycling = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/misc/check_error/coupling_itself.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./coupled]
    type = CoupledForce
    variable = u
    v = u
  [../]
[]

[Executioner]
  type = Steady
[]

(tutorials/tutorial02_multiapps/step03_coupling/01_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [ut]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = ut
    coef = 100
  []
  [td]
    type = TimeDerivative
    variable = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  end_time = 2
  dt = 0.2

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [average_v]
    type = ElementAverageValue
    variable = v
  []
[]

(test/tests/kernels/hfem/3d-prism.i)

[Problem]
  use_hash_table_matrix_assembly = true
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    nz = 2
    dim = 3
    elem_type = PRISM6
  []
  build_all_side_lowerd_mesh = true
[]

[Variables]
  [u]
    order = THIRD
    family = MONOMIAL
    block = 0
  []
  [uhat]
    order = CONSTANT
    family = MONOMIAL
    block = 'BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4 BOUNDARY_SIDE_LOWERD_SUBDOMAIN_TRI3'
  []
  [lambda]
    order = CONSTANT
    family = MONOMIAL
    block = 'INTERNAL_SIDE_LOWERD_SUBDOMAIN_QUAD4 INTERNAL_SIDE_LOWERD_SUBDOMAIN_TRI3'
  []
  [lambdab]
    order = CONSTANT
    family = MONOMIAL
    block = 'BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4 BOUNDARY_SIDE_LOWERD_SUBDOMAIN_TRI3'
  []
[]

[AuxVariables]
  [v]
    order = CONSTANT
    family = MONOMIAL
    block = 0
    initial_condition = '1'
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = '1'
    block = 0
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
    coef = '1'
    block = 0
  []
  [reaction]
    type = Reaction
    variable = uhat
    rate = '1'
    block = 'BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4 BOUNDARY_SIDE_LOWERD_SUBDOMAIN_TRI3'
  []
  [uhat_coupled]
    type = CoupledForce
    variable = uhat
    block = 'BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4 BOUNDARY_SIDE_LOWERD_SUBDOMAIN_TRI3'
    v = lambdab
    coef = '1'
  []
[]

[DGKernels]
  [surface]
    type = HFEMDiffusion
    variable = u
    lowerd_variable = lambda
  []
[]

[BCs]
  [all]
    type = HFEMDirichletBC
    boundary = 'left right top bottom back front'
    variable = u
    lowerd_variable = lambdab
    uhat = uhat
  []
[]

[Postprocessors]
  [intu]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  []
  [lambdanorm]
    type = ElementL2Norm
    variable = lambda
    block = 'INTERNAL_SIDE_LOWERD_SUBDOMAIN_QUAD4 INTERNAL_SIDE_LOWERD_SUBDOMAIN_TRI3'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Outputs]
  [out]
    # we hide lambda because it may flip sign due to element
    # renumbering with distributed mesh
    type = Exodus
    hide = lambda
  []
[]

(test/tests/misc/multiple-nl-systems/ad-test.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Problem]
  nl_sys_names = 'u v'
[]

[Variables]
  [u]
    solver_sys = 'u'
  []
  [v]
    solver_sys = 'v'
  []
[]

[Kernels]
  [diff_u]
    type = ADDiffusion
    variable = u
  []
  [diff_v]
    type = ADDiffusion
    variable = v
  []
  [force]
    type = ADCoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_u]
    type = ADDirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = ADDirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = ADDirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = ADDirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Preconditioning]
  [u]
    nl_sys = 'u'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
  [v]
    nl_sys = 'v'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
[]

[Executioner]
  type = SteadySolve2
  solve_type = 'NEWTON'
  first_nl_sys_to_solve = 'u'
  second_nl_sys_to_solve = 'v'
[]

[Outputs]
  print_nonlinear_residuals = false
  print_linear_residuals = false
  exodus = true
[]

(test/tests/multiapps/picard_catch_up/parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = 'v'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    preset = false
    boundary = 'left'
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    preset = false
    boundary = 'right'
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu mumps'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub.i'
    max_catch_up_steps = 100
    max_failures = 100
    catch_up = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(python/peacock/tests/input_tab/InputTree/gold/fsp_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [v]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [conv_v]
    type = CoupledForce
    variable = v
    v = 'u'
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  inactive = 'right_v'
  [left_u]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = '2'
    value = 100
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = '1'
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = '2'
    value = 0
  []
[]

[Executioner]
  # This is setup automatically in MOOSE (SetupPBPAction.C)
  # petsc_options = '-snes_mf_operator'
  # petsc_options_iname = '-pc_type'
  # petsc_options_value =  'asm'
  type = Steady
[]

[Preconditioning]
  [FSP]
    # It is the starting point of splitting
    type = FSP
    topsplit = 'uv' # uv should match the following block name
    [uv]
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      # An approximate solution to the original system
      # | A_uu  A_uv | | u | _ |f_u|
      # |  0    A_vv | | v | - |f_v|
      # is obtained by solving the following subsystems
      # A_uu u = f_u and A_vv v = f_v
      # If splitting type is specified as schur, we may also want to set more options to
      # control how schur works using PETSc options
      # petsc_options_iname = '-pc_fieldsplit_schur_fact_type -pc_fieldsplit_schur_precondition'
      # petsc_options_value = 'full selfp'
      splitting = 'u v' # u and v are the names of subsolvers
      splitting_type = additive
    []
    [u]
      # PETSc options for this subsolver
      # A prefix will be applied, so just put the options for this subsolver only
      symbol_names = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      # PETSc options for this subsolver
      symbol_names = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    []
  []
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ne_coupled
  execute_on = 'timestep_end'
[]

(test/tests/multiapps/picard/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_2d_pde_filter.i)

vol_frac = 0.4
E0 = 1e5
Emin = 1e-4
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 20
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []

  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []

  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = ProjectionAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.05
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_abs_tol = 1e-10
  line_search = none
  dt = 1.0
  num_steps = 30
[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(test/tests/multiapps/picard_multilevel/fullsolve_multilevel/parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 50
  []
[]

[Kernels]
  [diffusion]
    type = Diffusion
    variable = u
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [dirichlet0]
    type = DirichletBC
    variable = u
    boundary = '3'
    value = 0
  []
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 100
  []
[]

[Postprocessors]
  [avg_u]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial linear'
  []
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial linear'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  fixed_point_rel_tol = 1E-3
  fixed_point_abs_tol = 1.0e-05
  fixed_point_max_its = 12
[]

[MultiApps]
  [level1-]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = sub_level1.i
    execute_on = 'timestep_end'

    # We need to disable restoration within the multiapp so that the previous
    # picard iterate is used as the starting solution within each iteration
    no_restore = false
  []
[]

[Transfers]
  [u_to_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = u
    variable = u
    to_multi_app = level1-
    execute_on = 'timestep_end'
  []
  [v_from_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = v
    variable = v
    from_multi_app = level1-
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/external_petsc_solver/test/tests/external_petsc_problem/moose_as_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./cf]
    type = CoupledForce
    coef = 10000
    variable = u
    v=v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.2

  solve_type = 'PJFNK'

  fixed_point_max_its = 10
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [./picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[MultiApps]
  [./sub_app]
    type = TransientMultiApp
    input_files = 'petsc_transient_as_sub.i'
    app_type = ExternalPetscSolverApp
    library_path = '../../../../external_petsc_solver/lib'
  [../]
[]

[Transfers]
  [./fromsub]
    type = MultiAppShapeEvaluationTransfer
    from_multi_app = sub_app
    source_variable = u
    variable = v
  [../]
[]

(modules/optimization/test/tests/executioners/steady_and_adjoint/multi_variable.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 10
    ny = 10
  []
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [v]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
  [v_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [uv]
    type = CoupledForce
    variable = u
    v = v
    coef = 10
  []
  [vu]
    type = CoupledForce
    variable = v
    v = u
    coef = 1
  []
  [src_u]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_u_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 0
  []
  [src_v_adjoint]
    type = BodyForce
    variable = v_adjoint
    value = 1
  []
[]

[BCs]
  [dirichlet_u]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 0
  []
  [dirichlet_v]
    type = DirichletBC
    variable = v
    boundary = 'top right'
    value = 0
  []
[]

[Executioner]
  type = SteadyAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint

  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_cylinder.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = ${fparse 2 + rpv_core_gap_size}
rpv_outer_radius = ${fparse 2.5 + rpv_core_gap_size}

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  [Quadrature]
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/combined/examples/optimization/2d_mbb_pde.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(test/tests/preconditioners/fsp/fsp_test_image.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 41
    ny = 41
  []
  [./image]
    input = gen
    type = ImageSubdomainGenerator
    file = kitten.png
    threshold = 100
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = 1
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    block = 1
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u left_v right_u'
  [./left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 100
  [../]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Problem]
  type = FEProblem
  material_coverage_check = false
  kernel_coverage_check = false
[]

[Executioner]
  # This is setup automatically in MOOSE (SetupPBPAction.C)
  # petsc_options = '-snes_mf_operator'
  # petsc_options_iname = '-pc_type'
  # petsc_options_value =  'asm'
  type = Steady
[]

[Preconditioning]
  [./FSP]
    # It is the starting point of splitting
    type = FSP
    topsplit = 'uv' # 'uv'
    [./uv]
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      # An approximate solution to the original system
      # | A_uu  A_uv | | u | _ |f_u|
      # |  0    A_vv | | v | - |f_v|
      # is obtained by solving the following subsystems
      # A_uu u = f_u and A_vv v = f_v
      # If splitting type is specified as schur, we may also want to set more options to
      # control how schur works using PETSc options
      # petsc_options_iname = '-pc_fieldsplit_schur_fact_type -pc_fieldsplit_schur_precondition'
      # petsc_options_value = 'full selfp'
      splitting = 'u v' # 'u' and 'v'
      splitting_type = additive
    [../]
    [./u]
      # PETSc options for this subsolver
      # A prefix will be applied, so just put the options for this subsolver only
      vars = u
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    [../]
    [./v]
      # PETSc options for this subsolver
      vars = v
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    [../]
  [../]
[]

[Outputs]
  file_base = kitten_out
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/errors/multiapp_missing_sub_object.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/multiapps/picard/picard_rel_tol_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  fixed_point_max_its = 10
  fixed_point_rel_tol = 1e-7
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/multiapps/picard/steady_picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
    execute_on = 'initial timestep_end'
  []
  [vnorm]
    type = ElementL2Norm
    variable = v
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady
  nl_abs_tol = 1e-14
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 10
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = steady_picard_sub.i
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/multiapps/relaxation/sub_relaxed_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 1
  []
  [inverse_v]
    initial_condition = 1
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = inverse_v
  []
[]

[AuxKernels]
  [invert_v]
    type = QuotientAux
    variable = inverse_v
    denominator = v
    numerator = 20.0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [Neumann_right]
    type = NeumannBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = sub_relaxed_sub.i
    transformed_variables = v
    relaxation_factor = 0.94
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/multiapps/picard_multilevel/multilevel_dt_rejection/parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[AuxKernels]
  [set_v]
    type = FunctionAux
    variable = v
    function = 't'
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [coupled_force]
    type = CoupledForce
    variable = u
    v = v
  []
  [time]
    type = TimeDerivative
    variable = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  num_steps = 2
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 1
  auto_advance = false
[]

[MultiApps]
  [sub1]
    type = TransientMultiApp
    positions = '0 0 0'
    input_files = picard_sub.i
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [u_to_v2]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub1
    source_variable = u
    variable = v2
  []
  [time_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = time
    to_postprocessor = parent_time
    to_multi_app = sub1
  []
  [dt_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = dt
    to_postprocessor = parent_dt
    to_multi_app = sub1
  []
[]

[Postprocessors]
  [time]
    type = TimePostprocessor
    execute_on = 'timestep_end'
  []
  [dt]
    type = TimestepSize
    execute_on = 'timestep_end'
  []
[]

(test/tests/multiapps/steffensen/steady_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Postprocessors]
  [vnorm]
    type = ElementL2Norm
    variable = v
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'steffensen'
[]

[Outputs]
  csv = true
  exodus = false
[]

(test/tests/multiapps/picard_sub_cycling/fully_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_u]
    type = CoupledForce
    variable = u
    v = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./td_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

(test/tests/fvkernels/block-restriction/fv-and-fe-block-restriction.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 80
    xmax = 4
  []
  [subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '2.0 0 0'
    block_id = 1
    top_right = '4.0 1.0 0'
  []
  [left_right]
    input = subdomain1
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'left_right'
  []
  [right_left]
    input = left_right
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'right_left'
  []
[]

[Variables]
  [left_fv]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1
    block = 0
  []
  [left_fe]
    initial_condition = 1
    block = 0
  []
  [right_fv]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1
    block = 1
  []
  [right_fe]
    initial_condition = 1
    block = 1
  []
[]

[FVKernels]
  active = 'bad_left_diff left_coupled bad_right_diff right_coupled'
  [bad_left_diff]
    type = FVDiffusion
    variable = left_fv
    coeff = fv_prop
    block = 0
    coeff_interp_method = average
  []
  [good_left_diff]
    type = FVDiffusion
    variable = left_fv
    coeff = left_fv_prop
    block = 0
    coeff_interp_method = average
  []
  [left_coupled]
    type = FVCoupledForce
    v = left_fv
    variable = left_fv
    block = 0
  []
  [bad_right_diff]
    type = FVDiffusion
    variable = right_fv
    coeff = fv_prop
    block = 1
    coeff_interp_method = average
  []
  [good_right_diff]
    type = FVDiffusion
    variable = right_fv
    coeff = right_fv_prop
    block = 1
    coeff_interp_method = average
  []
  [right_coupled]
    type = FVCoupledForce
    v = right_fv
    variable = right_fv
    block = 1
  []
[]

[Kernels]
  [left_diff]
    type = ADFunctorMatDiffusion
    variable = left_fe
    diffusivity = fe_prop
  []
  [left_coupled]
    type = CoupledForce
    v = left_fv
    variable = left_fe
  []
  [right_diff]
    type = ADFunctorMatDiffusion
    variable = right_fe
    diffusivity = fe_prop
  []
  [right_coupled]
    type = CoupledForce
    v = right_fv
    variable = right_fe
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = left_fv
    boundary = left
    value = 0
  []
  [left_right]
    type = FVDirichletBC
    variable = left_fv
    boundary = left_right
    value = 1
  []
  [right_left]
    type = FVDirichletBC
    variable = right_fv
    boundary = right_left
    value = 0
  []
  [right]
    type = FVDirichletBC
    variable = right_fv
    boundary = right
    value = 1
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = left_fe
    boundary = left
    value = 0
  []
  [left_right]
    type = DirichletBC
    variable = left_fe
    boundary = left_right
    value = 1
  []
  [right_left]
    type = DirichletBC
    variable = right_fe
    boundary = right_left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = right_fe
    boundary = right
    value = 1
  []
[]

[Materials]
  active = 'fe_mat_left bad_fv_mat_left fe_mat_right bad_fv_mat_right'
  [fe_mat_left]
    type = FEFVCouplingMaterial
    fe_var = left_fe
    block = 0
  []
  [bad_fv_mat_left]
    type = FEFVCouplingMaterial
    fv_var = left_fv
    block = 0
  []
  [good_fv_mat_left]
    type = FEFVCouplingMaterial
    fv_var = left_fv
    fv_prop_name = 'left_fv_prop'
    block = 0
  []
  [fe_mat_right]
    type = FEFVCouplingMaterial
    fe_var = right_fe
    block = 1
  []
  [bad_fv_mat_right]
    type = FEFVCouplingMaterial
    fv_var = right_fv
    block = 1
  []
  [good_fv_mat_right]
    type = FEFVCouplingMaterial
    fv_var = right_fv
    fv_prop_name = 'right_fv_prop'
    block = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  line_search = 'none'
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/helmholtz_multimat_nostrip.i)

vol_frac = 0.35

power = 1.1

Emin = 1.0e-6
Ess = 0.475 # ss
Et = 1.0 # w

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [RenameBottom]
    type = RenameBoundaryGenerator
    input = Bottom
    old_boundary = 'top bottom right left'
    new_boundary = 'top_bottom bottom_bottom right_bottom left_bottom'
  []
  [Top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [MoveTop]
    type = TransformGenerator
    input = Top
    transform = TRANSLATE
    vector_value = '0 15 0'
  []
  [RenameTop]
    type = RenameBoundaryGenerator
    input = MoveTop
    old_boundary = 'top bottom right left'
    new_boundary = 'top_top bottom_top right_top left_top'
  []
  [bottom_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameBottom
    combinatorial_geometry = 'y <= 15'
    block_id = 1
  []
  [top_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameTop
    combinatorial_geometry = 'y > 15'
    block_id = 3
  []
  [stitch]
    type = StitchedMeshGenerator
    inputs = 'bottom_gen top_gen'
    stitch_boundaries_pairs = 'top_bottom bottom_top'
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = stitch
    new_boundary = left_load
    coord = '37.5 30 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 30 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 4.0
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'bottom_bottom right_bottom left_bottom top_top right_top left_top'
    coefficient = 10
  []
[]

[NodalKernels]
  [left_down]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
  [right_down]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor_one]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_one
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '1'
  []
  [elasticity_tensor_three]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_three
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '3'
  []
  # One: Tungsten
  [E_phys_one]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Et}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_one
    block = '1'
    outputs = 'exodus'
  []
  # Three: SS316
  [E_phys_three]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Ess}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_three
    block = '3'
    outputs = 'exodus'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc_one]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_one
    block = '1'
  []
  [dc_three]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_three
    block = '3'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update_one]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '1'
  []
  [update_three]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '3'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 90
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    block = '1 3'
  []
  [objective_one]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '1'
  []
  [objective_three]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '3'
  []
[]

(test/tests/multiapps/relaxation/bad_relax_factor_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 1
  []
  [inverse_v]
    initial_condition = 1
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = inverse_v
  []
[]

[AuxKernels]
  [invert_v]
    type = QuotientAux
    variable = inverse_v
    denominator = v
    numerator = 20.0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [Neumann_right]
    type = NeumannBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
  relaxation_factor = 2.0
  transformed_variables = u
[]

[Outputs]
  exodus = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = picard_relaxed_sub.i
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(modules/functional_expansion_tools/examples/3D_volumetric_cylindrical/main.i)

# Basic example coupling a master and sub app in a 3D cylindrical mesh from an input file
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable, the recommended approach.
#
# Note: this problem is not light, and may take a few minutes to solve.
[Mesh]
  type = FileMesh
  file = cyl-tet.e
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom outside'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = CylindricalDuo
    orders = '5   3' # Axial first, then (r, t) FX
    physical_bounds = '-2.5 2.5   0 0 1' # z_min z_max   x_center y_center radius
    z = Legendre # Axial in z
    disc = Zernike # (r, t) default to unit disc in x-y plane
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/transfers/coord_transform/single-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 1
  xmax = 3
  nx = 20
  ny = 10
[]

[Variables]
  [u][]
  [v][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/executioners/eigen_executioners/ne_coupled.i)

[Mesh]
 type = GeneratedMesh
 dim = 2
 xmin = 0
 xmax = 10
 ymin = 0
 ymax = 10
 elem_type = QUAD4
 nx = 8
 ny = 8

 uniform_refine = 0
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = MassEigenKernel
    variable = u
  [../]

  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm

# this coefficient will affect the eigenvalue.
    normal_factor = 10


    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = NonlinearEigen

  bx_norm = 'unorm'

  free_power_iterations = 2
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-50
  k0 = 1.0
  output_after_power_iterations = false

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
[]

[Postprocessors]
  active = 'unorm udiff'

  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    # execute on residual is important for nonlinear eigen solver!
    execute_on = linear
  [../]

  [./udiff]
    type = ElementL2Diff
    variable = u
    outputs = console
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = ne_coupled
  exodus = true
[]

(test/tests/transfers/coord_transform/both-transformed/pp_interpolation/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = new_val_x
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = CentroidMultiApp
    app_type = MooseTestApp
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [send]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    to_multi_app = sub
    source_variable = x_nodal
    postprocessor = rec_x
  []
  [send_elem]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    to_multi_app = sub
    source_variable = y_elem
    postprocessor = rec_y
  []

  [get_back]
    type = MultiAppPostprocessorInterpolationTransfer
    from_multi_app = sub
    variable = new_val_x
    postprocessor = rec_x
  []
  [get_back_elem]
    type = MultiAppPostprocessorInterpolationTransfer
    from_multi_app = sub
    variable = new_val_y_elem
    postprocessor = rec_y
  []
[]

[AuxVariables]
  [x_nodal]
    [InitialCondition]
      type = FunctionIC
      function = 'x'
    []
  []
  [y_elem]
    order = CONSTANT
    family = MONOMIAL
    [InitialCondition]
      type = FunctionIC
      function = 'y'
    []
  []
  [new_val_x]
  []
  [new_val_y_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

(tutorials/shield_multiphysics/inputs/step11_multiapps/step11_local.i)

[Mesh]
  # We make a 3D sphere, but really this could be done in 1D
  [sphere]
    type = SphereMeshGenerator
    radius = 10
    nr = 3
    n_smooth = 10
  []
  # Dimensions of each layer are not realistic
  [HDPE_inner]
    type = ParsedSubdomainMeshGenerator
    input = 'sphere'
    combinatorial_geometry = 'x*x + y*y + z*z < 2*2'
    block_id = 1
  []
  [boron_inner]
    type = ParsedSubdomainMeshGenerator
    input = 'HDPE_inner'
    combinatorial_geometry = '(x*x + y*y + z*z > 2*2) & (x*x + y*y + z*z < 3*3)'
    block_id = 2
  []
  [HDPE_mid]
    type = ParsedSubdomainMeshGenerator
    input = 'boron_inner'
    combinatorial_geometry = '(x*x + y*y + z*z > 3*3) & (x*x + y*y + z*z < 6*6)'
    block_id = 3
  []
  [boron_mid]
    type = ParsedSubdomainMeshGenerator
    input = 'HDPE_mid'
    combinatorial_geometry = '(x*x + y*y + z*z > 6*6) & (x*x + y*y + z*z < 7*7)'
    block_id = 4
  []
  [HDPE_outer]
    type = ParsedSubdomainMeshGenerator
    input = 'boron_mid'
    combinatorial_geometry = 'x*x + y*y + z*z > 7*7'
    block_id = 5
  []
  [rename]
    type = RenameBlockGenerator
    input = 'HDPE_outer'
    old_block = '1 2 3 4 5'
    new_block = 'HDPE_inner boron_inner HDPE_mid boron_mid HDPE_outer'
  []
  [rename_boundary]
    type = RenameBoundaryGenerator
    input = 'rename'
    old_boundary = '0'
    new_boundary = 'outer'
  []

  # length_unit = 0.01
  [scale]
    type = TransformGenerator
    input = rename_boundary
    transform = SCALE
    vector_value = '0.01 0.01 0.01'
  []
[]

[Variables]
  [T]
    initial_condition = 300
  []
[]

# Solve heat equation, with a source from boron absorption
[Kernels]
  [conduction]
    type = HeatConduction
    variable = T
  []
  [source]
    type = CoupledForce
    variable = T
    block = 'boron_inner boron_mid'
    v = flux
    # 2 is our arbitrary value for the group cross section
    coef = 2
  []
[]

[BCs]
  [outer]
    type = PostprocessorDirichletBC
    boundary = 'outer'
    variable = 'T'
    postprocessor = 'T_boundary'
  []
[]

[AuxVariables]
  # Received from the main solve
  [flux]
    initial_condition = 1e5
  []
[]

[Materials]
  [hdpe]
    type = HeatConductionMaterial
    block = 'HDPE_inner HDPE_mid HDPE_outer'
    # arbitrary
    thermal_conductivity = 10
  []
  [boron]
    type = HeatConductionMaterial
    block = 'boron_inner boron_mid'
    # arbitrary
    thermal_conductivity = 7
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Postprocessors]
  # Used for boundary condition, received from the main solve
  [T_boundary]
    type = Receiver
    default = 320
  []

  # Compute those then send to the main app
  [T_hdpe_out]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_outer'
  []
  [T_boron_mid]
    type = ElementAverageValue
    variable = 'T'
    block = 'boron_mid'
  []
  [T_hdpe_mid]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_mid'
  []
  [T_boron_inner]
    type = ElementAverageValue
    variable = 'T'
    block = 'boron_inner'
  []
  [T_hdpe_inner]
    type = ElementAverageValue
    variable = 'T'
    block = 'HDPE_inner'
  []
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere_mortar_error.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(test/tests/multiapps/picard/fully_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_u]
    type = CoupledForce
    variable = u
    v = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/picard/picard_adaptive_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10

  [./TimeStepper]
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 6
    dt = 0.1
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/secant/steady_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Postprocessors]
  [vnorm]
    type = ElementL2Norm
    variable = v
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'secant'
[]

[Outputs]
  csv = true
  exodus = false
[]

(test/tests/multiapps/steffensen/transient_main.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  parallel_type = replicated
  uniform_refine = 1
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [coupling_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
  [unorm]
    type = ElementL2Norm
    variable = u
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'steffensen'
  fixed_point_max_its = 30
  transformed_variables = 'u'
[]

[Outputs]
  csv = true
  exodus = false
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'transient_sub.i'
    clone_parent_mesh = true
    execute_on = 'timestep_begin'
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
    execute_on = 'timestep_begin'
  []
[]

(test/tests/restart/restart_transient_from_steady/restart_trans_with_sub_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[AuxVariables]
  [./power_density]
  [../]
[]

[Variables]
  [./temp]
#    initial_condition = 1000000
  [../]
[]

[Kernels]
  [./heat_conduction]
     type = Diffusion
     variable = temp
  [../]
  [./heat_ie]
    type = TimeDerivative
    variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  [../]
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '0 1 2 3'
    value = 450
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  start_time = 0
  end_time = 3
  dt = 1.0

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [./temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = '0'
    execute_on = 'initial timestep_end'
  [../]
  [./pwr_density]
    type = ElementIntegralVariablePostprocessor
    block = '0'
    variable = power_density
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/multiapps/picard/picard_custom_postprocessor.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm_begin]
    type = ElementL2Norm
    variable = u
    execute_on = 'initial timestep_begin'
    outputs = none
  []
  [unorm]
    type = ElementL2Norm
    variable = u
    execute_on = 'initial timestep_end'
  []
  [unorm_err]
    type = RelativeDifferencePostprocessor
    value1 = unorm
    value2 = unorm_begin
    outputs = none
  []
  [vnorm]
    type = ElementL2Norm
    variable = v
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  disable_fixed_point_residual_norm_check = true
  custom_pp = unorm_err
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = steady_picard_sub.i
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/transfers/coord_transform/both-transformed/interpolation/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
  [v_elem]
    order = CONSTANT
    family = MONOMIAL
  []
  [w][]
  [w_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [w]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w
  []
  [w_elem]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w_elem
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [from_sub_elem]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = sub
    source_variable = v_elem
    variable = v_elem
    execute_on = 'timestep_begin'
  []
  [to_sub]
    type = MultiAppGeometricInterpolationTransfer
    to_multi_app = sub
    source_variable = w
    variable = w
    execute_on = 'timestep_begin'
  []
  [to_sub_elem]
    type = MultiAppGeometricInterpolationTransfer
    to_multi_app = sub
    source_variable = w_elem
    variable = w_elem
    execute_on = 'timestep_begin'
  []
[]

(test/tests/multiapps/picard/pseudo_transient_picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./time]
    type = CoefTimeDerivative
    variable = v
    Coefficient = 0.1
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Postprocessors]
  [./vnorm]
    type = ElementL2Norm
    variable = v
  [../]
[]

[Executioner]
  type = Transient
  end_time = 10
  nl_abs_tol = 1e-12
  steady_state_detection = true
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/preconditioners/fdp/fdp_test.i)

[Mesh]
  type = GeneratedMesh
  nx = 2
  ny = 2
  dim = 2
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Preconditioning]
  [./FDP]
    type = FDP
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = false
[]

[ICs]
  [./u]
    variable = u
    type = RandomIC
    min = 0.1
    max = 0.9
  [../]
  [./v]
    variable = v
    type = RandomIC
    min = 0.1
    max = 0.9
  [../]
[]

(test/tests/problems/eigen_problem/jfnk_mo/ne_coupled_mo.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = u
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNKMO
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-14
[]

[Problem]
  type = EigenProblem
[]

[Postprocessors]
  [uint]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = 'initial linear nonlinear'
    outputs = 'console'
  []
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ne_coupled
  execute_on = 'timestep_end'
[]

(test/tests/multiapps/picard_multilevel/fullsolve_multilevel/sub_level2.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [w]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [time_derivative]
    type = TimeDerivative
    variable = w
  []
  [diffusion]
    type = Diffusion
    variable = w
  []
  [source]
    type = CoupledForce
    variable = w
    v = v
  []
[]

[BCs]
  [dirichlet]
    type = DirichletBC
    variable = w
    boundary = '0'
    value = 0
  []
[]

[Postprocessors]
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial linear'
  []
  [avg_w]
    type = ElementAverageValue
    variable = w
    execute_on = 'initial linear'
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  end_time = 0.1
  dt = 0.02
  # steady_state_detection = true
[]


[Outputs]
  exodus = true
  # print_linear_residuals = false
[]

(tutorials/tutorial02_multiapps/step03_coupling/02_sub_picard.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [ut]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = ut
    coef = 100
  []
  [td]
    type = TimeDerivative
    variable = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  end_time = 2
  dt = 0.2

  nl_abs_tol = 1e-10

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [average_v]
    type = ElementAverageValue
    variable = v
  []
[]

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/parent_ss.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 8
    ny = 8
    xmin = -82.627
    xmax = 82.627
    ymin = -82.627
    ymax = 82.627
    dim = 2
  []
[]

[Variables]
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = L2_LAGRANGE
    initial_condition = 350
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = 'power'
  [../]
[]

[BCs]
  [./all]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top left right'
    value = 300
  [../]
[]

[Materials]
  [./heat_material]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1000
    thermal_conductivity = 500
  [../]
  [./density]
    type = Density
    density = 2000
  [../]
[]

[Postprocessors]
  [./avg_temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]
  [./avg_power]
    type = ElementAverageValue
    variable = power
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-05
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-9

  l_max_its = 50
  nl_max_its = 25
[]

[Outputs]
  perf_graph = true
  color = true
  exodus = true

  [checkpoint]
    type = Checkpoint
    num_files = 2
    additional_execute_on = 'FINAL' # seems to be a necessary to avoid a Checkpoint bug
  []
[]

[MultiApps]
  [./bison]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = 'sub_ss.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_bison_mechanics]
    type = MultiAppProjectionTransfer
    to_multi_app = bison
    variable = temp
    source_variable = temp
    execute_on = 'timestep_end'
  [../]
[]

(python/peacock/tests/input_tab/InputFileEditor/gold/fsp_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [v]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [conv_v]
    type = CoupledForce
    variable = v
    v = 'u'
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  inactive = 'right_v'
  [left_u]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = '2'
    value = 100
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = '1'
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = '2'
    value = 0
  []
[]

[Executioner]
  # This is setup automatically in MOOSE (SetupPBPAction.C)
  # petsc_options = '-snes_mf_operator'
  # petsc_options_iname = '-pc_type'
  # petsc_options_value =  'asm'
  type = Steady
[]

[Preconditioning]
  [FSP]
    # It is the starting point of splitting
    type = FSP
    topsplit = 'uv' # uv should match the following block name
    [uv]
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      # An approximate solution to the original system
      # | A_uu  A_uv | | u | _ |f_u|
      # |  0    A_vv | | v | - |f_v|
      # is obtained by solving the following subsystems
      # A_uu u = f_u and A_vv v = f_v
      # If splitting type is specified as schur, we may also want to set more options to
      # control how schur works using PETSc options
      # petsc_options_iname = '-pc_fieldsplit_schur_fact_type -pc_fieldsplit_schur_precondition'
      # petsc_options_value = 'full selfp'
      splitting = 'u v' # u and v are the names of subsolvers
      splitting_type = additive
    []
    [u]
      # PETSc options for this subsolver
      # A prefix will be applied, so just put the options for this subsolver only
      vars = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      # PETSc options for this subsolver
      vars = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    []
  []
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/mortar/continuity-2d-conforming/conforming_two_var.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Functions]
  [./exact_sln]
    type = ParsedFunction
    expression= y
  [../]
  [./ffn]
    type = ParsedFunction
    expression= 0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm_u]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm_v]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]

[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./ffn]
    type = BodyForce
    variable = u
    function = ffn
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./coupled_u]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[Problem]
  extra_tag_vectors = 'ref'
[]

[Constraints]
  [./ced_u]
    type = EqualValueConstraint
    variable = lm_u
    secondary_variable = u
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    absolute_value_vector_tags = 'ref'
  [../]
  [./ced_v]
    type = EqualValueConstraint
    variable = lm_v
    secondary_variable = v
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
    absolute_value_vector_tags = 'ref'
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '1 2 3 4'
    function = exact_sln
  [../]
  [./allv]
    type = DirichletBC
    variable = v
    boundary = '1 2 3 4'
    value = 0
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = exact_sln
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
  [./l2_v]
    type = ElementL2Norm
    variable = v
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard_subT.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]
[]

[Kernels]
  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[BCs]
  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
  fixed_point_max_its = 20
  fixed_point_rel_tol = 1e-6
[]

[MultiApps]
  [./sub]
    type = FullSolveMultiApp
    keep_solution_during_restore = true
    input_files = ne_coupled_picard_subT_sub.i
    execute_on = timestep_end
  [../]
[]

[Transfers]
  [./T_to_sub]
    type = MultiAppShapeEvaluationTransfer
    to_multi_app = sub
    source_variable = T
    variable = T
    execute_on = timestep_end
  [../]
  [./power_from_sub]
    type = MultiAppShapeEvaluationTransfer
    from_multi_app = sub
    source_variable = power
    variable = power
    execute_on = timestep_end
  [../]
[]

[Outputs]
  csv = true
  exodus =true
  execute_on = 'timestep_end'
[]

(test/tests/misc/check_error/coupling_nonexistent_field.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./coupled]
    type = CoupledForce
    variable = u
    # 'a' does not exist -> error
    v = a
  [../]
[]

[Executioner]
  type = Steady
[]

(test/tests/preconditioners/fsp/penalty-fsp-test.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    dim = 2
  []
  second_order = true
[]

[Variables]
  [u]
    order = SECOND
  []
  [v]
    order = SECOND
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [conv_v]
    type = CoupledForce
    variable = v
    v = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  [left_u]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = u
    boundary = 3
    value = 0
  []
  [right_u]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = u
    boundary = 1
    value = 100
  []
  [left_v]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = v
    boundary = 3
    value = 0
  []
  [right_v]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = v
    boundary = 1
    value = 0
  []
[]

[Executioner]
  type = Steady
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'uv'
    [uv]
      splitting = 'u v'
      splitting_type = additive
    []
    [u]
      vars = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      vars = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     lu  preonly'
    []
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/multiple-nl-systems/problem.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Problem]
  nl_sys_names = 'u v'
[]

[Variables]
  [u]
    solver_sys = 'u'
  []
  [v]
    solver_sys = 'v'
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Preconditioning]
  [u]
    nl_sys = 'u'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
  [v]
    nl_sys = 'v'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  []
[]

[Executioner]
  type = SteadySolve2
  solve_type = 'NEWTON'
  first_nl_sys_to_solve = 'u'
  second_nl_sys_to_solve = 'v'
[]

(test/tests/transfers/coord_transform/both-transformed/user_object/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  # Quarter turn around Z axis
  alpha_rotation = -90
  # Flips around Y axis
  # beta_rotation = -180
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [from_sub_app_var][]
  [from_sub_app_var_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = from_sub_app_var
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[UserObjects]
  [main_uo]
    type = LayeredAverage
    direction = x
    num_layers = 5
    variable = u
  []
[]

[MultiApps]
  [sub_app]
    # Shift is offset by sub-app mesh + rotations
    # positions = '1 0 0.0'
    type = FullSolveMultiApp
    input_files = sub-app.i
    app_type = MooseTestApp
    bounding_box_padding = '0.25 0.25 0'
    bounding_box_inflation = 0
    use_displaced_mesh = true
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [layered_transfer_to_sub_app]
    type = MultiAppUserObjectTransfer
    user_object = main_uo
    variable = sub_app_var
    to_multi_app = sub_app
    displaced_target_mesh = true
  []
  [layered_transfer_to_sub_app_elem]
    type = MultiAppUserObjectTransfer
    user_object = main_uo
    variable = sub_app_var_elem
    to_multi_app = sub_app
    displaced_target_mesh = true
  []

  [layered_transfer_from_sub_app]
    type = MultiAppUserObjectTransfer
    user_object = sub_app_uo
    variable = from_sub_app_var
    from_multi_app = sub_app
    # displaced_source_mesh = true
  []
  [layered_transfer_from_sub_app_elem]
    type = MultiAppUserObjectTransfer
    user_object = sub_app_uo
    variable = from_sub_app_var_elem
    from_multi_app = sub_app
    # displaced_source_mesh = true
  []
[]

(test/tests/restart/restart_transient_from_steady/steady_with_2subs_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
  xmax = 0.3
  ymax = 0.3
[]

[AuxVariables]
  [power_density]
  []
[]

[Variables]
  [temp]
  []
[]

[Kernels]
  [heat_conduction]
     type = Diffusion
     variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  []
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '1 3'
    value = 100
  []
  [bc2]
    type = NeumannBC
    variable = temp
    boundary = '0 2'
    value = 10.0
  []
[]

[Executioner]
  type = Steady

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [pwr_density]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/transfers/coord_transform/transform-main-main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 1
  xmax = 3
  nx = 20
  ny = 10
  length_unit = '5*m'
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 5 0'
    input_files = 'transform-main-sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppNearestNodeTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
[]

(test/tests/multiapps/picard/pseudo_transient_picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
    execute_on = 'initial timestep_end'
  []
  [vnorm]
    type = ElementL2Norm
    variable = v
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  fixed_point_rel_tol = 1e-6
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    input_files = pseudo_transient_picard_sub.i
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/misc/check_error/multi_precond_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Preconditioning]
  active = 'PBP FDP'

  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'LU LU'
    off_diag_row    = 'v'
    off_diag_column = 'u'
  [../]

  [./FDP]
    type = FDP
    off_diag_row    = 'v'
    off_diag_column = 'u'
  [../]
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff_u conv_v diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]
[]

[Executioner]
  type = Steady

  l_max_its = 1
  nl_max_its = 1


  solve_type = JFNK

[]

[Outputs]
  file_base = pbp_out
[]

(test/tests/preconditioners/smp/smp_single_adapt_test.i)

#
# This is not very strong test since the problem being solved is linear, so the difference between
# full Jacobian and block diagonal preconditioner is not that big
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 5
  ny = 5
  elem_type = QUAD4
[]

[Functions]
  [./exact_v]
    type = ParsedFunction
    expression = sin(pi*x)*sin(pi*y)
  [../]
  [./force_fn_v]
    type = ParsedFunction
    expression = 2*pi*pi*sin(pi*x)*sin(pi*y)
  [../]
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    off_diag_row    = 'u'
    off_diag_column = 'v'
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./ffn_v]
    type = BodyForce
    variable = v
    function = force_fn_v
  [../]
[]

[BCs]
  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]

  [./all_v]
    type = FunctionDirichletBC
    variable = v
    boundary = '0 1 2 3'
    function = exact_v
  [../]
[]

[Executioner]
  type = Steady


  solve_type = 'PJFNK'

  [./Adaptivity]
    steps = 3
    coarsen_fraction = 0.1
    refine_fraction = 0.2
    max_h_level = 5
  [../]
[]

[Outputs]
  exodus = true
  print_mesh_changed_info = true
[]

(test/tests/convergence/reference_residual_convergence/abs_ref_acceptable.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]

[Convergence]
  [conv]
    type = ReferenceResidualConvergence
    reference_vector = 'absref'
    acceptable_iterations = 1
    acceptable_multiplier = 1e6
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 3
  nl_rel_tol = 1e-06
  nonlinear_convergence = conv
  verbose = true
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/bcs/advection_bc/2d_advection_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10.0
  ymax = 10
  nx = 10
  ny = 10
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    expression = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    expression = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    expression = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/functional_expansion_tools/test/tests/errors/multiapp_missing_local_object.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/multiapps/steffensen/transient_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [time]
    type = CoefTimeDerivative
    variable = v
    Coefficient = 0.1
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Postprocessors]
  [vnorm]
    type = ElementL2Norm
    variable = v
  []
[]

[Executioner]
  type = Transient
  end_time = 10
  nl_abs_tol = 1e-12
  steady_state_detection = true
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  fixed_point_algorithm = 'steffensen'
[]

[Outputs]
  [csv]
    type = CSV
    start_step = 6
  []
  exodus = false
[]

(test/tests/multiapps/relaxation/picard_relaxed_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 2
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/standard_use/volume_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = volume_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_deficient_b.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    eigen = true
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  [./rhs]
    type = CoupledForce
    variable = u
    v = v
    extra_vector_tags = 'eigen'
  [../]
  [./src_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./homogeneous_u]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./homogeneous_v]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigenBC_u]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
  [./eigenBC_v]
    type = EigenDirichletBC
    variable = v
    boundary = '0 1 2 3'
  [../]

[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ne_deficient_b
  execute_on = 'timestep_end'
[]

(test/tests/executioners/nullspace/singular.i)

[Mesh]
 type = GeneratedMesh
 dim = 1
 xmin = 0
 xmax = 10
 nx = 8
[]

[Problem]
  null_space_dimension = 1
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./eig]
    type = MassEigenKernel
    variable = u
    eigen_postprocessor = 1.0002920196258376e+01
    eigen = false
  [../]

  [./force]
    type = CoupledForce
    variable = u
    v = aux_v
  [../]
[]

[AuxVariables]
  [./aux_v]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = eigen_mode
    [../]
  [../]
[]

[AuxKernels]
  [./set_source]
    type = FunctionAux
    variable = aux_v
    function = second_harmonic
    execute_on = timestep_begin
  [../]
[]

[Functions]
  [./eigen_mode]
    type = ParsedFunction
    expression = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    symbol_names = 'L  mode'
    symbol_values = '10 1'
  [../]

  [./second_harmonic]
    type = ParsedFunction
    expression = 'sqrt(2.0 / L) * sin(mode * pi  * x / L)'
    symbol_names = 'L  mode'
    symbol_values = '10 2'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1'
    value = 0
  [../]
[]

[VectorPostprocessors]
  [./sample_solution]
    type = LineValueSampler
    variable = u
    start_point = '0 0 0'
    end_point = '10 0 0'
    sort_by = x
    num_points = 9
    execute_on = timestep_end
  [../]
[]

[Preconditioning]
  [./prec]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = SteadyWithNull
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_pc_side -snes_type -ksp_norm_type'
  petsc_options_value = 'hypre boomeramg  left ksponly preconditioned'
  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

(test/tests/outputs/console/multiapp/picard_parent_both.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v_begin]
  []
  [v_end]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u_begin]
    type = CoupledForce
    variable = u
    v = v_begin
  []
  [force_u_end]
    type = CoupledForce
    variable = u
    v = v_end
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[MultiApps]
  [sub_begin]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
  []
  [sub_end]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '1 1 1'
    input_files = picard_sub.i
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [v_from_sub_begin]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub_begin
    source_variable = v
    variable = v_begin
  []
  [u_to_sub_begin]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub_begin
    source_variable = u
    variable = u
  []
  [v_from_sub_end]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub_end
    source_variable = v
    variable = v_end
  []
  [u_to_sub_end]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub_end
    source_variable = u
    variable = u
  []
[]

(modules/functional_expansion_tools/examples/1D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 1D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_3D_mortar.i)

outer_htc = 10 # W/m^2/K
outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 6
    nz = 6
    xmin = -1
    xmax = -0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'left_bottom left_back left_right left_front left_left left_top'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []

  [right_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 8
    nz = 8
    xmin = 0.5
    xmax = 1
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3 4 5'
    # new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
    new_boundary = '100 101 102 103 104 105'
  []
  [right_block_sidesets_rename]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '100 101 102 103 104 105'
    new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sidesets_rename
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []

  [left_lower]
    type = LowerDBlockFromSidesetGenerator
    input = combined_mesh
    sidesets = 'left_right'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [right_lower]
    type = LowerDBlockFromSidesetGenerator
    input = left_lower
    sidesets = 'right_left'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 1
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = '1'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 'left_right'
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 'left_right'
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 'right_left'
    primary_subdomain = 'primary_lower'
    secondary_boundary = 'left_right'
    secondary_subdomain = 'secondary_lower'
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = PLATE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = 'right_right' # outer RPV
    coefficient = ${outer_htc}
    T_infinity = ${outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-8
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 'left_right'
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 'right_left'
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'left_right'
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'right_left'
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 1
  []
  [convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = 'right_right' # outer RVP
    T_fluid = ${outer_Tinf}
    htc = ${outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(convective_out - ptot) / ptot'
    pp_names = 'convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'left_right right_left'
    variable = temp
  []
[]

(test/tests/transfers/coord_transform/both-transformed/mesh-function/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
  [v_elem]
    order = CONSTANT
    family = MONOMIAL
  []
  [w][]
  [w_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [w]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w
  []
  [w_elem]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w_elem
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppShapeEvaluationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
    error_on_miss = true
    # extend the bounding box slightly since a transformed node
    # may miss the bounding box by machine precision
    bbox_factor = 1.1
  []
  [from_sub_elem]
    type = MultiAppShapeEvaluationTransfer
    from_multi_app = sub
    source_variable = v_elem
    variable = v_elem
    execute_on = 'timestep_begin'
    error_on_miss = true
  []
  [to_sub]
    type = MultiAppShapeEvaluationTransfer
    to_multi_app = sub
    source_variable = w
    variable = w
    execute_on = 'timestep_begin'
    error_on_miss = true
    # extend the bounding box slightly since a transformed node
    # may miss the bounding box by machine precision
    bbox_factor = 1.1
  []
  [to_sub_elem]
    type = MultiAppShapeEvaluationTransfer
    to_multi_app = sub
    source_variable = w_elem
    variable = w_elem
    execute_on = 'timestep_begin'
    error_on_miss = true
  []
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_scaled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK

  # Postprocessor value to normalize
  normalization = unorm
  # Value to set normilization to
  normal_factor = 17
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[Outputs]
  exodus = true
  execute_on = 'timestep_end'
[]

(test/tests/multiapps/picard_sub_cycling/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./td_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/convergence/reference_residual_convergence/ad_abs_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = ADTimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = ADCoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = ADTimeDerivative
    variable = v
  []
  [v_neg_force]
    type = ADBodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = ADBodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]

[Convergence]
  [conv]
    type = ReferenceResidualConvergence
    reference_vector = 'absref'
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nl_rel_tol = 1e-06
  nonlinear_convergence = conv
  verbose = true
[]

[Outputs]
  csv = true
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[BCs]
  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  execute_on = 'timestep_end'
[]

(test/tests/convergence/reference_residual_convergence/abs_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]

[Convergence]
  [conv]
    type = ReferenceResidualConvergence
    reference_vector = 'absref'
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nl_rel_tol = 1e-06
  nonlinear_convergence = conv
  verbose = true
[]

[Outputs]
  csv = true
[]

(test/tests/multiapps/picard_failure/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./nan]
    type = NanAtCountKernel
    variable = v
    count = 32
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Postprocessors]
  [./elem_average_value]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
  snesmf_reuse_base = false
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/standard_use/volume_coupling_custom_norm.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
    generation_type = 'sqrt_mu'
    expansion_type = 'sqrt_mu'
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
  file_base = 'volume_coupled_out'
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = volume_coupling_custom_norm_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/kernels/ad_coupled_force/fe_test.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []
[]

[Variables]
  [u]
  []
  [v]
  []
[]

[Kernels]
  [diff_u]
    type = ADDiffusion
    variable = u
  []
  [force_u]
    type = ADCoupledForce
    variable = u
    v = v
  []

  [diff_v]
    type = ADDiffusion
    variable = v
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []

  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 5
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 3
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

(modules/optimization/test/tests/executioners/transient_and_adjoint/multi_variable.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 10
    ny = 10
  []
[]

[Problem]
  nl_sys_names = 'nl0 adjoint'
[]

[Variables]
  [u]
  []
  [v]
  []
  [u_adjoint]
    solver_sys = adjoint
  []
  [v_adjoint]
    solver_sys = adjoint
  []
[]

[Kernels]
  [time_u]
    type = TimeDerivative
    variable = u
  []
  [time_v]
    type = TimeDerivative
    variable = v
  []
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [uv]
    type = CoupledForce
    variable = u
    v = v
    coef = 10
  []
  [vu]
    type = CoupledForce
    variable = v
    v = u
    coef = 1
  []
  [src_u]
    type = BodyForce
    variable = u
    value = 1
  []
  [src_u_adjoint]
    type = BodyForce
    variable = u_adjoint
    value = 0
  []
  [src_v_adjoint]
    type = BodyForce
    variable = v_adjoint
    value = 1
  []
[]

[BCs]
  [dirichlet_u]
    type = DirichletBC
    variable = u
    boundary = 'top right'
    value = 0
  []
  [dirichlet_v]
    type = DirichletBC
    variable = v
    boundary = 'top right'
    value = 0
  []
[]

[Executioner]
  type = TransientAndAdjoint
  forward_system = nl0
  adjoint_system = adjoint

  dt = 0.2
  num_steps = 5

  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END ADJOINT_TIMESTEP_END'
  []
  [u_adjoint_avg]
    type = ElementAverageValue
    variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END ADJOINT_TIMESTEP_END'
  []
  [v_adjoint_avg]
    type = ElementAverageValue
    variable = v_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
  [u_inner_product]
    type = VariableInnerProduct
    variable = u
    second_variable = u_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
  [v_inner_product]
    type = VariableInnerProduct
    variable = v
    second_variable = v_adjoint
    execute_on = ADJOINT_TIMESTEP_END
  []
[]

[Outputs]
  [forward]
    type = CSV
  []
  [adjoint]
    type = CSV
    execute_on = 'INITIAL ADJOINT_TIMESTEP_END'
  []
  [console]
    type = Console
    execute_postprocessors_on = 'INITIAL TIMESTEP_END ADJOINT_TIMESTEP_END'
  []
[]

(test/tests/outputs/variables/output_vars_hidden_shown_check.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD9
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = SECOND
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[AuxVariables]
  [./elemental]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./elemental_restricted]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./nodal]
    order = FIRST
    family = LAGRANGE
  [../]

  [./nodal_restricted]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[AuxKernels]
  [./elemental]
    type = ConstantAux
    variable = elemental
    value = 1
  [../]

  [./elemental_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 1
  [../]

  [./nodal]
    type = ConstantAux
    variable = elemental
    value = 2
  [../]

  [./nodal_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 2
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ImplicitODEx
    variable = x
    y = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ImplicitODEy
    variable = y
    x = x
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 9
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 5
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 2
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  dt = 0.01
  num_steps = 10
[]

[Outputs]
  file_base = out_hidden
  exodus = true
  hide = 'u elemental nodal x'
  show = u
[]

(test/tests/misc/multiple-nl-systems/different-vars-per-system.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Problem]
  nl_sys_names = 'u v'
[]

[Variables]
  [u]
    solver_sys = 'u'
  []
  [v]
    solver_sys = 'v'
  []
  [w]
    solver_sys = 'u'
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = u
  []
  [diff_w]
    type = Diffusion
    variable = w
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
  [left_w]
    type = DirichletBC
    variable = w
    boundary = left
    value = 0
  []
  [right_w]
    type = DirichletBC
    variable = w
    boundary = right
    value = 1
  []
[]

[Preconditioning]
  [u]
    nl_sys = 'u'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
  [v]
    nl_sys = 'v'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
[]

[Executioner]
  type = SteadySolve2
  solve_type = 'NEWTON'
  first_nl_sys_to_solve = 'u'
  second_nl_sys_to_solve = 'v'
[]

[Outputs]
  print_nonlinear_residuals = false
  print_linear_residuals = false
  exodus = true
[]

(test/tests/multisystem/picard/one_way.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [u]
  []
  [v]
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [source_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Convergence]
  [multisys]
    type = IterationCountConvergence
    min_iterations = 0
    max_iterations = 10
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'hypre'

  # We are over-converging these problems
  line_search = 'none'
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_sphere3D_mortar.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = sphere3D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  # [gap_conductance]
  #   order = CONSTANT
  #   family = MONOMIAL
  # []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

# [AuxKernels]
#   [gap_cond]
#     type = MaterialRealAux
#     property = gap_conductance
#     variable = gap_conductance
#     boundary = 2
#   []
# []

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

(test/tests/preconditioners/fsp/scfsp_test.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    dim = 2
  []
  second_order = true
[]

[Variables]
  [u]
    order = SECOND
  []

  [v]
    order = SECOND
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []

  [conv_v]
    type = CoupledForce
    variable = v
    v = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  [left_u]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = u
    boundary = 3
    value = 0
  []
  [right_u]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = u
    boundary = 1
    value = 100
  []
  [left_v]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = v
    boundary = 3
    value = 0
  []
  [right_v]
    type = PenaltyDirichletBC
    penalty = 1e6
    variable = v
    boundary = 1
    value = 0
  []
[]

[Executioner]
  type = Steady
[]

[Preconditioning]
  [FSP]
    type = SCFSP
    topsplit = 'uv'
    [uv]
      splitting = 'u v'
      splitting_type = additive
    []
    [u]
      vars = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      vars = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     lu  preonly'
    []
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/hfem/3d-lower-d-volumes.i)

[Problem]
  use_hash_table_matrix_assembly = true
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 3
    ny = 3
    nz = 3
    dim = 3
  []
  build_all_side_lowerd_mesh = true
[]

[Variables]
  [u]
    order = THIRD
    family = MONOMIAL
    block = 0
  []
  [uhat]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4
  []
  [lambda]
    order = CONSTANT
    family = MONOMIAL
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_QUAD4
  []
  [lambdab]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4
  []
[]

[AuxVariables]
  [v]
    order = CONSTANT
    family = MONOMIAL
    block = 0
    initial_condition = '1'
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = '1'
    block = 0
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
    coef = '1'
    block = 0
  []
  [reaction]
    type = Reaction
    variable = uhat
    rate = '1'
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4
  []
  [uhat_coupled]
    type = CoupledForce
    variable = uhat
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_QUAD4
    v = lambdab
    coef = '1'
  []
[]

[DGKernels]
  [surface]
    type = TestLowerDVolumes
    variable = u
    lowerd_variable = lambda
    l = 1
    n = 3
  []
[]

[BCs]
  [all]
    type = HFEMDirichletBC
    boundary = 'left right top bottom back front'
    variable = u
    lowerd_variable = lambdab
    uhat = uhat
  []
[]

[Postprocessors]
  [intu]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  []
  [lambdanorm]
    type = ElementL2Norm
    variable = lambda
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_QUAD4
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Outputs]
  [out]
    # we hide lambda because it may flip sign due to element
    # renumbering with distributed mesh
    type = Exodus
    hide = lambda
  []
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_3d_pde_filter.i)

vol_frac = 0.4
E0 = 1e5
Emin = 1e-4
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 24
    ny = 12
    nz = 12
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [middle_bottom_left_edge]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    coord = '0 0 5'
  []
[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []

  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []

  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.05
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_abs_tol = 1e-10
  line_search = none
  dt = 1.0
  num_steps = 10
[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(modules/fsi/test/tests/2d-finite-strain-steady/thermal-me.i)

# Units: specific_heat_capacity--cp--J/(kg.K); density--rho--kg/(cm^3);
# dynamic_viscosity--mu--kg/(cm.s); thermal_conductivity--k--W/(cm.K);
# pressure--kg/(cm.s^2); force--kg.cm/s^2

outlet_pressure = 0
inlet_velocity = 150 # cm/s
ini_temp = 593 # K
heat_transfer_coefficient = 9 # W/(cm2.K)
g = -981 # cm/s2
alpha_fluid = 2e-4 # thermal expansion coefficient of fluid used in INSADBoussinesqBodyForce

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  file = '2layers_2d_midline.msh'
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
    order = FIRST
    block = 'fluid'
  []
  [p]
    family = LAGRANGE
    order = FIRST
    block = 'fluid'
  []
  [Tf]
    family = LAGRANGE
    order = FIRST
    block = 'fluid'
  []
  [Ts]
    family = LAGRANGE
    order = FIRST
    block = 'solid'
  []
  [disp_x]
    family = LAGRANGE
    order = FIRST
    block = 'solid fluid'
  []
  [disp_y]
    family = LAGRANGE
    order = FIRST
    block = 'solid fluid'
  []
[]

[AuxVariables]
  [heat_source]
    family = MONOMIAL
    order = FIRST
    block = 'solid'
  []
[]

[ICs]
  [initial_velocity]
    type = VectorConstantIC
    variable = velocity
    x_value = 0
    y_value = ${inlet_velocity}
    z_value = 0
  []
  [initial_p]
    type = FunctionIC
    variable = p
    function = ini_p
  []
  [initial_Tf]
    type = ConstantIC
    variable = Tf
    value = ${ini_temp}
  []
  [initial_Ts]
    type = ConstantIC
    variable = Ts
    value = ${ini_temp}
  []
[]

[Kernels]
  [fluid_mass]
    type = INSADMass
    variable = p
    use_displaced_mesh = true
  []
  [fluid_mass_pspg]
    type = INSADMassPSPG
    variable = p
    use_displaced_mesh = true
  []
  [fluid_momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
    use_displaced_mesh = true
  []
  [fluid_momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
    use_displaced_mesh = true
  []
  [fluid_momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    use_displaced_mesh = true
  []
  [fluid_momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
    use_displaced_mesh = true
  []
  [fluid_momentum_gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 ${g} 0'
    use_displaced_mesh = true
  []
  [fluid_momentum_buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    gravity = '0 ${g} 0'
    alpha_name = 'alpha_fluid'
    ref_temp = 'T_ref'
    temperature = Tf
    use_displaced_mesh = true
  []
  [fluid_momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
    use_displaced_mesh = true
  []
  [fluid_temperature_time]
    type = INSADHeatConductionTimeDerivative
    variable = Tf
    use_displaced_mesh = true
  []
  [fluid_temperature_conduction]
    type = ADHeatConduction
    variable = Tf
    thermal_conductivity = 'k'
    use_displaced_mesh = true
  []
  [fluid_temperature_advection]
    type = INSADEnergyAdvection
    variable = Tf
    use_displaced_mesh = true
  []
  [fluid_temperature_supg]
    type = INSADEnergySUPG
    variable = Tf
    velocity = velocity
    use_displaced_mesh = true
  []

  [solid_temperature_time]
    type = ADHeatConductionTimeDerivative
    variable = Ts
    density_name = 'rho'
    specific_heat = 'cp'
    block = 'solid'
    use_displaced_mesh = true
  []
  [solid_temperature_conduction]
    type = ADHeatConduction
    variable = Ts
    thermal_conductivity = 'k'
    block = 'solid'
    use_displaced_mesh = true
  []
  [heat_source]
    type = ADCoupledForce
    variable = Ts
    v = heat_source
    block = 'solid'
    use_displaced_mesh = true
  []

  [disp_x_smooth]
    type = Diffusion
    variable = disp_x
    block = fluid
  []
  [disp_y_smooth]
    type = Diffusion
    variable = disp_y
    block = fluid
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  strain = FINITE
  material_output_order = FIRST
  generate_output = 'vonmises_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
  [solid]
    block = 'solid'
    temperature = Ts
    automatic_eigenstrain_names = true
  []
[]

[InterfaceKernels]
  [convection_heat_transfer]
    type = ConjugateHeatTransfer
    variable = Tf
    T_fluid = Tf
    neighbor_var = 'Ts'
    boundary = 'solid_wall'
    htc = 'htc'
    use_displaced_mesh = true
  []
[]

[AuxKernels]
  [heat_source_distribution_auxk]
    type = FunctionAux
    variable = heat_source
    function = heat_source_distribution_function
    block = 'solid'
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
[]

[BCs]
  [no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'solid_wall'
    use_displaced_mesh = true
  []
  [inlet_velocity]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'fluid_bottom'
    function_y = ${inlet_velocity}
    use_displaced_mesh = true
  []
  [symmetry]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'fluid_wall'
    function_x = 0
    set_x_comp = true
    set_y_comp = false
    set_z_comp = false
    use_displaced_mesh = true
  []
  [outlet_p]
    type = DirichletBC
    variable = p
    boundary = 'fluid_top'
    value = ${outlet_pressure}
    use_displaced_mesh = true
  []
  [inlet_T]
    type = DirichletBC
    variable = Tf
    boundary = 'fluid_bottom'
    value = ${ini_temp}
    use_displaced_mesh = true
  []

  [pin1_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'pin1'
    value = 0
    use_displaced_mesh = true
  []
  [pin1_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'pin1'
    value = 0
    use_displaced_mesh = true
  []
  [top_and_bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'solid_bottom solid_top fluid_top fluid_bottom'
    value = 0
    use_displaced_mesh = true
  []
  [left_and_right_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'fluid_wall fluid_bottom'
    value = 0
    use_displaced_mesh = true
  []
[]

[Materials]
  [rho_solid]
    type = ADParsedMaterial
    property_name = rho
    expression = '0.0110876 * pow(9.9672e-1 + 1.179e-5 * Ts - 2.429e-9 * pow(Ts,2) + 1.219e-12 * pow(Ts,3),-3)'
    coupled_variables = 'Ts'
    block = 'solid'
    use_displaced_mesh = true
  []
  [cp_solid]
    type = ADParsedMaterial
    property_name = cp
    expression = '0.76 * ((302.27 * pow((548.68 / Ts),2) * exp(548.68 / Ts)) / pow((exp(548.68 / Ts) - 1),2) + 2 * 8.463e-3 * Ts + 8.741e7 * 18531.7 * exp(-18531.7 / Ts) / pow(Ts,2)) + 0.24 * ((322.49 * pow((587.41/Ts),2) * exp(587.41 / Ts)) / pow((exp(587.41 / Ts) - 1),2) + 2 * 1.4679e-2 * Ts)'
    coupled_variables = 'Ts'
    block = 'solid'
    use_displaced_mesh = true
  []
  [k_solid]
    type = ADParsedMaterial
    property_name = k
    expression = '1.158/(7.5408 + 17.692 * (Ts / 1000) + 3.6142 * pow((Ts/1000),2)) + 74.105 * pow((Ts / 1000),-2.5) * exp(-16.35 / (Ts / 1000))'
    coupled_variables = 'Ts'
    block = 'solid'
    use_displaced_mesh = true
  []

  [rho_fluid]
    type = ADParsedMaterial
    property_name = rho
    expression = '(11096 - 1.3236 * Tf) * 1e-6'
    coupled_variables = 'Tf'
    block = 'fluid'
    use_displaced_mesh = true
  []
  [cp_fluid]
    type = ADParsedMaterial
    property_name = cp
    expression = '159 - 2.72e-2 * Tf + 7.12e-6 * pow(Tf,2)'
    coupled_variables = 'Tf'
    block = 'fluid'
    use_displaced_mesh = true
  []
  [k_fluid]
    type = ADParsedMaterial
    property_name = k
    expression = '(3.61 + 1.517e-2 * Tf - 1.741e-6 * pow(Tf,2)) * 1e-2'
    coupled_variables = 'Tf'
    block = 'fluid'
    use_displaced_mesh = true
  []
  [mu_fluid]
    type = ADParsedMaterial
    property_name = mu
    expression = '4.94e-6 * exp(754.1/Tf)'
    coupled_variables = 'Tf'
    block = 'fluid'
    use_displaced_mesh = true
  []
  [buoyancy_thermal_expansion_coefficient_fluid]
    type = ADGenericConstantMaterial
    prop_names = 'alpha_fluid'
    prop_values = '${alpha_fluid}'
    block = 'fluid'
    use_displaced_mesh = true
  []
  [buoyancy_reference_temperature_fluid]
    type = GenericConstantMaterial
    prop_names = 'T_ref'
    prop_values = '${ini_temp}'
    block = 'fluid'
    use_displaced_mesh = true
  []

  [ins_mat_fluid]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = Tf
    block = 'fluid'
    use_displaced_mesh = true
  []

  [htc]
    type = ADGenericFunctionMaterial
    prop_names = htc
    prop_values = htc_function
    use_displaced_mesh = true
  []

  [elasticity_solid]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2e7
    poissons_ratio = 0.32
    block = 'solid'
    use_displaced_mesh = true
  []
  [thermal_expansion_solid]
    type = ComputeThermalExpansionEigenstrain
    temperature = Ts
    thermal_expansion_coeff = 2e-4
    stress_free_temperature = 593
    eigenstrain_name = thermal_expansion
    block = 'solid'
    use_displaced_mesh = true
  []
  [stress_solid]
    type = ComputeFiniteStrainElasticStress
    block = 'solid'
  []
[]

[Functions]
  [htc_function]
    type = ParsedFunction
    expression = ${heat_transfer_coefficient}
  []
  [ini_p]
    type = ParsedFunction
    expression = '0.010302 * 981 * (10 - y)'
  []
  [heat_source_distribution_function]
    type = ParsedFunction
    expression = '300 * sin(pi * y / 10)'
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    solve_type = 'PJFNK'
  []
[]

[Executioner]
  type = Transient
  end_time = 1e4

  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  line_search = 'none'

  nl_max_its = 30
  l_max_its = 100
  automatic_scaling = true
  compute_scaling_once = true
  off_diagonals_in_auto_scaling = true
  dtmin = 1
  nl_abs_tol = 1e-12

  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 6
    growth_factor = 1.5
    dt = 1
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = 'thermal-me'
    execute_on = 'final'
  []
[]

[Postprocessors]
  [average_solid_Ts]
    type = ElementAverageValue
    variable = Ts
    block = 'solid'
    use_displaced_mesh = true
  []
  [average_fluid_Tf]
    type = ElementAverageValue
    variable = Tf
    block = 'fluid'
    use_displaced_mesh = true
  []
  [max_solid_Ts]
    type = ElementExtremeValue
    variable = Ts
    value_type = max
    block = 'solid'
    use_displaced_mesh = true
  []
  [max_fluid_Tf]
    type = ElementExtremeValue
    variable = Tf
    value_type = max
    block = 'fluid'
    use_displaced_mesh = true
  []
  [min_solid_Ts]
    type = ElementExtremeValue
    variable = Ts
    value_type = min
    block = 'solid'
    use_displaced_mesh = true
  []
  [min_fluid_Tf]
    type = ElementExtremeValue
    variable = Tf
    value_type = min
    block = 'fluid'
    use_displaced_mesh = true
  []
[]

[Debug]
  show_var_residual_norms = true
[]

(test/tests/quadrature/qweights/positive_qweights.i)

[Mesh]
  [./square]
    type = FileMeshGenerator
    file = cube.e
  [../]
[]

[Variables]
  [u][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = u
    v = power_density
  []
[]

[BCs]
  [robin]
    type = RobinBC
    variable = u
    boundary = '1 2 3 4 5 6'
  []
[]

[AuxVariables]
  [power_density]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [source]
    type = ParsedAux
    variable = power_density
    use_xyzt = true
    expression = 'if(x>0.1,100,1)'
  []
[]

[Executioner]
  type = Steady
  [./Quadrature]
    allow_negative_qweights = false
  [../]
  solve_type = 'NEWTON'
  petsc_options_iname = "-pc_type"
  petsc_options_value = "hypre"
[]

[Outputs]
  exodus = true
[]

(test/tests/outputs/debug/show_functors.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 40
    xmax = 2
  []
[]

[Debug]
  show_functors = true
[]

[Variables]
  [fv]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1
  []
  [fe]
    initial_condition = 1
  []
[]

[FVKernels]
  [diff]
    type = FVDiffusion
    variable = fv
    coeff = fv_prop
    coeff_interp_method = average
  []
  [coupled]
    type = FVCoupledForce
    v = fv
    variable = fv
  []
[]

[Kernels]
  [diff]
    type = ADFunctorMatDiffusion
    variable = fe
    diffusivity = fe_prop
  []
  [coupled]
    type = CoupledForce
    v = fv
    variable = fe
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = fv
    boundary = left
    value = 0
  []
  [right]
    type = FVDirichletBC
    variable = fv
    boundary = right
    value = 1
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = fe
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = fe
    boundary = right
    value = 1
  []
[]

[Materials]
  active = 'fe_mat fv_mat'
  [bad_mat]
    type = FEFVCouplingMaterial
    fe_var = fe
    fv_var = fv
    execute_on = 'linear nonlinear'
  []
  [fe_mat]
    type = FEFVCouplingMaterial
    fe_var = fe
    execute_on = 'linear nonlinear'
  []
  [fv_mat]
    type = FEFVCouplingMaterial
    fv_var = fv
  []
  [fe_mat_bad_dep]
    type = FEFVCouplingMaterial
    fe_var = fe
    declared_prop_name = bad
  []
  [fv_mat_bad_dep]
    type = FEFVCouplingMaterial
    fv_var = fv
    retrieved_prop_name = bad
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  line_search = 'none'
[]

[Outputs]
  exodus = true
[]

(test/tests/preconditioners/fsp/fsp_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff_u conv_v diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]
[]

[Executioner]
  type = Steady

  # This is setup automatically in MOOSE (SetupPBPAction.C)
  # petsc_options = '-snes_mf_operator'
  # petsc_options_iname = '-pc_type'
  # petsc_options_value =  'asm'
[]

[Preconditioning]
  active = 'FSP'

  [./FSP]
    type = FSP
    # It is the starting point of splitting
    topsplit = 'uv' # 'uv' should match the following block name
    [./uv]
      splitting = 'u v' # 'u' and 'v' are the names of subsolvers
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      splitting_type  = additive
      # An approximate solution to the original system
      # | A_uu  A_uv | | u | _ |f_u|
      # |  0    A_vv | | v | - |f_v|
      #  is obtained by solving the following subsystems
      #  A_uu u = f_u and A_vv v = f_v
      # If splitting type is specified as schur, we may also want to set more options to
      # control how schur works using PETSc options
      # petsc_options_iname = '-pc_fieldsplit_schur_fact_type -pc_fieldsplit_schur_precondition'
      # petsc_options_value = 'full selfp'
    [../]
    [./u]
      vars = 'u'
      # PETSc options for this subsolver
      # A prefix will be applied, so just put the options for this subsolver only
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    [../]
    [./v]
      vars = 'v'
      # PETSc options for this subsolver
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     lu  preonly'
    [../]
  [../]
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/functional_expansion_tools/examples/3D_volumetric_cylindrical_subapp_mesh_refine/main.i)

# Derived from the example '3D_volumetric_cylindrical' with the following differences:
#
#   1) The model mesh is refined in the MasterApp by 1
#   2) Mesh adaptivity is enabled for the SubApp
#   3) Output from the SubApp is enabled so that the mesh changes can be visualized
[Mesh]
  type = FileMesh
  file = cyl-tet.e
  uniform_refine = 1
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom outside'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = CylindricalDuo
    orders = '5   3' # Axial first, then (r, t) FX
    physical_bounds = '-2.5 2.5   0 0 1' # z_min z_max   x_center y_center radius
    z = Legendre # Axial in z
    disc = Zernike # (r, t) default to unit disc in x-y plane
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
    output_sub_cycles = true
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/problems/reference_residual_problem/no_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Problem]
  type = ReferenceResidualProblem
  # reference_vector = 'absref'
  # extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]


[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nl_rel_tol = 1e-06
  verbose = true
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_3D.i)

outer_htc = 10 # W/m^2/K
outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 6
    nz = 6
    xmin = -1
    xmax = -0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'left_bottom left_back left_right left_front left_left left_top'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []

  [right_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 4
    ny = 8
    nz = 8
    xmin = 0.5
    xmax = 1
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
    elem_type = HEX27
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3 4 5'
    # new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
    new_boundary = '100 101 102 103 104 105'
  []
  [right_block_sidesets_rename]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '100 101 102 103 104 105'
    new_boundary = 'right_bottom right_back right_right right_front right_left right_top'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sidesets_rename
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 1
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 1
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 'left_right'
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 'right_left'
    secondary = 'left_right'
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 5
    gap_geometry_type = PLATE
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = 'right_right' # outer RPV
    coefficient = ${outer_htc}
    T_infinity = ${outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-8

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 'left_right'
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 'right_left'
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'left_right'
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 'right_left'
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 1
  []
  [convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = 'right_right' # outer RVP
    T_fluid = ${outer_Tinf}
    htc = ${outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(convective_out - ptot) / ptot'
    pp_names = 'convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'left_right right_left'
    variable = temp
  []
[]

(test/tests/transfers/general_field/user_object/coord_transform/main-app.i)

# This input is a duplicate of test/tests/transfers/coord_transform/both_transformed/user_object
# The parameters are different between the GeneralFieldUserObject transfer and its deprecated
# ancestor

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  # Quarter turn around Z axis
  alpha_rotation = -90
  # Flips around Y axis
  # beta_rotation = -180
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [from_sub_app_var]
  []
  [from_sub_app_var_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = from_sub_app_var
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[UserObjects]
  [main_uo]
    type = LayeredAverage
    direction = x
    num_layers = 5
    variable = u
  []
[]

[MultiApps]
  [sub_app]
    # Shift is offset by sub-app mesh + rotations
    # positions = '1 0 0.0'
    type = FullSolveMultiApp
    input_files = sub-app.i
    app_type = MooseTestApp
    bounding_box_padding = '0.25 0.25 0'
    bounding_box_inflation = 0
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [layered_transfer_to_sub_app]
    type = MultiAppGeneralFieldUserObjectTransfer
    source_user_object = main_uo
    variable = sub_app_var
    to_multi_app = sub_app
  []
  [layered_transfer_to_sub_app_elem]
    type = MultiAppGeneralFieldUserObjectTransfer
    source_user_object = main_uo
    variable = sub_app_var_elem
    to_multi_app = sub_app
  []

  [layered_transfer_from_sub_app]
    type = MultiAppGeneralFieldUserObjectTransfer
    source_user_object = sub_app_uo
    variable = from_sub_app_var
    from_multi_app = sub_app
  []
  [layered_transfer_from_sub_app_elem]
    type = MultiAppGeneralFieldUserObjectTransfer
    source_user_object = sub_app_uo
    variable = from_sub_app_var_elem
    from_multi_app = sub_app
  []
[]

(test/tests/outputs/console/multiapp/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder_mortar.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = 'Tsolid'
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               1e-15'
  snesmf_reuse_base = false

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/combined/examples/optimization/helmholtz_multimat_strip.i)

vol_frac = 0.35

power = 1.1

Emin = 1.0e-6
Ess = 0.475 # ss
Et = 1.0 # w

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [RenameBottom]
    type = RenameBoundaryGenerator
    input = Bottom
    old_boundary = 'top bottom right left'
    new_boundary = 'top_bottom bottom_bottom right_bottom left_bottom'
  []
  [Middle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 6
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 3
  []
  [MoveMiddle]
    type = TransformGenerator
    input = Middle
    transform = TRANSLATE
    vector_value = '0 15 0'
  []
  [RenameMiddle]
    type = RenameBoundaryGenerator
    input = MoveMiddle
    old_boundary = 'top bottom right left'
    new_boundary = 'top_middle bottom_middle right_middle left_middle'
  []
  [Top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [MoveTop]
    type = TransformGenerator
    input = Top
    transform = TRANSLATE
    vector_value = '0 18 0'
  []
  [RenameTop]
    type = RenameBoundaryGenerator
    input = MoveTop
    old_boundary = 'top bottom right left'
    new_boundary = 'top_top bottom_top right_top left_top'
  []
  [bottom_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameBottom
    combinatorial_geometry = 'y <= 15'
    block_id = 1
  []
  [middle_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameMiddle
    combinatorial_geometry = 'y <= 18 & y > 15'
    block_id = 2
  []
  [top_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameTop
    combinatorial_geometry = 'y > 18'
    block_id = 3
  []
  [stitch]
    type = StitchedMeshGenerator
    inputs = 'bottom_gen middle_gen top_gen'
    stitch_boundaries_pairs = 'top_bottom bottom_middle; top_middle bottom_top'
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = stitch
    new_boundary = left_load
    coord = '37.5 33 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 33 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
    block = '1 2 3'
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 4.0
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'bottom_bottom right_bottom left_bottom top_top right_top left_top left_middle '
               'right_middle'
    coefficient = 10
  []
[]

[NodalKernels]
  [left_down]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
  [right_down]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [sensitivity]
    type = ParsedMaterial
    property_name = 'sensitivity'
    block = '2'
    expression = '0'
  []
  [elasticity_tensor_one]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_one
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '1'
  []
  [elasticity_tensor_three]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_three
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '3'
  []
  [elasticity_tensor_two]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.0
    poissons_ratio = 0.3
    block = '2'
  []
  # One: Tungsten
  [E_phys_one]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Et}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_one
    block = '1'
    outputs = 'exodus'
  []
  # Three: SS316
  [E_phys_three]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Ess}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_three
    block = '3'
    outputs = 'exodus'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc_one]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_one
    block = '1'
  []
  [dc_three]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_three
    block = '3'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update_one]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '1'
  []
  [update_three]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '3'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 90
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    block = '1 3'
  []
  [objective_one]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '1'
  []
  [objective_three]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '3'
  []
[]

(tutorials/tutorial02_multiapps/step03_coupling/03_sub_subcycling_picard.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [ut]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = ut
    coef = 100
  []
  [td]
    type = TimeDerivative
    variable = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  end_time = 2
  dt = 0.05

  nl_abs_tol = 1e-10

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [average_v]
    type = ElementAverageValue
    variable = v
  []
[]

(test/tests/multiapps/steffensen/steady_main.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  parallel_type = replicated
  uniform_refine = 1
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
  []
[]

[Executioner]
  type = Steady

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'steffensen'
  fixed_point_max_its = 30
  transformed_variables = 'u'
  accept_on_max_fixed_point_iteration = true
[]

[Outputs]
  csv = true
  exodus = false
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'steady_sub.i'
    clone_parent_mesh = true

    transformed_variables = 'v'
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(modules/functional_expansion_tools/examples/2D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 2D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
[Mesh]
  type = GeneratedMesh
  dim = 2

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4'
    physical_bounds = '0.0  10.0    1.0 11.0'
    x = Legendre
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/phase_field/test/tests/KKS_system/nonlinear.i)

#
# This test checks if the thwo phase and lagrange multiplier solutions can be replicated
# with a two order parameter approach, where the second order parameter eta2 is a
# nonlinear variable that is set as eta2 := 1 - eta1 (using Reaction, CoupledForce, and BodyForce)
# The solution is reproduced.
#

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 5
[]

[AuxVariables]
  [Fglobal]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Variables]
  # concentration
  [c]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = FunctionIC
      function = x/5
    []
  []

  # order parameter 1
  [eta1]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.5
  []
  # order parameter 2
  [eta2]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.5
  []

  # phase concentration 1
  [c1]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.9
  []

  # phase concentration 2
  [c2]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  []
[]

[Materials]
  # simple toy free energies
  [f1] # = fd
    type = DerivativeParsedMaterial
    property_name = F1
    coupled_variables = 'c1'
    expression = '(0.9-c1)^2'
  []
  [f2] # = fm
    type = DerivativeParsedMaterial
    property_name = F2
    coupled_variables = 'c2'
    expression = '(0.1-c2)^2'
  []

  # Switching functions for each phase
  [h1_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta1
    function_name = h1
  []
  [h2_eta]
    type = SwitchingFunctionMaterial
    h_order = HIGH
    eta = eta2
    function_name = h2
  []

  # Coefficients for diffusion equation
  [Dh1]
    type = DerivativeParsedMaterial
    material_property_names = 'D h1(eta1)'
    expression = D*h1
    property_name = Dh1
    coupled_variables = eta1
  []
  [Dh2]
    type = DerivativeParsedMaterial
    material_property_names = 'D h2(eta2)'
    expression = D*h2
    property_name = Dh2
    coupled_variables = eta2
  []

  # Barrier functions for each phase
  [g1]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta1
    function_name = g1
  []
  [g2]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta2
    function_name = g2
  []

  # constant properties
  [constants]
    type = GenericConstantMaterial
    prop_names  = 'D   L   kappa'
    prop_values = '0.7 0.7 0.2'
  []
[]

[Kernels]
  #Kernels for diffusion equation
  [diff_time]
    type = TimeDerivative
    variable = c
  []
  [diff_c1]
    type = MatDiffusion
    variable = c
    diffusivity = Dh1
    v = c1
    args = 'eta1'
  []
  [diff_c2]
    type = MatDiffusion
    variable = c
    diffusivity = Dh2
    v = c2
    args = 'eta2'
  []

  # Kernels for Allen-Cahn equation for eta1
  [deta1dt]
    type = TimeDerivative
    variable = eta1
  []
  [ACBulkF1]
    type = KKSMultiACBulkF
    variable = eta1
    Fj_names = 'F1 F2 '
    hj_names = 'h1 h2 '
    gi_name = g1
    eta_i = eta1
    wi = 0.2
    coupled_variables = 'c1 c2 eta2'
  []
  [ACBulkC1]
    type = KKSMultiACBulkC
    variable = eta1
    Fj_names = 'F1 F2'
    hj_names = 'h1 h2'
    cj_names = 'c1 c2'
    eta_i = eta1
    coupled_variables = 'eta2'
  []
  [ACInterface1]
    type = ACInterface
    variable = eta1
    kappa_name = kappa
  []

  # Phase concentration constraints
  [chempot12]
    type = KKSPhaseChemicalPotential
    variable = c1
    cb = c2
    fa_name = F1
    fb_name = F2
  []
  [phaseconcentration]
    type = KKSMultiPhaseConcentration
    variable = c2
    cj = 'c1 c2'
    hj_names = 'h1 h2'
    etas = 'eta1 eta2'
    c = c
  []

  # equation for eta2 = 1 - eta1
  # 0 = eta2 + eta1 -1
  [constraint_eta1] #   eta2
    type = Reaction
    variable = eta2
  []
  [constraint_eta2] # + eta1
    type = CoupledForce
    variable = eta2
    coef = -1
    v = eta1
  []
  [constraint_one]  # - 1
    type = BodyForce
    variable = eta2
  []
[]

[AuxKernels]
  [Fglobal_total]
    type = KKSMultiFreeEnergy
    Fj_names = 'F1 F2 '
    hj_names = 'h1 h2 '
    gj_names = 'g1 g2 '
    variable = Fglobal
    w = 0.2
    interfacial_vars = 'eta1  eta2 '
    kappa_names      = 'kappa kappa'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -sub_pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero'
  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-10
  nl_abs_tol = 1.0e-11

  end_time = 350
  dt = 10
[]

[VectorPostprocessors]
  [c]
    type = LineValueSampler
    variable = c
    start_point = '0 0 0'
    end_point = '5 0 0'
    num_points = 21
    sort_by = x
  []
[]

[Outputs]
  csv = true
  execute_on = FINAL
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder_mortar_error.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = ${fparse 2 + rpv_core_gap_size}
rpv_outer_radius = ${fparse 2.5 + rpv_core_gap_size}

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
  [lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = 'Tsolid'
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               '
                        '1e-15'
  snesmf_reuse_base = false

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(test/tests/multiapps/picard/picard_abs_tol_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-12
  fixed_point_max_its = 10
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/multiapps/relaxation/sub_relaxed_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 2
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/relaxation/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./time_v]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 2
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/functormaterials/functor_change/fp_parent.i)

# Heat conduction with fixed temperature on left and convection BC on right:
#
#   d/dx(-k dT/dx) = S'''(T)    (0,1)X(0,1)
#   T = T_inf                    x = 0
#   -k dT/dx = htc (T - T_inf)   x = 1
#
# Source is temperature-dependent and is calculated in the child app:
#   S(T) = B - A * (T - T_inf)^2

k = 15.0
htc = 100.0
T_ambient = 300.0

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [T_nodal]
  []
  [T_elem]
    type = MooseVariableFVReal
  []
[]

[AuxVariables]
  [S_parent]
  []
[]

[FunctorMaterials]
  [heat_flux_mat_nodal]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T_nodal ${T_ambient} ${htc}'
    property_name = 'heat_flux_nodal'
  []
  [heat_flux_mat_elem]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T_elem ${T_ambient} ${htc}'
    property_name = 'heat_flux_elem'
  []
[]

[Kernels]
  [T_nodal_diff]
    type = FunctionDiffusion
    variable = T_nodal
    function = ${k}
  []
  [T_nodal_source]
    type = CoupledForce
    variable = T_nodal
    v = S_parent
  []
[]

[FVKernels]
  [T_elem_diff]
    type = FVDiffusion
    variable = T_elem
    coeff = ${k}
  []
  [T_elem_source]
    type = FVCoupledForce
    variable = T_elem
    v = S_parent
  []
[]

[BCs]
  [left_bc_nodal]
    type = DirichletBC
    variable = T_nodal
    boundary = left
    value = ${T_ambient}
  []
  [right_bc_nodal]
    type = FunctorNeumannBC
    variable = T_nodal
    boundary = right
    functor = heat_flux_nodal
    flux_is_inward = false
  []
[]

[FVBCs]
  [left_bc_elem]
    type = FVDirichletBC
    variable = T_elem
    boundary = left
    value = ${T_ambient}
  []
  [right_bc_elem]
    type = FVFunctorNeumannBC
    variable = T_elem
    boundary = right
    functor = heat_flux_elem
    factor = -1
  []
[]

[MultiApps]
  [source_app]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = fp_child.i
    execute_on = 'TIMESTEP_END'
  []
[]

[Transfers]
  [T_to_child]
    type = MultiAppCopyTransfer
    to_multi_app = source_app
    source_variable = T_nodal
    variable = T_child
    execute_on = 'SAME_AS_MULTIAPP'
  []
  [S_from_child]
    type = MultiAppCopyTransfer
    from_multi_app = source_app
    source_variable = S
    variable = S_parent
    execute_on = 'SAME_AS_MULTIAPP'
  []
[]

[FunctorMaterials]
  [nodal_mat]
    type = ADFunctorChangeFunctorMaterial
    functor = T_nodal
    change_over = fixed_point
    take_absolute_value = false
    prop_name = T_nodal_change
  []
  [elem_mat]
    type = ADFunctorChangeFunctorMaterial
    functor = T_elem
    change_over = fixed_point
    take_absolute_value = false
    prop_name = T_elem_change
  []
  [S_mat]
    type = ADFunctorChangeFunctorMaterial
    functor = S_parent
    change_over = fixed_point
    take_absolute_value = false
    prop_name = S_change
  []
[]

[Postprocessors]
  [T_nodal_avg]
    type = AverageNodalVariableValue
    variable = T_nodal
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [T_elem_avg]
    type = ElementAverageValue
    variable = T_elem
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [S_avg]
    type = ElementAverageValue
    variable = S_parent
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [T_nodal_max_change]
    type = ElementExtremeFunctorValue
    functor = T_nodal_change
    value_type = max
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [T_elem_max_change]
    type = ElementExtremeFunctorValue
    functor = T_elem_change
    value_type = max
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [S_max_change]
    type = ElementExtremeFunctorValue
    functor = S_change
    value_type = max
    execute_on = 'TIMESTEP_BEGIN'
  []
  [fp_it]
    type = NumFixedPointIterations
    get_index_instead_of_count = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Convergence]
  [fp_conv]
    type = IterationCountConvergence
    max_iterations = 5
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  multiapp_fixed_point_convergence = fp_conv
[]

[Outputs]
  [console]
    type = Console
    new_row_detection_columns = all
    execute_postprocessors_on = 'INITIAL MULTIAPP_FIXED_POINT_ITERATION_END'
  []
  [out]
    type = CSV
    new_row_detection_columns = all
    execute_on = 'INITIAL MULTIAPP_FIXED_POINT_ITERATION_END'
  []
[]

(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-resid-scaling.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [u]
    initial_condition = 1
  []
  [T]
    initial_condition = 1
  []
[]

[AuxVariables]
  [power][]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = CoefDiffusion
    variable = T
    coef = 1e30
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
    coef = 1e30
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenT]
    type = EigenDirichletBC
    variable = T
    boundary = '0 1 2 3'
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  automatic_scaling = true
  petsc_options = '-pc_svd_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'svd'
  verbose = true
  resid_vs_jac_scaling_param = 1
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/multiapps/picard_catch_up/sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
  [./nan]
    type = NanAtCountKernel
    variable = v
    count = 32
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    preset = false
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = FunctionDirichletBC
    variable = v
    preset = false
    boundary = right
    function = 't + 1'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu mumps'
  nl_abs_tol = 1e-10
  snesmf_reuse_base = false
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/picard_multilevel/2level_picard/mutilevel_app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 50
  []
[]

[Kernels]
  [diffusion]
    type = Diffusion
    variable = u
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [dirichlet0]
    type = DirichletBC
    variable = u
    boundary = '3'
    value = 0
  []
  [dirichlet]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 100
  []
[]

[Postprocessors]
  [avg_u]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial timestep_begin timestep_end'
  []
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial timestep_begin timestep_end'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  fixed_point_rel_tol = 1E-3
  fixed_point_abs_tol = 1.0e-05
  fixed_point_max_its = 2
  accept_on_max_fixed_point_iteration = true
[]

[MultiApps]
  [level1-]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = sub_level1.i
    execute_on = 'timestep_end'
    keep_solution_during_restore = true
  []
[]

[Transfers]
  [u_to_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = u
    variable = u
    to_multi_app = level1-
    execute_on = 'timestep_end'
  []
  [v_from_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = v
    variable = v
    from_multi_app = level1-
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
  [screen]
    type = Console
    execute_postprocessors_on = "timestep_end timestep_begin"
  []
[]

(test/tests/preconditioners/pbp/pbp_test_options.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
#  init_unif_refine = 6
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Preconditioning]
  active = 'PBP'

  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'LU LU'
    off_diag_row    = 'v'
    off_diag_column = 'u'

    petsc_options = ''  # Test petsc options in PBP block
  [../]
[]

[Kernels]
  active = 'diff_u conv_v diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]
[]

[Executioner]
  type = Steady

  l_max_its = 1
  nl_max_its = 2

  solve_type = JFNK
[]

[Outputs]
  file_base = out_dummy
  exodus = true
[]

(test/tests/kernels/hfem/dirichlet.i)

[Problem]
  use_hash_table_matrix_assembly = true
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 3
    ny = 3
    dim = 2
  []
  build_all_side_lowerd_mesh = true
[]

[Variables]
  [u]
    order = THIRD
    family = MONOMIAL
    block = 0
  []
  [uhat]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambda]
    order = CONSTANT
    family = MONOMIAL
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambdab]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
[]

[AuxVariables]
  [v]
    order = CONSTANT
    family = MONOMIAL
    block = 0
    initial_condition = '1'
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = '1'
    block = 0
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
    coef = '1'
    block = 0
  []
  [reaction]
    type = Reaction
    variable = uhat
    rate = '1'
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [uhat_coupled]
    type = CoupledForce
    variable = uhat
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
    v = lambdab
    coef = '1'
  []
[]

[DGKernels]
  [surface]
    type = HFEMDiffusion
    variable = u
    lowerd_variable = lambda
  []
[]

[BCs]
  [all]
    type = HFEMDirichletBC
    boundary = 'left right top bottom'
    variable = u
    lowerd_variable = lambdab
    uhat = uhat
  []
[]

[Postprocessors]
  [intu]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  []
  [lambdanorm]
    type = ElementL2Norm
    variable = lambda
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Outputs]
  [out]
    # we hide lambda because it may flip sign due to element
    # renumbering with distributed mesh
    type = Exodus
    hide = lambda
  []
[]

(test/tests/multiapps/picard_multilevel/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [coupled_force]
    type = CoupledForce
    variable = u
    v = v
  []
  [time]
    type = TimeDerivative
    variable = u
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub1]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
    execute_on = 'timestep_end'
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub1
    source_variable = v
    variable = v
  []
[]

(test/tests/fvkernels/fv-to-fe-coupling/1d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 40
    xmax = 2
  []
[]

[Variables]
  [fv]
    family = MONOMIAL
    order = CONSTANT
    fv = true
    initial_condition = 1
  []
  [fe]
    initial_condition = 1
  []
[]

[FVKernels]
  [diff]
    type = FVDiffusion
    variable = fv
    coeff = fv_prop
    coeff_interp_method = average
  []
  [coupled]
    type = FVCoupledForce
    v = fv
    variable = fv
  []
[]

[Kernels]
  [diff]
    type = ADFunctorMatDiffusion
    variable = fe
    diffusivity = fe_prop
  []
  [coupled]
    type = CoupledForce
    v = fv
    variable = fe
  []
[]

[FVBCs]
  [left]
    type = FVDirichletBC
    variable = fv
    boundary = left
    value = 0
  []
  [right]
    type = FVDirichletBC
    variable = fv
    boundary = right
    value = 1
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = fe
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = fe
    boundary = right
    value = 1
  []
[]

[Materials]
  active = 'fe_mat fv_mat'
  [bad_mat]
    type = FEFVCouplingMaterial
    fe_var = fe
    fv_var = fv
    execute_on = 'linear nonlinear'
  []
  [fe_mat]
    type = FEFVCouplingMaterial
    fe_var = fe
    execute_on = 'linear nonlinear'
  []
  [fv_mat]
    type = FEFVCouplingMaterial
    fv_var = fv
  []
  [fe_mat_bad_dep]
    type = FEFVCouplingMaterial
    fe_var = fe
    declared_prop_name = bad
  []
  [fv_mat_bad_dep]
    type = FEFVCouplingMaterial
    fv_var = fv
    retrieved_prop_name = bad
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  line_search = 'none'
[]

[Outputs]
  exodus = true
[]

(test/tests/convergence/parent.i)

# Heat conduction with fixed temperature on left and convection BC on right:
#
#   d/dx(-k dT/dx) = S'''(T)    (0,1)X(0,1)
#   T = T_inf                    x = 0
#   -k dT/dx = htc (T - T_inf)   x = 1
#
# Source is temperature-dependent and is calculated in the child app:
#   S(T) = B - A * (T - T_inf)^2

k = 15.0
htc = 100.0
T_ambient = 300.0

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [T]
  []
[]

[AuxVariables]
  [S_parent]
  []
[]

[FunctorMaterials]
  [heat_flux_mat]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T ${T_ambient} ${htc}'
    property_name = 'heat_flux'
  []
[]

[Kernels]
  [diff]
    type = FunctionDiffusion
    variable = T
    function = ${k}
  []
  [source]
    type = CoupledForce
    variable = T
    v = S_parent
  []
[]

[BCs]
  [left_bc]
    type = DirichletBC
    variable = T
    boundary = left
    value = ${T_ambient}
  []
  [right_bc]
    type = FunctorNeumannBC
    variable = T
    boundary = right
    functor = heat_flux
    flux_is_inward = false
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  multiapp_fixed_point_convergence = fp_conv
[]

[MultiApps]
  [source_app]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = child.i
    execute_on = 'TIMESTEP_END'
  []
[]

[Transfers]
  [T_to_child]
    type = MultiAppCopyTransfer
    to_multi_app = source_app
    source_variable = T
    variable = T_child
    execute_on = 'SAME_AS_MULTIAPP'
  []
  [S_from_child]
    type = MultiAppCopyTransfer
    from_multi_app = source_app
    source_variable = S
    variable = S_parent
    execute_on = 'SAME_AS_MULTIAPP'
  []
[]

[Postprocessors]
  [n_fp_its]
    type = NumFixedPointIterations
    execute_on = 'TIMESTEP_END'
  []
[]

[Outputs]
  csv = true
  execute_on = 'FINAL'
[]

(test/tests/preconditioners/pbp/pbp_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
#  init_unif_refine = 6
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Preconditioning]
  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'LU LU'
    off_diag_row    = 'v'
    off_diag_column = 'u'

    petsc_options = ''  # Test petsc options in PBP block
  [../]
[]

[Problem]
  type = FEProblem
  error_on_jacobian_nonzero_reallocation = true
[]

[Kernels]
  active = 'diff_u conv_v diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]
[]

[Executioner]
  type = Steady

  l_max_its = 10
  nl_max_its = 10

  solve_type = JFNK
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/kernels/ad_coupled_force/aux_test.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [a]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [diff]
    type = ADDiffusion
    variable = u
  []
  [force]
    type = ADCoupledForce
    variable = u
    v = a
  []
[]

[AuxKernels]
  [a]
    variable = a
    type = ConstantAux
    value = 10
  []
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = ADDirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

(test/tests/preconditioners/smp/smp_single_test.i)

#
# This is not very strong test since the problem being solved is linear, so the difference between
# full Jacobian and block diagonal preconditioner are not that big
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    off_diag_row    = 'u'
    off_diag_column = 'v'
  [../]
[]

[Kernels]
  active = 'diff_u conv_u diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u top_v bottom_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 9
  [../]

  [./bottom_v]
    type = DirichletBC
    variable = v
    boundary = 0
    value = 5
  [../]

  [./top_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 2
  [../]
[]

[Executioner]
  type = Steady

#  l_max_its = 1
#  nl_max_its = 1

#  nl_rel_tol = 1e-10


  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/standard_use/multiapp_different_physical_boundaries.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '1.0  9.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/multisystem/picard/two_way.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [u]
  []
  [v]
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [source_v]
    type = CoupledForce
    variable = v
    v = u
  []
  [source_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Convergence]
  [multisys]
    type = IterationCountConvergence
    min_iterations = 0
    max_iterations = 10
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'hypre'

  # We are over-converging these problems
  line_search = 'none'
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

(test/tests/preconditioners/smp/smp_group_test.i)

###########################################################
# This test exercises the customer Preconditioner System.
# A Single Matrix Preconditioner is built using
# coupling specified by the user.
#
# @Requirement F1.40
###########################################################


[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]

  [./p]
  [../]
  [./q]
  [../]
[]

# Single Matrix Preconditioner
[Preconditioning]
  [./SMP]
    type = SMP
    coupled_groups = 'u,v p,q'
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  [./diff_p]
    type = Diffusion
    variable = p
  [../]
  [./conv_p]
    type = CoupledForce
    variable = p
    v = q
  [../]
  [./diff_q]
    type = Diffusion
    variable = q
  [../]
[]

[BCs]
  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
  [./bottom_v]
    type = DirichletBC
    variable = v
    boundary = 0
    value = 5
  [../]
  [./top_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 2
  [../]

  [./left_p]
    type = DirichletBC
    variable = p
    boundary = 1
    value = 2
  [../]
  [./bottom_q]
    type = DirichletBC
    variable = q
    boundary = 0
    value = 3
  [../]
  [./top_q]
    type = DirichletBC
    variable = q
    boundary = 2
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  nl_max_its = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/outputs/csv/all_columns_parent.i)

# Heat conduction with fixed temperature on left and convection BC on right:
#
#   d/dx(-k dT/dx) = S'''(T)    (0,1)X(0,1)
#   T = T_inf                    x = 0
#   -k dT/dx = htc (T - T_inf)   x = 1
#
# Source is temperature-dependent and is calculated in the child app:
#   S(T) = B - A * (T - T_inf)^2

k = 15.0
htc = 100.0
T_ambient = 300.0

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [T]
  []
[]

[AuxVariables]
  [S_parent]
  []
  [Tavg_scalar]
    family = SCALAR
    order = FIRST
  []
[]

[Functions]
  [Tavg_scalar_fn]
    type = PostprocessorFunction
    pp = Tavg_pp
  []
[]

[AuxScalarKernels]
  [Tavg_scalar_kernel]
    type = FunctionScalarAux
    variable = Tavg_scalar
    function = Tavg_scalar_fn
    execute_on = 'TIMESTEP_END'
  []
[]

[FunctorMaterials]
  [heat_flux_mat]
    type = ADParsedFunctorMaterial
    expression = 'htc * (T - T_inf)'
    functor_symbols = 'T T_inf htc'
    functor_names = 'T ${T_ambient} ${htc}'
    property_name = 'heat_flux'
  []
[]

[Kernels]
  [diff]
    type = FunctionDiffusion
    variable = T
    function = ${k}
  []
  [source]
    type = CoupledForce
    variable = T
    v = S_parent
  []
[]

[BCs]
  [left_bc]
    type = DirichletBC
    variable = T
    boundary = left
    value = ${T_ambient}
  []
  [right_bc]
    type = FunctorNeumannBC
    variable = T
    boundary = right
    functor = heat_flux
    flux_is_inward = false
  []
[]

[Convergence]
  [fp_conv]
    type = IterationCountConvergence
    max_iterations = 3
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  multiapp_fixed_point_convergence = fp_conv
[]

[MultiApps]
  [source_app]
    type = FullSolveMultiApp
    positions = '0 0 0'
    input_files = all_columns_child.i
    execute_on = 'TIMESTEP_END'
  []
[]

[Transfers]
  [T_to_child]
    type = MultiAppCopyTransfer
    to_multi_app = source_app
    source_variable = T
    variable = T_child
    execute_on = 'SAME_AS_MULTIAPP'
  []
  [S_from_child]
    type = MultiAppCopyTransfer
    from_multi_app = source_app
    source_variable = S
    variable = S_parent
    execute_on = 'SAME_AS_MULTIAPP'
  []
[]

[Postprocessors]
  [Tavg_pp]
    type = AverageNodalVariableValue
    variable = T
    execute_on = 'TIMESTEP_END'
  []
  [fp_it]
    type = NumFixedPointIterations
    get_index_instead_of_count = true
    execute_on = 'TIMESTEP_END'
  []
[]

[Outputs]
  [console]
    type = Console
    new_row_detection_columns = ALL
    execute_postprocessors_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
    execute_scalars_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
    execute_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
  []
  [out]
    type = CSV
    new_row_detection_columns = ALL
    execute_postprocessors_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
    execute_scalars_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
    execute_on = 'MULTIAPP_FIXED_POINT_ITERATION_END'
  []
[]

(test/tests/problems/reference_residual_problem/abs_ref_acceptable.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'absref'
  extra_tag_vectors = 'absref'
  acceptable_iterations = 1
  acceptable_multiplier = 1e6
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]


[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 3
  nl_rel_tol = 1e-06
  verbose = true
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(test/tests/auxkernels/element_aux_var/element_aux_var_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [one]
    order = CONSTANT
    family = MONOMIAL
  []
  [five]
    order = FIRST
    family = LAGRANGE
  []
  [three]
    order = CONSTANT
    family = MONOMIAL
  []
  [coupled_nine]
    order = CONSTANT
    family = MONOMIAL
  []
  [coupled_fifteen]
    order = CONSTANT
    family = MONOMIAL
  []
  [coupled]
    order = CONSTANT
    family = MONOMIAL
  []
  [coupled_nl]
    order = CONSTANT
    family = MONOMIAL
  []
  [coupled_grad_nl]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  # Coupling of nonlinear to Aux
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = one
  []
[]

[AuxKernels]
  # Simple Aux Kernel
  # Shows coupling of Element to Nodal
  # Shows coupling of Element to non-linear
  # Shows coupling of Element to non-linear grad
  [constant]
    variable = one
    type = ConstantAux
    value = 1
  []
  [coupled_nine]
    variable = coupled_nine
    type = CoupledAux
    value = 3
    operator = *
    coupled = three
  []
  [coupled_three]
    variable = three
    type = CoupledAux
    value = 2
    operator = +
    coupled = one
  []
  [coupled_fifteen]
    variable = coupled_fifteen
    type = CoupledAux
    value = 5
    operator = *
    coupled = three
  []
  [coupled]
    variable = coupled
    type = CoupledAux
    value = 2
    coupled = five
  []
  [coupled_nl]
    variable = coupled_nl
    type = CoupledAux
    value = 2
    coupled = u
  []
  [coupled_grad_nl]
    variable = coupled_grad_nl
    type = CoupledGradAux
    grad = '2 0 0'
    coupled = u
  []
  [five]
    type = ConstantAux
    variable = five
    boundary = '3 1'
    value = 5
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'

[]

[Outputs]
  file_base = out
  [exodus]
    type = Exodus
    elemental_as_nodal = true
  []
[]

(test/tests/multiapps/picard_multilevel/2level_picard/sub_level1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
  [w]
  []
[]

[Kernels]
  [time_derivative]
    type = TimeDerivative
    variable = v
  []
  [diffusion]
    type = Diffusion
    variable = v
  []
  [source]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [dirichlet0]
    type = DirichletBC
    variable = v
    boundary = '0'
    value = 0
  []
  [dirichlet]
    type = DirichletBC
    variable = v
    boundary = '2'
    value = 100
  []
[]

[Postprocessors]
  [avg_u]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial timestep_begin timestep_end'
  []
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial timestep_begin timestep_end'
  []
  [avg_w]
    type = ElementAverageValue
    variable = w
    execute_on = 'initial timestep_begin timestep_end'
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  end_time = 0.1
  dt = 0.02
[]

[MultiApps]
  [level2-]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = sub_level2.i
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [v_to_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = v
    variable = v
    to_multi_app = level2-
    execute_on = 'timestep_end'
  []
  [w_from_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = w
    variable = w
    from_multi_app = level2-
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
  [screen]
    type = Console
    execute_postprocessors_on = "timestep_end timestep_begin"
  []
[]

(test/tests/preconditioners/pbp/pbp_adapt_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  [./forcing_fn]
    type = ParsedFunction
    expression = -4
  [../]

  [./exact_fn]
    type = ParsedFunction
    expression = ((x*x)+(y*y))
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 0
  [../]
[]

[Postprocessors]
  [./l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Preconditioning]
  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'AMG ASM'
    off_diag_row    = 'v'
    off_diag_column = 'u'
  [../]
[]

[Executioner]
  type = Steady

  solve_type = JFNK

  [./Adaptivity]
    steps = 3
    coarsen_fraction = 0.1
    refine_fraction = 0.2
    max_h_level = 5
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = out_pbp_adapt
  print_mesh_changed_info = true
  exodus = true
[]

(test/tests/multiapps/picard_multilevel/2level_picard/sub_level2.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [w]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [time_derivative]
    type = TimeDerivative
    variable = w
  []
  [diffusion]
    type = Diffusion
    variable = w
  []
  [source]
    type = CoupledForce
    variable = w
    v = v
  []
[]

[BCs]
  [dirichlet0]
    type = DirichletBC
    variable = w
    boundary = '3'
    value = 0
  []
  [dirichlet]
    type = DirichletBC
    variable = w
    boundary = '1'
    value = 100
  []
[]

[Postprocessors]
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial timestep_begin timestep_end'
  []
  [avg_w]
    type = ElementAverageValue
    variable = w
    execute_on = 'initial  timestep_begin timestep_end'
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  end_time = 0.1
  dt = 0.02
[]


[Outputs]
  exodus = true
  [screen]
    type = Console
    execute_postprocessors_on= "timestep_end timestep_begin"
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_rz_cylinder.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []

[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100
  [Quadrature]
    # order = fifth
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/3d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 30
    ny = 10
    nz = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    coord = '0 0 0; 0 0 10'
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 5'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 2
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(test/tests/auxkernels/nodal_aux_var/nodal_aux_ts_test.i)

#
# Testing nodal aux variables that are computed only at the end of the time step
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 3
  ny = 3
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  active = 'aux1 aux2'

  [./aux1]
    order = FIRST
    family = LAGRANGE
  [../]

  [./aux2]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'ie diff force'

  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  #Coupling of nonlinear to Aux
  [./force]
    type = CoupledForce
    variable = u
    v = aux2
  [../]
[]

[AuxKernels]
  active = 'constant field'

  #Simple Aux Kernel
  [./constant]
    variable = aux1
    type = ConstantAux
    value = 1
  [../]

  #Shows coupling of Aux to nonlinear
  [./field]
    variable = aux2
    type = CoupledAux
    value = 2
    coupled = u
    execute_on = timestep_end
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0
  dt = 0.1
  num_steps = 2


  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out_ts
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/gap_heat_transfer_sphere3D.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  file = sphere3D.e
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0
    emissivity_secondary = 0
    gap_conductivity = 5
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []
  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

(test/tests/kernels/hfem/lower-d-volumes.i)

[Problem]
  use_hash_table_matrix_assembly = true
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 3
    ny = 3
    dim = 2
  []
  build_all_side_lowerd_mesh = true
[]

[Variables]
  [u]
    order = THIRD
    family = MONOMIAL
    block = 0
  []
  [uhat]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambda]
    order = CONSTANT
    family = MONOMIAL
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambdab]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
[]

[AuxVariables]
  [v]
    order = CONSTANT
    family = MONOMIAL
    block = 0
    initial_condition = '1'
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = '1'
    block = 0
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
    coef = '1'
    block = 0
  []
  [reaction]
    type = Reaction
    variable = uhat
    rate = '1'
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [uhat_coupled]
    type = CoupledForce
    variable = uhat
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
    v = lambdab
    coef = '1'
  []
[]

[DGKernels]
  [surface]
    type = TestLowerDVolumes
    variable = u
    lowerd_variable = lambda
    l = 1
    n = 3
  []
[]

[BCs]
  [all]
    type = HFEMDirichletBC
    boundary = 'left right top bottom'
    variable = u
    lowerd_variable = lambdab
    uhat = uhat
  []
[]

[Postprocessors]
  [intu]
    type = ElementIntegralVariablePostprocessor
    variable = u
    block = 0
  []
  [lambdanorm]
    type = ElementL2Norm
    variable = lambda
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Outputs]
  [out]
    # we hide lambda because it may flip sign due to element
    # renumbering with distributed mesh
    type = Exodus
    hide = lambda
  []
[]

(test/tests/outputs/variables/output_vars_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD9
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = SECOND
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[AuxVariables]
  [./elemental]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./elemental_restricted]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./nodal]
    order = FIRST
    family = LAGRANGE
  [../]

  [./nodal_restricted]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[AuxKernels]
  [./elemental]
    type = ConstantAux
    variable = elemental
    value = 1
  [../]

  [./elemental_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 1
  [../]

  [./nodal]
    type = ConstantAux
    variable = elemental
    value = 2
  [../]

  [./nodal_restricted]
    type = ConstantAux
    variable = elemental_restricted
    value = 2
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ImplicitODEx
    variable = x
    y = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ImplicitODEy
    variable = y
    x = x
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 9
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 5
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 2
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  dt = 0.01
  num_steps = 1
[]

[Outputs]
  show = 'x u nodal elemental'
  [./out]
    type = Exodus
    elemental_as_nodal = true
    scalar_as_nodal = true
  [../]
[]

(test/tests/multiapps/secant/transient_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [time]
    type = CoefTimeDerivative
    variable = v
    Coefficient = 0.1
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Postprocessors]
  [vnorm]
    type = ElementL2Norm
    variable = v
  []
[]

[Executioner]
  type = Transient
  end_time = 10
  nl_abs_tol = 1e-12
  steady_state_detection = true
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  fixed_point_algorithm = 'secant'
[]

[Outputs]
  [csv]
    type = CSV
    start_step = 6
  []
  exodus = false
[]

(test/tests/preconditioners/fsp/nested-split.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []
[]

[Variables]
  [u][]
  [v][]
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []

  [conv_v]
    type = CoupledForce
    variable = v
    v = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  []

  [left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  []
[]

[Executioner]
  type = Steady
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'by_var'
    [by_var]
      splitting = 'u v'
      splitting_type  = multiplicative
      petsc_options_iname = '-ksp_type'
      petsc_options_value = 'fgmres'
    []
      [u]
        vars = 'u'
        splitting = 'u_diri u_bulk'
        splitting_type = multiplicative
        petsc_options_iname = '-ksp_type'
        petsc_options_value = 'fgmres'
      []
        [u_diri]
          vars = 'u'
          petsc_options = '-ksp_view_pmat'
          sides = 'left right'
        []
        [u_bulk]
          vars = 'u'
          petsc_options = '-ksp_view_pmat'
          petsc_options_iname = '-ksp_type'
          petsc_options_value = 'cg'
          unsides = 'left right'
        []
      [v]
        vars = 'v'
        splitting = 'v_diri v_bulk'
        splitting_type = multiplicative
        petsc_options_iname = '-ksp_type'
        petsc_options_value = 'fgmres'
      []
        [v_diri]
          vars = 'v'
          petsc_options = '-ksp_view_pmat'
          sides = 'left right'
        []
        [v_bulk]
          vars = 'v'
          petsc_options = '-ksp_view_pmat'
          petsc_options_iname = '-ksp_type'
          petsc_options_value = 'cg'
          unsides = 'left right'
        []
  []
[]

[Outputs]
  exodus = true
[]

(python/peacock/tests/common/fsp_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff_u conv_v diff_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  active = 'left_u right_u left_v'

  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]

  [./right_u]
    type = DirichletBC
    variable = u
    boundary = 2
    value = 100
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  [../]

  [./right_v]
    type = DirichletBC
    variable = v
    boundary = 2
    value = 0
  [../]
[]

[Executioner]
  type = Steady

  # This is setup automatically in MOOSE (SetupPBPAction.C)
  # petsc_options = '-snes_mf_operator'
  # petsc_options_iname = '-pc_type'
  # petsc_options_value =  'asm'
[]

[Preconditioning]
  active = 'FSP'

  [./FSP]
    type = FSP
    # It is the starting point of splitting
    topsplit = 'uv' # uv should match the following block name
    [./uv]
      splitting = 'u v' # u and v are the names of subsolvers
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      splitting_type  = additive
      # An approximate solution to the original system
      # | A_uu  A_uv | | u | _ |f_u|
      # |  0    A_vv | | v | - |f_v|
      #  is obtained by solving the following subsystems
      #  A_uu u = f_u and A_vv v = f_v
      # If splitting type is specified as schur, we may also want to set more options to
      # control how schur works using PETSc options
      # petsc_options_iname = '-pc_fieldsplit_schur_fact_type -pc_fieldsplit_schur_precondition'
      # petsc_options_value = 'full selfp'
    [../]
    [./u]
      vars = 'u'
      # PETSc options for this subsolver
      # A prefix will be applied, so just put the options for this subsolver only
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    [../]
    [./v]
      vars = 'v'
      # PETSc options for this subsolver
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    [../]
  [../]
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/multiapps/picard_failure/picard_sub_no_fail.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Postprocessors]
  [./elem_average_value]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere_mortar.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Problem]
  kernel_coverage_check = false
  material_coverage_check = false
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = file
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
  [lm]
    order = SECOND
    family = LAGRANGE
    block = 'secondary_lower'
  []
[]

[AuxVariables]
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    block = '1 2'
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = temp
    boundary = 2
    primary_emissivity = 0.0
    secondary_emissivity = 0.0
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = temp
    boundary = 2
    gap_conductivity = 5.0
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = temp
    primary_boundary = 3
    primary_subdomain = 10000
    secondary_boundary = 2
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(test/tests/multiapps/picard_sub_cycling/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v]
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  [../]
  [./time]
    type = TimeDerivative
    variable = u
  [../]
  [./force_u]
    type = CoupledForce
    variable = u
    v = v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
    sub_cycling = true
    interpolate_transfers = true
  [../]
[]

[Transfers]
  [./v_from_sub]
    type = MultiAppNearestNodeTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  [../]
  [./u_to_sub]
    type = MultiAppNearestNodeTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  [../]
[]

(test/tests/multiapps/secant/steady_main.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  parallel_type = replicated
  uniform_refine = 1
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
  []
[]

[Executioner]
  type = Steady

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'secant'
  fixed_point_max_its = 30
  transformed_variables = 'u'
[]

[Outputs]
  csv = true
  exodus = false
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'steady_sub.i'
    clone_parent_mesh = true

    transformed_variables = 'v'
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_cylinder.i)

rpv_core_gap_size = 0.15

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [core_gap_rpv]
    type = ConcentricCircleMeshGenerator
    num_sectors = 10
    radii = '${core_outer_radius} ${rpv_inner_radius} ${rpv_outer_radius}'
    rings = '2 1 2'
    has_outer_square = false
    preserve_volumes = true
    portion = full
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = core_gap_rpv
    primary_block = 1
    paired_block = 2
    new_boundary = 'core_outer'
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = rename_core_bdy
    primary_block = 3
    paired_block = 2
    new_boundary = 'rpv_inner'
  []
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 2
  []
  allow_renumbering = false
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'outer' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[ThermalContact]
  [RPV_gap]
    type = GapHeatTransfer
    gap_geometry_type = 'CYLINDER'
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    variable = Tsolid
    primary = 'core_outer'
    secondary = 'rpv_inner'
    gap_conductivity = 0.1
    quadrature = true
    cylinder_axis_point_1 = '0 0 0'
    cylinder_axis_point_2 = '0 0 5'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'outer' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady
  automatic_scaling = true
  compute_scaling_once = false
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  [Quadrature]
    side_order = seventh
  []
  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(test/tests/executioners/eigen_executioners/ne_deficient_b.i)

[Mesh]
 type = GeneratedMesh
 dim = 2
 xmin = 0
 xmax = 10
 ymin = 0
 ymax = 10
 elem_type = QUAD4
 nx = 8
 ny = 8

 uniform_refine = 0
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    eigen = true
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  [./rhs]
    type = CoupledEigenKernel
    variable = u
    v = v
  [../]
  [./src_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./homogeneous_u]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./homogeneous_v]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Executioner]
  type = NonlinearEigen

  bx_norm = 'vnorm'

  free_power_iterations = 2
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-50
  k0 = 1.0
  output_after_power_iterations = false

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
[]

[Postprocessors]
  [./vnorm]
    type = ElementIntegralVariablePostprocessor
    variable = v
    # execute on residual is important for nonlinear eigen solver!
    execute_on = linear
  [../]

  [./udiff]
    type = ElementL2Diff
    variable = u
    outputs = console
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = ne_deficient_b
  exodus = true
[]

(test/tests/auxkernels/nodal_aux_var/nodal_aux_var_test.i)

###########################################################
# This is a simple test of the AuxKernel System.
# Several explicit calculations are being done
# using spatial variables.
# This simulation demonstrates coupling, and dependency
# resolution. For simplicity all AuxVariables in this
# simulation are constant.
#
# @Requirement F5.30
###########################################################


[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  active = 'one five coupled'

  [./one]
    order = FIRST
    family = LAGRANGE
  [../]

  [./five]
    order = FIRST
    family = LAGRANGE
  [../]

  [./coupled]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff force'

  [./diff]
    type = Diffusion
    variable = u
  [../]

  #Coupling of nonlinear to Aux
  [./force]
    type = CoupledForce
    variable = u
    v = one
  [../]
[]

# AuxKernel System
[AuxKernels]
  #Simple Aux Kernel
  [./constant]
    variable = one
    type = ConstantAux
    value = 1
  [../]

  #Shows coupling of Aux to nonlinear
  [./coupled]
    variable = coupled
    type = CoupledAux
    value = 2
    coupled = u
  [../]

  [./five]
    type = ConstantAux
    variable = five
    boundary = '3 1'
    value = 5
  [../]

[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = out
  exodus = true
[]

(test/tests/restart/restart_transient_from_steady/restart_trans_with_2subs_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
  xmax = 0.3
  ymax = 0.3
[]

[AuxVariables]
  [power_density]
  []
[]

[Variables]
  [temp]
  []
[]

[Kernels]
  [heat_conduction]
     type = Diffusion
     variable = temp
  []
  [heat_ie]
    type = TimeDerivative
    variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  []
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '1 3'
    value = 100
  []
  [bc2]
    type = NeumannBC
    variable = temp
    boundary = '0 2'
    value = 10.0
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  start_time = 0
  end_time = 3
  dt = 1.0

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = '0'
    execute_on = 'initial timestep_end'
  []
  [pwr_density]
    type = ElementIntegralVariablePostprocessor
    block = '0'
    variable = power_density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/time_steppers/fixed_point_iteration_adaptive_dt/sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

(examples/ex11_prec/default.i)

[Mesh]
  file = square.e
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  [./forced]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_diffused]
    type = Diffusion
    variable = diffused
  [../]

  [./conv_forced]
    type = CoupledForce
    variable = forced
    v = diffused
  [../]

  [./diff_forced]
    type = Diffusion
    variable = forced
  [../]
[]

[BCs]
  #Note we have active on and neglect the right_forced BC
  active = 'left_diffused right_diffused left_forced'

  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'left'
    value = 0
  [../]

  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'right'
    value = 100
  [../]

  [./left_forced]
    type = DirichletBC
    variable = forced
    boundary = 'left'
    value = 0
  [../]

  [./right_forced]
    type = DirichletBC
    variable = forced
    boundary = 'right'
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(test/tests/problems/reference_residual_problem/abs_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'absref'
  extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]


[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nl_rel_tol = 1e-06
  verbose = true
[]

[Outputs]
  csv = true
[]

(test/tests/problems/reference_residual_problem/ad_abs_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[GlobalParams]
  absolute_value_vector_tags = 'absref'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'absref'
  extra_tag_vectors = 'absref'
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = ADTimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = ADCoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = ADTimeDerivative
    variable = v
  []
  [v_neg_force]
    type = ADBodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = ADBodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]


[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nl_rel_tol = 1e-06
  verbose = true
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_balance/large_gap_heat_transfer_test_sphere.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0.8
    emissivity_secondary = 0.8
    gap_conductivity = 0.1
    quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = false
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(modules/combined/examples/optimization/2d_mbb_pde_amr.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 30
    ny = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = pull
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 40
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

[Adaptivity]
  max_h_level = 2
  recompute_markers_during_cycles = true
  interval = 1
  cycles_per_step = 1
  marker = density_marker
  [Indicators]
    [density_jump]
      type = ValueJumpIndicator
      variable = mat_den_nodal
    []
  []
  [Markers]
    [density_marker]
      type = ErrorToleranceMarker
      indicator = density_jump
      coarsen = 0.1
      refine = 0.1
    []
  []
[]

(test/tests/auxkernels/nodal_aux_var/nodal_aux_init_test.i)

#
# Testing nodal aux variables that are computed only at the end of the time step
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 3
  ny = 3
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
    initial_condition = 5
  [../]
[]

[AuxVariables]
  active = 'aux1 aux2'

  [./aux1]
    order = FIRST
    family = LAGRANGE
    initial_condition = 2
  [../]

  [./aux2]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'ie diff force'

  [./ie]
    type = TimeDerivative
    variable = u
  [../]

  [./diff]
    type = Diffusion
    variable = u
  [../]

  #Coupling of nonlinear to Aux
  [./force]
    type = CoupledForce
    variable = u
    v = aux2
  [../]
[]

[AuxKernels]
  active = 'constant field'

  #Simple Aux Kernel
  [./constant]
    variable = aux1
    type = ConstantAux
    value = 1
    execute_on = nonlinear
  [../]

  #AuxKernel that is setup only before the simulation starts
  [./field]
    variable = aux2
    type = CoupledAux
    value = 2
    coupled = u
    execute_on = initial
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]
[]

[Executioner]
  type = Transient

  start_time = 0
  dt = 0.1
  num_steps = 2


  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
  file_base = out_init
[]

(test/tests/transfers/coord_transform/both-transformed/projection/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
  [v_elem]
    order = CONSTANT
    family = MONOMIAL
  []
  [w][]
  [w_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [w]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w
  []
  [w_elem]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w_elem
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppProjectionTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [from_sub_elem]
    type = MultiAppProjectionTransfer
    from_multi_app = sub
    source_variable = v_elem
    variable = v_elem
    execute_on = 'timestep_begin'
  []
  [to_sub]
    type = MultiAppProjectionTransfer
    to_multi_app = sub
    source_variable = w
    variable = w
    execute_on = 'timestep_begin'
  []
  [to_sub_elem]
    type = MultiAppProjectionTransfer
    to_multi_app = sub
    source_variable = w_elem
    variable = w_elem
    execute_on = 'timestep_begin'
  []
[]

(test/tests/transfers/multiapp_high_order_variable_transfer/sub_L2_Lagrange_conservative.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmax = 0.5
  ymax = 0.5
[]

[AuxVariables]
  [./power_density]
    family = L2_LAGRANGE
    order = FIRST
  [../]
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./heat_conduction]
     type = Diffusion
     variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  [../]
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '0 1 2 3'
    value = 450
  []
[]

[Executioner]
  type = Steady

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [./temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
  [../]
  [./pwr_density]
    type = ElementIntegralVariablePostprocessor
    block = '0'
    variable = power_density
    execute_on = 'transfer'
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/preconditioners/fsp/unside-by-var.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []
[]

[Variables]
  [u][]
  [v][]
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []

  [conv_v]
    type = CoupledForce
    variable = v
    v = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 100
  []

  [left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 0
  []
[]

[Executioner]
  type = Steady
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'top'
    [top]
      splitting = 'u_diri rest'
      splitting_type  = multiplicative
      petsc_options_iname = '-ksp_type'
      petsc_options_value = 'fgmres'
    []
      [u_diri]
        vars = 'u'
        sides = 'left right'
      []
      [rest]
        unside_by_var_var_name = 'u u'
        unside_by_var_boundary_name = 'left right'
      []
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/multiapps/secant/transient_main.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  parallel_type = replicated
  uniform_refine = 1
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [unorm]
    type = ElementL2Norm
    variable = u
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14

  fixed_point_algorithm = 'secant'
  fixed_point_max_its = 30
  transformed_variables = 'u'
[]

[Outputs]
  csv = true
  exodus = false
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'transient_sub.i'
    clone_parent_mesh = true
    execute_on = 'timestep_begin'
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
    execute_on = 'timestep_begin'
  []
[]

(test/tests/multiapps/picard_multilevel/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [v2]
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [coupled_force]
    type = CoupledForce
    variable = v
    v = v2
  []
  [td_v]
    type = TimeDerivative
    variable = v
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Postprocessors]
  # Accumulate the number of times 'timestep_end' is reached
  # (which is an indicator of the number of Picard iterations)
  [cumulative_picard_its_pp]
    type = TestPostprocessor
    test_type = custom_execute_on
    execute_on = 'timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = 1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub2]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub2.i
    sub_cycling = true
    execute_on = timestep_end
  []
[]

[Transfers]
  [v2]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub2
    source_variable = v
    variable = v2
  []
[]

(test/tests/misc/multiple-nl-systems/fully-coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
[]

[Variables]
  [u]
  []
  [v]
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/conservative_advection/no_upwinding_1D_coupled.i)

# ConservativeAdvection with upwinding_type = None
# Coupled a variable of (1, 0, 0) and see a pulse advect to the right
# Note there are overshoots and undershoots

!include no_upwinding_1D.i

[Variables]
  [coupled]
  []
[]

[ICs]
  [coupled]
    type = FunctionIC
    function = x
    variable = coupled
  []
[]

[Kernels]
  [coupled_udot]
    type = TimeDerivative
    variable = coupled
  []
  [coupled_kernel]
    type = CoupledForce
    v = 1
    coef = 1
    variable = coupled
  []
  [advection]
    velocity_as_variable_gradient = coupled
  []
[]

[Executioner]
  solve_type := NEWTON
[]

(examples/ex11_prec/smp.i)

[Mesh]
  file = square.e
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  [./forced]
    order = FIRST
    family = LAGRANGE
  [../]
[]

# The Preconditioning block
[Preconditioning]
  active = 'SMP_jfnk'

  [./SMP_jfnk]
    type = SMP

    off_diag_row    = 'forced'
    off_diag_column = 'diffused'


  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  [../]

  [./SMP_jfnk_full]
    type = SMP

    full = true


  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  [../]

  [./SMP_n]
    type = SMP

    off_diag_row    = 'forced'
    off_diag_column = 'diffused'


    solve_type = 'NEWTON'

    petsc_options_iname = '-pc_type'
    petsc_options_value = 'lu'
  [../]
[]

[Kernels]
  [./diff_diffused]
    type = Diffusion
    variable = diffused
  [../]

  [./conv_forced]
    type = CoupledForce
    variable = forced
    v = diffused
  [../]

  [./diff_forced]
    type = Diffusion
    variable = forced
  [../]
[]

[BCs]
  #Note we have active on and neglect the right_forced BC
  active = 'left_diffused right_diffused left_forced'
  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 1
    value = 0
  [../]

  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 2
    value = 100
  [../]

  [./left_forced]
    type = DirichletBC
    variable = forced
    boundary = 1
    value = 0
  [../]

  [./right_forced]
    type = DirichletBC
    variable = forced
    boundary = 2
    value = 0
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/errors/multiapp_bad_user_object.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
  [./AnotheruserObject]
    type = EmptyPostprocessor
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = AnotheruserObject
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/bcs/coupled_dirichlet_bc/coupled_dirichlet_bc.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./coupled_force_u]
    type = CoupledForce
    variable = u
    v = v
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]
[]

[BCs]
  # BCs on left
  # u: u=1
  # v: v=2
  [./left_u]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 1
  [../]

  [./left_v]
    type = DirichletBC
    variable = v
    boundary = 3
    value = 2
  [../]

  # BCs on right
  # u: c*u + u^2 + v^2 = 9
  # v: no flux
  [./right_u]
    type = CoupledDirichletBC
    variable = u
    boundary = 1
    value = 9
    v=v
  [../]
[]

[Preconditioning]
  [./precond]
    type = SMP
    # 'full = true' is required for computeOffDiagJacobian() to get
    # called.  If you comment this out, you should see that this test
    # requires a different number of linear and nonlinear iterations.
    full = true
  [../]
[]

[Executioner]
  type = Steady

  # solve_type = 'PJFNK'
  solve_type = 'NEWTON'

  # Uncomment next line to disable line search.  With line search enabled, you must use full=true with Newton or else it will fail.
  # line_search = 'none'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  nl_rel_tol = 1e-10
  l_tol = 1e-12
  nl_max_its = 10
[]

[Outputs]
  file_base = out
  exodus = true
[]

(modules/functional_expansion_tools/test/tests/standard_use/multiapp_print_coefficients.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3'
    physical_bounds = '0.0  10.0'
    x = Legendre
    print_when_set = true # Print coefficients when a MultiAppFXTransfer is executed
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
    print_state = true # Print after the FX coefficients are computer
    print_when_set = true # Print coefficients when a MultiAppFXTransfer is executed
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/multiapps/keep_aux_solution/picard_sub.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
  []
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[AuxKernels]
  [increment_u]
    type = ParsedAux
    execute_on = TIMESTEP_BEGIN
    expression = 'u + 1'
    coupled_variables = u
    variable = 'u'
  []
[]


[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
  show = 'u'
[]

(modules/porous_flow/examples/multiapp_fracture_flow/diffusion_multiapp/matrix_app_heat.i)

# Heat energy from this fracture app is transferred to the matrix app
[Mesh]
  [generate]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = 50.0
  []
[]

[Variables]
  [matrix_T]
  []
[]

[AuxVariables]
  [heat_from_frac]
  []
[]

[Kernels]
  [dot]
    type = TimeDerivative
    variable = matrix_T
  []
  [matrix_diffusion]
    type = Diffusion
    variable = matrix_T
  []
  [fromFrac]
    type = CoupledForce
    variable = matrix_T
    v = heat_from_frac
  []
[]

[Preconditioning]
  [entire_jacobian]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 100
  end_time = 100
[]


[Outputs]
  print_linear_residuals = false
[]

(test/tests/executioners/solve_type_linear/linear_with_full_smp.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
[]

[Variables]
  [u]
  []
  [v]
  []
[]

[Kernels]
  [u_diffusion]
    type = Diffusion
    variable = u
  []
  [v_diffusion]
    type = Diffusion
    variable = v
  []

  [u_reaction]
    type = Reaction
    variable = u
  []
  [v_reaction]
    type = Reaction
    variable = v
  []

  [u_force]
    type = BodyForce
    variable = u
  []
  [v_force]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[Executioner]
  type = Steady
  solve_type = LINEAR
[]

[Outputs]
  exodus = true
[]

(test/tests/misc/check_error/coupling_scalar_into_field.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
[]

[Variables]
  [./u]
  [../]
  [./a]
    family = SCALAR
    order = FIRST
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./coupled]
    type = CoupledForce
    variable = u
    # this should trigger an error message, 'v' should a field variable
    v = a
  [../]
[]

[ScalarKernels]
  [./alpha]
    type = AlphaCED
    variable = a
    value = 1
  [../]
[]

[BCs]
  [./all]
    type = DirichletBC
    boundary = 'left right top bottom'
    variable = u
    value = 0
  [../]
[]

[Executioner]
  type = Steady
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mbb_pde.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(modules/functional_expansion_tools/examples/3D_volumetric_Cartesian/main.i)

# Basic example coupling a master and sub app in a 3D Cartesian volume.
#
# The master app provides field values to the sub app via Functional Expansions, which then performs
# its calculations. The sub app's solution field values are then transferred back to the master app
# and coupled into the solution of the master app solution.
#
# This example couples Functional Expansions via AuxVariable.
#
# Note: this problem is not light, and may take a few minutes to solve.
[Mesh]
  type = GeneratedMesh
  dim = 3

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25

  zmin = 2.0
  zmax = 12.0
  nz = 35
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right front back'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4   5'
    physical_bounds = '0.0  10.0    1.0 11.0    2.0 12.0'
    x = Legendre
    y = Legendre
    z = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_rz_cylinder_mortar.i)

rpv_core_gap_size = 0.2

core_outer_radius = 2
rpv_inner_radius = '${fparse 2 + rpv_core_gap_size}'
rpv_outer_radius = '${fparse 2.5 + rpv_core_gap_size}'
rpv_width = '${fparse rpv_outer_radius - rpv_inner_radius}'

rpv_outer_htc = 10 # W/m^2/K
rpv_outer_Tinf = 300 # K

core_blocks = '1'
rpv_blocks = '3'

[Mesh]
  [gmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '${core_outer_radius} ${rpv_core_gap_size} ${rpv_width}'
    ix = '400 1 100'
    dy = 1
    iy = '5'
  []
  [set_block_id1]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '0 0 0'
    top_right = '${core_outer_radius} 1 0'
    block_id = 1
    location = INSIDE
  []
  [rename_core_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id1
    primary_block = 1
    paired_block = 0
    new_boundary = 'core_outer'
  []
  [set_block_id3]
    type = SubdomainBoundingBoxGenerator
    input = rename_core_bdy
    bottom_left = '${rpv_inner_radius} 0 0'
    top_right = '${rpv_outer_radius} 1 0'
    block_id = 3
    location = INSIDE
  []
  [rename_inner_rpv_bdy]
    type = SideSetsBetweenSubdomainsGenerator
    input = set_block_id3
    primary_block = 3
    paired_block = 0
    new_boundary = 'rpv_inner'
  []
  # comment out for test without gap
  [2d_mesh]
    type = BlockDeletionGenerator
    input = rename_inner_rpv_bdy
    block = 0
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rpv_inner'
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    input = 2d_mesh
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'core_outer'
    new_block_id = 10000
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Variables]
  [Tsolid]
    initial_condition = 500
  []
    [lm]
      order = FIRST
      family = LAGRANGE
      block = 'secondary_lower'
    []
[]

[Kernels]
  [heat_source]
    type = CoupledForce
    variable = Tsolid
    block = '${core_blocks}'
    v = power_density
  []
  [heat_conduction]
    type = HeatConduction
    variable = Tsolid
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = Tsolid
    boundary = 'right' # outer RPV
    coefficient = ${rpv_outer_htc}
    T_infinity = ${rpv_outer_Tinf}
  []
[]

[UserObjects]
  [radiation]
    type = GapFluxModelRadiation
    temperature = Tsolid
    boundary = 'rpv_inner'
    primary_emissivity = 0.8
    secondary_emissivity = 0.8
  []
  [conduction]
    type = GapFluxModelConduction
    temperature = Tsolid
    boundary = 'rpv_inner'
    gap_conductivity = 0.1
  []
[]

[Constraints]
  [ced]
    type = ModularGapConductanceConstraint
    variable = lm
    secondary_variable = Tsolid
    primary_boundary = 'core_outer'
    primary_subdomain = 10000
    secondary_boundary = 'rpv_inner'
    secondary_subdomain = 10001
    gap_flux_models = 'radiation conduction'
    gap_geometry_type = 'CYLINDER'
  []
[]

[AuxVariables]
  [power_density]
    block = '${core_blocks}'
    initial_condition = 50e3
  []
[]

[Materials]
  [simple_mat]
    type = HeatConductionMaterial
    thermal_conductivity = 34.6 # W/m/K
  []
[]

[Postprocessors]
  [Tcore_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Tcore_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${core_blocks}'
  []
  [Trpv_avg]
    type = ElementAverageValue
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_max]
    type = ElementExtremeValue
    value_type = max
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [Trpv_min]
    type = ElementExtremeValue
    value_type = min
    variable = Tsolid
    block = '${rpv_blocks}'
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = '${core_blocks}'
  []
  [rpv_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = Tsolid
    boundary = 'right' # outer RVP
    T_fluid = ${rpv_outer_Tinf}
    htc = ${rpv_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(rpv_convective_out - ptot) / ptot'
    pp_names = 'rpv_convective_out ptot'
  []
  [flux_from_core] # converges to ptot as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = core_outer
    diffusivity = thermal_conductivity
  []
  [flux_into_rpv] # converges to rpv_convective_out as the mesh is refined
    type = SideDiffusiveFluxIntegral
    variable = Tsolid
    boundary = rpv_inner
    diffusivity = thermal_conductivity
  []

[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = 'rpv_inner core_outer'
    variable = Tsolid
  []
[]

[Executioner]
  type = Steady

  petsc_options = '-snes_converged_reason -pc_svd_monitor'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                  1e-5          NONZERO               '
                        '1e-15'
  snesmf_reuse_base = false
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_max_its = 100

  line_search = none
[]

[Outputs]
  exodus = false
  csv = true
[]

(test/tests/multiapps/picard/steady_picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  [../]
[]

[Postprocessors]
  [./vnorm]
    type = ElementL2Norm
    variable = v
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mbb_pde_amr.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 30
    ny = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 40
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

[Adaptivity]
  max_h_level = 2
  recompute_markers_during_cycles = true
  interval = 1
  cycles_per_step = 1
  marker = density_marker
  [Indicators]
    [density_jump]
      type = ValueJumpIndicator
      variable = mat_den_nodal
    []
  []
  [Markers]
    [density_marker]
      type = ErrorToleranceMarker
      indicator = density_jump
      coarsen = 0.1
      refine = 0.1
    []
  []
[]

(test/tests/convergence/reference_residual_convergence/no_ref.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Variables]
  [u][]
  [v]
    scaling = 1e-6
  []
[]

[Functions]
  [ramp]
    type = ParsedFunction
    expression = 'if(t < 5, t - 5, 0) * x'
  []
[]

[Kernels]
  [u_dt]
    type = TimeDerivative
    variable = u
  []
  [u_coupled_rx]
    type = CoupledForce
    variable = u
    v = v
    coef = 1
  []

  [v_dt]
    type = TimeDerivative
    variable = v
  []
  [v_neg_force]
    type = BodyForce
    variable = v
    value = ${fparse -1 / 2}
    function = ramp
  []
  [v_force]
    type = BodyForce
    variable = v
    value = 1
    function = ramp
  []
[]

[Postprocessors]
  [u_avg]
    type = ElementAverageValue
    variable = u
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [v_avg]
    type = ElementAverageValue
    variable = v
    execute_on = 'TIMESTEP_END INITIAL'
  []
  [timestep]
    type = TimePostprocessor
    outputs = 'none'
  []
  [v_old]
    type = ElementAverageValue
    variable = v
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [u_old]
    type = ElementAverageValue
    variable = u
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [v_exact]
    type = ParsedPostprocessor
    pp_names = 'timestep v_old'
    expression = 't := if(timestep > 5, 5, timestep); (t^2 - 9 * t) / 8'
  []
  [u_exact]
    type = ParsedPostprocessor
    pp_names = 'u_old v_exact'
    expression = 'u_old + v_exact'
  []
[]

[Convergence]
  [conv]
    type = ReferenceResidualConvergence
    nl_rel_tol = 1e-6
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = none
  num_steps = 10
  nonlinear_convergence = conv
  verbose = true
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/scalar_transport/test/tests/ncp-lms/interpolated-ncp-lm-nodal-enforcement.i)

l=10
num_steps=10
nx=100

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
  elem_type = EDGE3
[]

[Variables]
  [u]
    order = SECOND
  []
  [lm]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = '${l} - x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = '-1'
  []
  [lm_coupled_force]
    type = CoupledForce
    variable = u
    v = lm
  []
[]

[NodalKernels]
  [positive_constraint]
    type = LowerBoundNodalKernel
    variable = lm
    v = u
    exclude_boundaries = 'left right'
  []
[]


[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = ${l}
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = 0
    variable = u
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          16                basic'
[]

[Outputs]
  exodus = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm
    execute_on = 'nonlinear timestep_end'
    value = 1e-12
  []
  [violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-12
    comparator = 'less'
  []
[]

(examples/ex12_pbp/ex12.i)

[Mesh]
  file = square.e
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  [./forced]
    order = FIRST
    family = LAGRANGE
  [../]
[]

# The Preconditioning block
[Preconditioning]
  [./PBP]
    type = PBP
    solve_order = 'diffused forced'
    preconditioner  = 'LU LU'
    off_diag_row    = 'forced'
    off_diag_column = 'diffused'
  [../]
[]

[Kernels]
  [./diff_diffused]
    type = Diffusion
    variable = diffused
  [../]

  [./conv_forced]
    type = CoupledForce
    variable = forced
    v = diffused
  [../]

  [./diff_forced]
    type = Diffusion
    variable = forced
  [../]
[]

[BCs]
  #Note we have active on and neglect the right_forced BC
  active = 'left_diffused right_diffused left_forced'

  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'left'
    value = 0
  [../]

  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'right'
    value = 100
  [../]

  [./left_forced]
    type = DirichletBC
    variable = forced
    boundary = 'left'
    value = 0
  [../]

  [./right_forced]
    type = DirichletBC
    variable = forced
    boundary = 'right'
    value = 0
  [../]
[]

[Executioner]
  type = Steady
  solve_type = JFNK
[]

[Outputs]
  exodus = true
[]

(examples/ex11_prec/fdp.i)

[Mesh]
  file = square.e
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  [./forced]
    order = FIRST
    family = LAGRANGE
  [../]
[]

# The Preconditioning block
[Preconditioning]
  active = 'FDP_jfnk'

  [./FDP_jfnk]
    type = FDP

    off_diag_row    = 'forced'
    off_diag_column = 'diffused'


  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


    petsc_options_iname = '-pc_type -mat_fd_coloring_err -mat_fd_type'
    petsc_options_value = 'lu       1e-6                 ds'
  [../]

  [./FDP_n]
    type = FDP

    off_diag_row    = 'forced'
    off_diag_column = 'diffused'


    solve_type = 'NEWTON'

    petsc_options_iname = '-pc_type -mat_fd_coloring_err -mat_fd_type'
    petsc_options_value = 'lu       1e-6                 ds'
  [../]

  [./FDP_n_full]
    type = FDP

    full = true


    solve_type = 'NEWTON'

    petsc_options_iname = '-pc_type -mat_fd_coloring_err -mat_fd_type'
    petsc_options_value = 'lu       1e-6                 ds'
  [../]
[]

[Kernels]
  [./diff_diffused]
    type = Diffusion
    variable = diffused
  [../]

  [./conv_forced]
    type = CoupledForce
    variable = forced
    v = diffused
  [../]

  [./diff_forced]
    type = Diffusion
    variable = forced
  [../]
[]

[BCs]
  #Note we have active on, and neglect the right_forced BC
  active = 'left_diffused right_diffused left_forced'

  [./left_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'left'
    value = 0
  [../]

  [./right_diffused]
    type = DirichletBC
    variable = diffused
    boundary = 'right'
    value = 100
  [../]

  [./left_forced]
    type = DirichletBC
    variable = forced
    boundary = 'left'
    value = 0
  [../]

  [./right_forced]
    type = DirichletBC
    variable = forced
    boundary = 'right'
    value = 0
  [../]
[]

[Executioner]
  type = Steady



[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/large_gap_heat_transfer_test_sphere.i)

sphere_outer_htc = 10 # W/m^2/K
sphere_outer_Tinf = 300 # K

[GlobalParams]
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = cyl2D.e
  []
  allow_renumbering = false
  coord_type = RZ
[]

[Functions]
  [temp]
    type = PiecewiseLinear
    x = '0   1'
    y = '100 200'
  []
[]

[Variables]
  [temp]
    initial_condition = 500
  []
[]

[AuxVariables]
  [gap_conductance]
    order = CONSTANT
    family = MONOMIAL
  []
  [power_density]
    block = 'fuel'
    initial_condition = 50e3
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = CoupledForce
    variable = temp
    block = 'fuel'
    v = power_density
  []
[]

[AuxKernels]
  [gap_cond]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_conductance
    boundary = 2
  []
[]

[Materials]
  [heat1]
    type = HeatConductionMaterial
    block = '1 2'
    specific_heat = 1.0
    thermal_conductivity = 34.6
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 3
    secondary = 2
    emissivity_primary = 0.0
    emissivity_secondary = 0.0
    gap_conductivity = 5
  #  quadrature = true
    gap_geometry_type = SPHERE
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [RPV_out_BC] # k \nabla T = h (T- T_inf) at RPV outer boundary
    type = ConvectiveFluxFunction # (Robin BC)
    variable = temp
    boundary = '4' # outer RPV
    coefficient = ${sphere_outer_htc}
    T_infinity = ${sphere_outer_Tinf}
  []
[]

[VectorPostprocessors]
  [NodalTemperature]
    type = NodalValueSampler
    sort_by = id
    boundary = '2 3'
    variable = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  dt = 1
  dtmin = 0.01
  end_time = 1

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-7

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Outputs]
  exodus = true
  csv = true
  [Console]
    type = Console
  []
[]

[Postprocessors]
  [temp_left]
    type = SideAverageValue
    boundary = 2
    variable = temp
  []

  [temp_right]
    type = SideAverageValue
    boundary = 3
    variable = temp
  []

  [flux_left]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 2
    diffusivity = thermal_conductivity
  []

  [flux_right]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 3
    diffusivity = thermal_conductivity
  []
  [ptot]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    block = 'fuel'
  []
  [sphere_convective_out]
    type = ConvectiveHeatTransferSideIntegral
    T_solid = temp
    boundary = '4' # outer RVP
    T_fluid = ${sphere_outer_Tinf}
    htc = ${sphere_outer_htc}
  []
  [heat_balance] # should be equal to 0 upon convergence
    type = ParsedPostprocessor
    expression = '(sphere_convective_out - ptot) / ptot'
    pp_names = 'sphere_convective_out ptot'
  []
[]

(modules/external_petsc_solver/test/tests/external_petsc_problem/moose_as_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./v]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./cf]
    type = CoupledForce
    coef = 10000
    variable = u
    v=v
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [./picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

(test/tests/multiapps/picard/picard_adaptive_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.1
    # cutback_factor, growth_factor, optimal_iterations, time_dt and time_t added through CLI args
  []
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_adaptive_sub.i
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/transfers/coord_transform/both-transformed/copy/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = -1
  ymax = 0
  nx = 10
  ny = 10
  alpha_rotation = 90
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
  [v_elem]
    order = CONSTANT
    family = MONOMIAL
  []
  [w][]
  [w_elem]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[ICs]
  [w]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w
  []
  [w_elem]
    type = FunctionIC
    function = 'cos(x)*sin(y)'
    variable = w_elem
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  verbose = true
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppCopyTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
  [from_sub_elem]
    type = MultiAppCopyTransfer
    from_multi_app = sub
    source_variable = v_elem
    variable = v_elem
    execute_on = 'timestep_begin'
  []
  [to_sub]
    type = MultiAppCopyTransfer
    to_multi_app = sub
    source_variable = w
    variable = w
    execute_on = 'timestep_begin'
  []
  [to_sub_elem]
    type = MultiAppCopyTransfer
    to_multi_app = sub
    source_variable = w_elem
    variable = w_elem
    execute_on = 'timestep_begin'
  []
[]

(modules/functional_expansion_tools/examples/3D_volumetric_Cartesian_different_submesh/main.i)

# Derived from the example '3D_volumetric_Cartesian' with the following differences:
#
#   1) The number of x and y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in x and z
[Mesh]
  type = GeneratedMesh
  dim = 3

  xmin = 0.0
  xmax = 10.0
  nx = 15

  ymin = 1.0
  ymax = 11.0
  ny = 25

  zmin = 2.0
  zmax = 12.0
  nz = 35
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./s_in] # Add in the contribution from the SubApp
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[Materials]
  [./Unobtanium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'top bottom left right front back'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '3   4   5'
    physical_bounds = '0.0  10.0    1.0 11.0    2.0 12.0'
    x = Legendre
    y = Legendre
    z = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/multiapps/picard_catch_up/sub_failing_problem.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
[]

[Variables]
  [./v]
  [../]
[]

[AuxVariables]
  [./u]
  [../]
[]

[Kernels]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./force_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  [../]
  [./right_v]
    type = FunctionDirichletBC
    variable = v
    boundary = right
    function = 't + 1'
  [../]
[]

[Problem]
  type = FailingProblem
  fail_steps = '2'
[../]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/functions/parsed/mms_transient_coupled.i)

###########################################################
# This is a simple test of the Function System. This
# test uses forcing terms produced from analytical
# functions of space and time to verify a solution
# using MMS.
#
# @Requirement F6.20
###########################################################


[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 1.0
  nx = 10
  ymin = 0.0
  ymax = 1.0
  ny = 10
  uniform_refine = 2
  elem_type = QUAD4
[]

[Variables]
  [./u]
  [../]
  [./v]
  [../]
[]

[Functions]
  [./v_left_bc]
    # Left-side boundary condition for v equation, v(0,y,t) = u(0.5,y,t). This is accomplished using a PointValue postprocessor, which is what this input file was designed to test.
    type = ParsedFunction
    expression = a
    symbol_values = u_midpoint
    symbol_names = a
  [../]
  [./u_mms_func]
    # MMS Forcing function for the u equation.
    type = ParsedFunction
    expression = ' 20*exp(20*t)*x*x*x-6*exp(20*t)*x-(2-0.125*exp(20*t))*sin(5/2*x*pi)-0.125*exp(20*t)-1
'
  [../]
  [./v_mms_func]
    # MMS forcing function for the v equation.
    type = ParsedFunction
    expression = -2.5*exp(20*t)*sin(5/2*x*pi)+2.5*exp(20*t)+25/4*(2-0.125*exp(20*t))*sin(5/2*x*pi)*pi*pi
  [../]
  [./u_right_bc]
    type = ParsedFunction
    expression = 3*exp(20*t) # \nabla{u}|_{x=1} = 3\exp(20*t)
  [../]
  [./u_exact]
    # Exact solution for the MMS function for the u variable.
    type = ParsedFunction
    expression = exp(20*t)*pow(x,3)+1
  [../]
  [./v_exact]
    # Exact MMS solution for v.
    type = ParsedFunction
    expression = (2-0.125*exp(20*t))*sin(5/2*pi*x)+0.125*exp(20*t)+1
  [../]
[]

[Kernels]
  # Strong Form:
  # \frac{\partial u}{\partial t} - \nabla \cdot 0.5 \nabla u - v = 0
  # \frac{\partial u}{\partial t} - \nabla \cdot \nabla v = 0
  #
  # BCs:
  # u(0,y,t) = 1
  # \nabla u |_{x=1} = 3\exp(20*t)
  # v(0,y,t) = u(0.5,y,t)
  # v(1,y,t) = 3
  # \nabla u |_{y=0,1} = 0
  # \nabla v |_{y=0,1} = 0
  #
  [./u_time]
    type = TimeDerivative
    variable = u
  [../]
  [./u_diff]
    type = Diffusion
    variable = u
  [../]
  [./u_source]
    type = CoupledForce
    variable = u
    v = v
  [../]
  [./v_diff]
    type = Diffusion
    variable = v
  [../]
  [./u_mms]
    type = BodyForce
    variable = u
    function = u_mms_func
  [../]
  [./v_mms]
    type = BodyForce
    variable = v
    function = v_mms_func
  [../]
  [./v_time]
    type = TimeDerivative
    variable = v
  [../]
[]

[BCs]
  [./u_left]
    type = DirichletBC
    variable = u
    boundary = left # x=0
    value = 1 # u(0,y,t)=1
  [../]
  [./u_right]
    type = FunctionNeumannBC
    variable = u
    boundary = right # x=1
    function = u_right_bc # \nabla{u}|_{x=1}=3\exp(20t)
  [../]
  [./v_left]
    type = FunctionDirichletBC
    variable = v
    boundary = left # x=0
    function = v_left_bc # v(0,y,t) = u(0.5,y,t)
  [../]
  [./v_right]
    type = DirichletBC
    variable = v
    boundary = right # x=1
    value = 3 # v(1,y,t) = 3
  [../]
[]

[Postprocessors]
  [./u_midpoint]
    type = PointValue
    variable = u
    point = '0.5 0.5 0'
    execute_on = 'initial timestep_begin timestep_end'
  [../]
  [./u_midpoint_exact]
    type = FunctionValuePostprocessor
    function = u_exact
    point = '0.5 0.5 0.0'
    execute_on = 'initial timestep_end'
  [../]
  [./u_error]
    type = ElementL2Error
    variable = u
    function = u_exact
    execute_on = 'initial timestep_end'
  [../]
  [./v_error]
    type = ElementL2Error
    variable = v
    function = v_exact
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.01

  solve_type = NEWTON

  end_time = 0.1
  scheme = crank-nicolson
[]

[Outputs]
  exodus = true
[]

[ICs]
  [./u_initial]
    # Use the MMS exact solution to compute the initial conditions.
    function = u_exact
    variable = u
    type = FunctionIC
  [../]
  [./v_exact]
    # Use the MMS exact solution to compute the initial condition.
    function = v_exact
    variable = v
    type = FunctionIC
  [../]
[]

(test/tests/restart/restart_transient_from_transient/pseudo_trans_with_2subs_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3
  xmax = 0.3
  ymax = 0.3
[]

[AuxVariables]
  [power_density]
  []
[]

[Variables]
  [temp]
  []
[]

[Kernels]
  [heat_timedt]
    type = TimeDerivative
    variable = temp
  []
  [heat_conduction]
     type = Diffusion
     variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  []
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '1 3'
    value = 100
  []
  [bc2]
    type = NeumannBC
    variable = temp
    boundary = '0 2'
    value = 10.0
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7

  end_time = 20
  dt = 2.0
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [pwr_density]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(test/tests/multiapps/relaxation/picard_relaxed_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 1
  []
  [inverse_v]
    initial_condition = 1
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = inverse_v
  []
[]

[AuxKernels]
  [invert_v]
    type = QuotientAux
    variable = inverse_v
    denominator = v
    numerator = 20.0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [Neumann_right]
    type = NeumannBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
  relaxation_factor = 0.95
  transformed_variables = u
[]

[Outputs]
  exodus = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = picard_relaxed_sub.i
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/outputs/console/multiapp/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force_v]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 1
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  nl_abs_tol = 1e-10
[]

(test/tests/multiapps/picard/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 5
  parallel_type = replicated
  uniform_refine = 1
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 20
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
    clone_parent_mesh = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-scaling.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [u][]
  [T][]
[]

[AuxVariables]
  [power][]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = CoefDiffusion
    variable = T
    coef = 1e30
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
    coef = 1e30
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  automatic_scaling = true
  petsc_options = '-pc_svd_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'svd'
  verbose = true
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/transfers/coord_transform/main-app.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 1
  xmax = 3
  nx = 20
  ny = 10
[]

[Variables]
  [u][]
[]

[AuxVariables]
  [v][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [force]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    positions = '1 0 0'
    input_files = 'sub-app.i'
    execute_on = 'timestep_begin'
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppNearestNodeTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
    execute_on = 'timestep_begin'
  []
[]

(test/tests/multiapps/picard_failure/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 0.1
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  active = 'sub' # will be modified by CLI overrides
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub.i
  []
  [sub_no_fail]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = picard_sub_no_fail.i
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/multiapps/relaxation/picard_parent.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  parallel_type = replicated
[]

[Variables]
  [u]
  []
[]

[AuxVariables]
  [v]
    initial_condition = 1
  []
  [inverse_v]
    initial_condition = 1
  []
[]

[Kernels]
  [diff]
    type = CoefDiffusion
    variable = u
    coef = 0.1
  []
  [time]
    type = TimeDerivative
    variable = u
  []
  [force_u]
    type = CoupledForce
    variable = u
    v = inverse_v
  []
[]

[AuxKernels]
  [invert_v]
    type = QuotientAux
    variable = inverse_v
    denominator = v
    numerator = 20.0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [Neumann_right]
    type = NeumannBC
    variable = u
    boundary = right
    value = 1
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_abs_tol = 1e-14
[]

[Outputs]
  exodus = true
  execute_on = 'INITIAL TIMESTEP_END'
[]

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    positions = '0 0 0'
    input_files = picard_relaxed_sub.i
    # The input was originally created with effectively no restore
    # see the changes made for #5554 then reverted in #28115
    no_restore = true
  []
[]

[Transfers]
  [v_from_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub
    source_variable = v
    variable = v
  []
  [u_to_sub]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub
    source_variable = u
    variable = u
  []
[]

(test/tests/restart/restart_transient_from_steady/steady_with_sub_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[AuxVariables]
  [./power_density]
  [../]
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./heat_conduction]
     type = Diffusion
     variable = temp
  [../]
  [./heat_ie]
    type = TimeDerivative
    variable = temp
  [../]
  [./heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = power_density
  [../]
[]

[BCs]
  [bc]
    type = DirichletBC
    variable = temp
    boundary = '0 1 2 3'
    value = 450
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  start_time = 0
  end_time = 10
  dt = 1.0

  nl_abs_tol = 1e-7
  nl_rel_tol = 1e-7
[]

[Postprocessors]
  [./temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]
  [./pwr_density]
    type = ElementIntegralVariablePostprocessor
    variable = power_density
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = true
[]

(modules/combined/examples/optimization/3d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 60
    ny = 20
    nz = 20
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    coord = '0 0 0; 0 0 10'
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 5'
  []
[]

[Variables]
  [disp_z]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(test/tests/multiapps/picard_multilevel/multilevel_dt_rejection/picard_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [v2]
  []
  [v3]
  []
  [w]
  []
[]

[AuxKernels]
  [set_w]
    type = NormalizationAux
    variable = w
    source_variable = v
    normal_factor = 0.1
  []
[]

[Kernels]
  [diff_v]
    type = Diffusion
    variable = v
  []
  [coupled_force]
    type = CoupledForce
    variable = v
    v = v2
  []
  [coupled_force2]
    type = CoupledForce
    variable = v
    v = v3
  []
  [td_v]
    type = TimeDerivative
    variable = v
  []
[]

[BCs]
  [left_v]
    type = FunctionDirichletBC
    variable = v
    boundary = left
    function = func
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 0
  []
[]

[Functions]
  [func]
    type = ParsedFunction
    expression = 'if(t < 2.5, 1, 1 / t)'
  []
[]

[Postprocessors]
  [picard_its]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  []
  [parent_time]
    type = Receiver
    execute_on = 'timestep_end'
  []
  [parent_dt]
    type = Receiver
    execute_on = 'timestep_end'
  []
  [time]
    type = TimePostprocessor
    execute_on = 'timestep_end'
  []
  [dt]
    type = TimestepSize
    execute_on = 'timestep_end'
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 2 # deliberately make it fail at 2 to test the time step rejection behavior
  nl_rel_tol = 1e-5 # loose enough to force multiple Picard iterations on this example
  l_tol = 1e-5 # loose enough to force multiple Picard iterations on this example
  fixed_point_rel_tol = 1e-8
  num_steps = 2
[]

[MultiApps]
  [sub2]
    type = TransientMultiApp
    positions = '0 0 0'
    input_files = picard_sub2.i
    execute_on = timestep_end
  []
[]

[Transfers]
  [v_to_v3]
    type = MultiAppGeneralFieldNearestLocationTransfer
    from_multi_app = sub2
    source_variable = v
    variable = v3
  []
  [w]
    type = MultiAppGeneralFieldNearestLocationTransfer
    to_multi_app = sub2
    source_variable = w
    variable = w
  []
  [time_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = time
    to_postprocessor = sub_time
    to_multi_app = sub2
  []
  [dt_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = dt
    to_postprocessor = sub_dt
    to_multi_app = sub2
  []
  [matser_time_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = time
    to_postprocessor = parent_time
    to_multi_app = sub2
  []
  [parent_dt_to_sub]
    type = MultiAppPostprocessorTransfer
    from_postprocessor = dt
    to_postprocessor = parent_dt
    to_multi_app = sub2
  []
[]

(test/tests/kernels/array_kernels/standard_save_in.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  []
  [subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0.5 0.5 0'
    top_right = '1 1 0'
    block_id = 1
  []
[]

[Variables]
  [u_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_1]
    order = FIRST
    family = L2_LAGRANGE
  []
[]

[AuxVariables]
  [u_diff_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_diff_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_vacuum_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_vacuum_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_dg_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_dg_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []

  [u_diff_diag_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_diff_diag_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_vacuum_diag_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_vacuum_diag_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_dg_diag_save_in_0]
    order = FIRST
    family = L2_LAGRANGE
  []
  [u_dg_diag_save_in_1]
    order = FIRST
    family = L2_LAGRANGE
  []
[]

[Kernels]
  [diff0]
    type = MatCoefDiffusion
    variable = u_0
    conductivity = dc
    save_in = u_diff_save_in_0
    diag_save_in = u_diff_diag_save_in_0
  []
  [diff1]
    type = Diffusion
    variable = u_1
    save_in = u_diff_save_in_1
    diag_save_in = u_diff_diag_save_in_1
  []
  [reaction0]
    type = CoefReaction
    variable = u_0
  []
  [reaction1]
    type = CoefReaction
    variable = u_1
  []
  [reaction01]
    type = CoupledForce
    variable = u_1
    v = u_0
    coef = 0.1
  []
[]

[DGKernels]
  [dgdiff0]
    type = DGDiffusion
    variable = u_0
    diff = dc
    sigma = 4
    epsilon = 1
    save_in = u_dg_save_in_0
    diag_save_in = u_dg_diag_save_in_0
  []
  [dgdiff1]
    type = DGDiffusion
    variable = u_1
    sigma = 4
    epsilon = 1
    save_in = u_dg_save_in_1
    diag_save_in = u_dg_diag_save_in_1
  []
[]

[BCs]
  [left0]
    type = VacuumBC
    variable = u_0
    boundary = 1
    save_in = u_vacuum_save_in_0
    diag_save_in = u_vacuum_diag_save_in_0
  []
  [left1]
    type = VacuumBC
    variable = u_1
    boundary = 1
    save_in = u_vacuum_save_in_1
    diag_save_in = u_vacuum_diag_save_in_1
  []

  [right0]
    type = PenaltyDirichletBC
    variable = u_0
    boundary = 2
    value = 1
    penalty = 4
  []
  [right1]
    type = PenaltyDirichletBC
    variable = u_1
    boundary = 2
    value = 2
    penalty = 4
  []
[]

[Materials]
  [dc0]
    type = GenericConstantMaterial
    block = 0
    prop_names = dc
    prop_values = 1
  []
  [dc1]
    type = GenericConstantMaterial
    block = 1
    prop_names = dc
    prop_values = 2
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Postprocessors]
  [intu0]
    type = ElementIntegralVariablePostprocessor
    variable = u_0
  []
  [intu1]
    type = ElementIntegralVariablePostprocessor
    variable = u_1
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  file_base = array_save_in_out
  exodus = true
[]

(test/tests/misc/multiple-nl-systems/restart_problem.i)

[Mesh]
  file = 'gold/restart_problem_out.e'
[]

[Problem]
  nl_sys_names = 'u v'
  allow_initial_conditions_with_restart = true
  solve = false
[]

[Variables]
  [u]
    solver_sys = 'u'
    initial_from_file_var = u
    initial_from_file_timestep = LATEST
  []
  [v]
    solver_sys = 'v'
    initial_from_file_var = v
    initial_from_file_timestep = LATEST
  []
[]

[Kernels]
  [diff_u]
    type = Diffusion
    variable = u
  []
  [diff_v]
    type = Diffusion
    variable = v
  []
  [force]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [left_u]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  []
  [right_u]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1.01
  []
  [left_v]
    type = DirichletBC
    variable = v
    boundary = left
    value = 0
  []
  [right_v]
    type = DirichletBC
    variable = v
    boundary = right
    value = 1.01
  []
[]

[Preconditioning]
  [u]
    nl_sys = 'u'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
  [v]
    nl_sys = 'v'
    type = SMP
    petsc_options = '-snes_monitor'
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = 'hypre boomeramg'
  []
[]

[Executioner]
  type = SteadySolve2
  solve_type = 'NEWTON'
  first_nl_sys_to_solve = 'u'
  second_nl_sys_to_solve = 'v'
[]
[Outputs]
  exodus = true
  execute_on = FINAL
[]

(test/tests/userobjects/side_user_object_no_boundary_error/lower_d_side_boundary.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 3
    ny = 3
    dim = 2
  []
  build_all_side_lowerd_mesh = true
[]

[Variables]
  [u]
    order = THIRD
    family = MONOMIAL
    block = 0
  []
  [uhat]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambda]
    order = CONSTANT
    family = MONOMIAL
    block = INTERNAL_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [lambdab]
    order = CONSTANT
    family = MONOMIAL
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
[]

[AuxVariables]
  [v]
    order = CONSTANT
    family = MONOMIAL
    block = 0
    initial_condition = '1'
  []
[]

[Kernels]
  [diff]
    type = MatDiffusion
    variable = u
    diffusivity = '1'
    block = 0
  []
  [source]
    type = CoupledForce
    variable = u
    v = v
    coef = '1'
    block = 0
  []
  [reaction]
    type = Reaction
    variable = uhat
    rate = '1'
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
  []
  [uhat_coupled]
    type = CoupledForce
    variable = uhat
    block = BOUNDARY_SIDE_LOWERD_SUBDOMAIN_EDGE2
    v = lambdab
    coef = '1'
  []
[]

[DGKernels]
  [surface]
    type = HFEMDiffusion
    variable = u
    lowerd_variable = lambda
  []
[]

[BCs]
  [all]
    type = HFEMDirichletBC
    boundary = 'left right top bottom'
    variable = u
    lowerd_variable = lambdab
    uhat = uhat
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Postprocessors]
  [avg]
    type = SideAverageValue
    boundary = 'left right top bottom'
  []
[]

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/parent_tr.i)

[Problem]
  restart_file_base = parent_ss_checkpoint_cp/LATEST
  force_restart = true

  # The auxiliary field has an initial condition
  allow_initial_conditions_with_restart = true
[]

[Mesh]
  file = parent_ss_checkpoint_cp/LATEST
[]

[Variables]
  [temp]
    # no initial condition for restart.
  []
[]

[AuxVariables]
  [power]
    order = FIRST
    family = L2_LAGRANGE
    initial_condition = 350
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
  [heat_source_fuel]
    type = CoupledForce
    variable = temp
    v = 'power'
  []
[]

[BCs]
  [all]
    type = DirichletBC
    variable = temp
    boundary = 'bottom top left right'
    value = 300
  []
[]

[Materials]
  [heat_material]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1000
    thermal_conductivity = 500
  []
  [density]
    type = Density
    density = 2000
  []
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'timestep_end'
  []
  [avg_power]
    type = ElementAverageValue
    variable = power
    execute_on = 'timestep_end'
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-02
  nl_rel_tol = 5e-05
  nl_abs_tol = 5e-05

  l_max_its = 50
  nl_max_its = 25

  start_time = 0
  end_time = 40
  dt = 10
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  color = true
  exodus = true
[]

[MultiApps]
  [bison]
    type = TransientMultiApp
    positions = '0 0 0'
    input_files = 'sub_tr.i'
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [to_bison_mechanics]
    type = MultiAppProjectionTransfer
    to_multi_app = bison
    variable = temp
    source_variable = temp
    execute_on = 'timestep_end'
  []
[]

(test/tests/multiapps/picard_multilevel/fullsolve_multilevel/sub_level1.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Variables]
  [v]
  []
[]

[AuxVariables]
  [u]
  []
  [w]
  []
[]

[Kernels]
  [time_derivative]
    type = TimeDerivative
    variable = v
  []
  [diffusion]
    type = Diffusion
    variable = v
  []
  [source]
    type = CoupledForce
    variable = v
    v = u
  []
[]

[BCs]
  [dirichlet0]
    type = DirichletBC
    variable = v
    boundary = '0'
    value = 0
  []
  [dirichlet]
    type = DirichletBC
    variable = v
    boundary = '2'
    value = 100
  []
[]

[Postprocessors]
  [avg_u]
    type = ElementAverageValue
    variable = u
    execute_on = 'initial linear'
  []
  [avg_v]
    type = ElementAverageValue
    variable = v
    execute_on = 'initial linear'
  []
  [avg_w]
    type = ElementAverageValue
    variable = w
    execute_on = 'initial linear'
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart '
  petsc_options_value = 'hypre boomeramg 100'

  end_time = 0.1
  dt = 0.02
[]

[MultiApps]
  [level2-]
    type = TransientMultiApp
    app_type = MooseTestApp
    positions = '0 0 0'
    input_files = sub_level2.i
    execute_on = 'timestep_end'
    # sub_cycling = true
  []
[]

[Transfers]
  [v_to_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = v
    variable = v
    to_multi_app = level2-
    execute_on = 'timestep_end'
  []
  [w_from_sub]
    type = MultiAppGeneralFieldShapeEvaluationTransfer
    source_variable = w
    variable = w
    from_multi_app = level2-
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
  # print_linear_residuals = false
[]

(modules/functional_expansion_tools/test/tests/errors/multiapp_incompatible_orders.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  xmin = 0.0
  xmax = 10.0
  nx = 15
[]

[Variables]
  [./m]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./s_in]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff_m]
    type = Diffusion
    variable = m
  [../]
  [./time_diff_m]
    type = TimeDerivative
    variable = m
  [../]
  [./s_in]
    type = CoupledForce
    variable = m
    v = s_in
  [../]
[]

[AuxKernels]
  [./reconstruct_s_in]
    type = FunctionSeriesToAux
    variable = s_in
    function = FX_Basis_Value_Main
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    variable = m
    value = 1
  [../]
[]

[BCs]
  [./surround]
    type = DirichletBC
    variable = m
    value = 1
    boundary = 'left right'
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '36'
    physical_bounds = '0.0  10.0'
    x = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Main]
    type = FXVolumeUserObject
    function = FX_Basis_Value_Main
    variable = m
  [../]
[]

[Postprocessors]
  [./average_value]
    type = ElementAverageValue
    variable = m
  [../]
  [./peak_value]
    type = ElementExtremeValue
    value_type = max
    variable = m
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.5
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  fixed_point_max_its = 30
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  fixed_point_rel_tol = 1e-8
  fixed_point_abs_tol = 1e-9
[]

[MultiApps]
  [./FXTransferApp]
    type = TransientMultiApp
    input_files = multiapp_sub.i
  [../]
[]

[Transfers]
  [./ValueToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Value_UserObject_Main
    multi_app_object_name = FX_Basis_Value_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
[]

(test/tests/transfers/multiapp_conservative_transfer/sub_conservative_transfer.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmin = 0.05
  xmax = 1.2
  ymin = 0.05
  ymax = 1.1
[]

[Variables]
  [./u]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./coupledforce]
    type = CoupledForce
    variable = u
    v = aux_u
  [../]
[]

[AuxVariables]
  [./aux_u]
    family = LAGRANGE
    order = FIRST
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Postprocessors]
  [./to_postprocessor]
    type = ElementIntegralVariablePostprocessor
    variable = aux_u
    execute_on = 'transfer'
  [../]
[]

[Problem]
  type = FEProblem
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/auxkernels/element_aux_var/element_high_order_aux_test.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./high_order]
    order = NINTH
    family = MONOMIAL
  [../]
  [./one]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  # Coupling of nonlinear to Aux
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./force]
    type = CoupledForce
    variable = u
    v = one
  [../]
[]

[AuxKernels]
  [./coupled_high_order]
    variable = high_order
    type = CoupledAux
    value = 2
    operator = +
    coupled = u
    execute_on = 'initial timestep_end'
  [../]
  [./constant]
    variable = one
    type = ConstantAux
    value = 1
    execute_on = 'initial timestep_end'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Postprocessors]
 [./int2_u]
   type = ElementL2Norm
   variable = u
   execute_on = 'initial timestep_end'
 [../]
 [./int2_ho]
   type = ElementL2Norm
   variable = high_order
   execute_on = 'initial timestep_end'
 [../]
 [./int_u]
   type = ElementIntegralVariablePostprocessor
   variable = u
   execute_on = 'initial timestep_end'
 [../]
 [./int_ho]
   type = ElementIntegralVariablePostprocessor
   variable = high_order
   execute_on = 'initial timestep_end'
 [../]
[]

[Outputs]
  [./ex_out]
    type = Exodus
    file_base = ho
    elemental_as_nodal = true
  [../]
[]

(test/tests/preconditioners/pbp/pbp_dg_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  elem_type = QUAD4
[]

[Variables]
  [./u]
    order = FIRST
    family = MONOMIAL
  [../]

  [./v]
    order = FIRST
    family = MONOMIAL
  [../]
[]

[Preconditioning]
  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'AMG AMG'
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./abs_u]
    type = Reaction
    variable = u
  [../]

  [./forcing_u]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  [./abs_v]
    type = Reaction
    variable = v
  [../]

  [./forcing_v]
    type = BodyForce
    variable = v
    function = forcing_fn
  [../]

  [./conv_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[DGKernels]
  [./dg_diff]
    type = DGDiffusion
    variable = u
    epsilon = -1
    sigma = 6
  [../]

  [./dg_diff_2]
    type = DGDiffusion
    variable = v
    epsilon = -1
    sigma = 6
  [../]
[]

[Functions]
  [./forcing_fn]
    type = ParsedFunction
    expression = 2*pow(e,-x-(y*y))*(1-2*y*y)
  [../]

  [./exact_fn]
    type = ParsedGradFunction
    value = pow(e,-x-(y*y))
    grad_x = -pow(e,-x-(y*y))
    grad_y = -2*y*pow(e,-x-(y*y))
  [../]
[]

[BCs]
  [./all_u]
    type = DGFunctionDiffusionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = exact_fn
    epsilon = -1
    sigma = 6
  [../]

  [./all_v]
    type = DGFunctionDiffusionDirichletBC
    variable = v
    boundary = '0 1 2 3'
    function = exact_fn
    epsilon = -1
    sigma = 6
  [../]
[]

[Problem]
  type = FEProblem
  error_on_jacobian_nonzero_reallocation = true
[]

[Executioner]
  type = Steady

  l_max_its = 10
  nl_max_its = 10

  solve_type = JFNK
[]

[Outputs]
  exodus = true
[]

(modules/thermal_hydraulics/include/kernels/CoupledForceRZ.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "CoupledForce.h"
#include "RZSymmetry.h"

/**
 * Source term proportional to the coupled variable in RZ coordinates
 */
class CoupledForceRZ : public CoupledForce, public RZSymmetry
{
public:
  CoupledForceRZ(const InputParameters & parameters);

protected:
  virtual Real computeQpResidual() override;
  virtual Real computeQpJacobian() override;
  virtual Real computeQpOffDiagJacobian(unsigned int jvar) override;

public:
  static InputParameters validParams();
};