HeatConductionTimeDerivative

density_name

Default:density

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Property name of the density material property

specific_heat

Default:specific_heat

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Name of the volumetric isobaric specific heat material property

density_name_dT

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Name of material property for the derivative of the density with respect to the variable.

specific_heat_dT

C++ Type:MaterialPropertyName

Unit:(no unit assumed)

Controllable:No

Description:Name of the material property for the derivative of the specific heat with respect to the variable.

(modules/heat_transfer/test/tests/transient_heat/transient_heat_derivatives.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 2
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

  [ie]
    type = HeatConductionTimeDerivative
    variable = temp
    specific_heat_dT = specific_heat_dT
    density_name_dT = density_dT
  []
[]

[Functions]
  [spheat]
    type = ParsedFunction
    expression = 't^4'
  []
  [thcond]
    type = ParsedFunction
    expression = 'exp(t)'
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 4
  []

  [top]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 1
  []
[]

[Materials]
  [constant]
    type = HeatConductionMaterial
    thermal_conductivity_temperature_function = thcond
    specific_heat_temperature_function = spheat
    temp = temp
  []
  [density]
    type = ParsedMaterial
    property_name = density
    coupled_variables = temp
    expression = 'temp^3 + 2/temp'
  []
  [density_dT]
    type = ParsedMaterial
    property_name = density_dT
    coupled_variables = temp
    expression = '3 * temp^2 - 2/temp/temp'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 1
  dt = .1
  nl_max_its = 10
  dtmin = .1
[]

[Postprocessors]
  [avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/transient_2d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    dim = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    specific_heat = specific_heat_layer
    density = density_layer
    heat_source = heat_source_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1 1 1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer specific_heat_layer heat_source_layer density_layer'
    prop_values = '0.05 1 10000 1'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 2
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/heat_transfer/tutorials/introduction/therm_step03.i)

#
# Single block thermal input with time derivative term
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step03.html
#

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

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[VectorPostprocessors]
  [t_sampler]
    type = LineValueSampler
    variable = T
    start_point = '0 0.5 0'
    end_point = '2 0.5 0'
    num_points = 20
    sort_by = x
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = therm_step03_out
    execute_on = final
  []
[]

(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
  [../]
[]

(modules/combined/test/tests/heat_convection/heat_convection_3d_test.i)

# Test cases for convective boundary conditions.
# Input file for htc_3dtest1

# TKLarson
# 11/02/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is concocted from an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004).  I turned a cylinder model into a rectangular parallelpiped,
# because I already had the cylinder model.
# The model is 3-d xyz coordinates.
#
# Brazillian Parallelpiped sample dimensions:
#       z = 10.3 cm, 0.103 m, (4 in)
#       y = 5.08 cm, 0.0508 m, (2 in)
#       x = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial parallelpiped temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use an h representative of natural convection conditions as the boundary condition for all sides
# on the parallelpiped.  Akin to putting the object in an oven and turning the oven on.
#  This is essentially a thermal soak.
#
# What we expect for this problem:
#  1) Use of h = 284 w/m^2-K (50 BTU/hr-ft^2-F) should cause the parallelpiped to slowly heat up to 477K.
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should show the convective BC is working as desired.
#
[Mesh]    # Mesh Start
# 5cm x 5cm x 10cm parallelpiped not so detailed mesh, 4 elements each end, 8 elements each long face
# Only one block (Block 1), all concrete
# Sideset definitions:
#    1 - xy plane at z=0,
#    2 - xy plane at z=-0.103,
#    3 - xz plane at y=0,
#    4 - yz plane at x=0,
#    5 - xz plane at y=0.0508,
#    6 - yz plane at x=0.0508
  file = heat_convection_3d_mesh.e
#
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial parallelpiped temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
#    type = HeatConductionRZ
     type = HeatConduction
     variable = temp
  [../]

  [./heat_ie]
#  type = HeatConductionTimeDerivativeRZ
  type = HeatConductionTimeDerivative
  variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer parallelpiped radius and ends
  [./convective_clad_surface]    # Convective Start
#         type = ConvectiveFluxRZ  # Convective flux, e.g. q'' = h*(Tw - Tf)
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3 4 5 6'  # BC applied on top, along length, and bottom
         variable = temp
   rate = 284.      # convective heat transfer coefficient (w/m^2-K)[50 BTU/hr-ft^2-F]
         initial = 294.26    # initial ambient (lab or oven) temperature (K)
         final = 477.6      # final ambient (lab or oven) temperature (K)
   duration = 600.    # length of time in seconds that it takes the ambient
           #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    #thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
    thermal_conductivity = 193.7  # this makes alpha 9.74e-5 m^2/s
          # above conductivity arbitrarily increased by 2 decades to make the
          #   object soak faster for the present purposes

  [../]

  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_3d
  exodus = true
[]      # Output END
#      # Input file END

(modules/heat_transfer/test/tests/joule_heating/transient_jouleheating.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 5
  ymax = 5
[]

[Variables]
  [./T]
    initial_condition = 293.0 #in K
  [../]
  [./elec]
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = T
  [../]
  [./HeatSrc]
    type = JouleHeatingSource
    variable = T
    elec = elec
  [../]
  [./electric]
    type = HeatConduction
    variable = elec
    diffusion_coefficient = electrical_conductivity
  [../]
[]

[BCs]
  [./lefttemp]
    type = DirichletBC
    boundary = left
    variable = T
    value = 293 #in K
  [../]
  [./elec_left]
    type = DirichletBC
    variable = elec
    boundary = left
    value = 1 #in V
  [../]
  [./elec_right]
    type = DirichletBC
    variable = elec
    boundary = right
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '397.48' #copper in W/(m K)
    block = 0
  [../]
  [./cp]
    type = GenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '385.0' #copper in J/(kg K)
    block = 0
  [../]
  [./rho]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '8920.0' #copper in kg/(m^3)
    block = 0
  [../]
  [./sigma] #copper is default material
    type = ElectricalConductivity
    temperature = T
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         101   preonly   ilu      1'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-4
  dt = 1
  end_time = 5
  automatic_scaling = true
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/combined/test/tests/heat_convection/heat_convection_3d_tf_test.i)

# Test cases for convective boundary conditions.
# Input file for htc_3dtest0

# TKLarson
# 11/02/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is concocted from an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004).  I turned a cylinder model into a rectangular parallelpiped,
# because I already had the cylinder model.
# The model is 3-d xyz coordinates.
#
# Brazillian Parallelpiped sample dimensions:
#       z = 10.3 cm, 0.103 m, (4 in)
#       y = 5.08 cm, 0.0508 m, (2 in)
#       x = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial parallelpiped temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a very large h (1000000) to make the surface temperature mimick the fluid temperature.

# What we expect for this problem:
#  1) Use of h = 1000000 should cause the parallelpiped surface temperature to track the fluid temperature
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should prove that the Tf boundary condition is ramping as desired.
# Note, we do the above because there is no way to plot a variable that is not on a mesh node!

[Mesh]    # Mesh Start
# 5cm x 5cm x 10cm parallelpiped not so detailed mesh, 4 elements each end, 8 elements each long face
# Only one block (Block 1), all concrete
# Sideset definitions:
#    1 - xy plane at z=0,
#    2 - xy plane at z=-0.103,
#    3 - xz plane at y=0,
#    4 - yz plane at x=0,
#    5 - xz plane at y=0.0508,
#    6 - yz plane at x=0.0508
  file = heat_convection_3d_mesh.e
#
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial parallelpiped temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
#    type = HeatConductionRZ
     type = HeatConduction
     variable = temp
  [../]

  [./heat_ie]
#  type = HeatConductionTimeDerivativeRZ
  type = HeatConductionTimeDerivative
  variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer parallelpiped radius and ends
  [./convective_clad_surface]    # Convective Start
#         type = ConvectiveFluxRZ  # Convective flux, e.g. q'' = h*(Tw - Tf)
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3 4 5 6'  # BC applied on top, along length, and bottom
         variable = temp
   rate = 1000000.   # convective heat transfer coefficient (w/m^2-K)[176000 "]
#         #  the above h is ~ infinity for present purposes
         initial = 294.26         # initial ambient (lab or oven) temperature (K)
         final = 477.6            # final ambient (lab or oven) temperature (K)
   duration = 600.   # length of time in seconds that it takes the ambient
         #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_3d_tf
  exodus = true
[]      # Output END
#      # Input file END

(modules/functional_expansion_tools/examples/2D_interface/sub.i)

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[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_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(tutorials/tutorial03_verification/app/test/tests/step04_mms/2d_main.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    ymax = 0
    ymin = -0.2
    nx = 20
    ny = 4
  []
[]

[Variables]
  [T]
  []
[]

[ICs]
  [T_O]
    type = ConstantIC
    variable = T
    value = 263.15
  []
[]

[Functions]
  [source]
    type = ParsedFunction
    symbol_names = 'hours shortwave kappa'
    symbol_values = '9     650      40'
    expression = 'shortwave*sin(0.5*x*pi)*exp(kappa*y)*sin(1/(hours*3600)*pi*t)'
  []
[]

[Kernels]
  [T_time]
    type = HeatConductionTimeDerivative
    variable = T
    density_name = 150
    specific_heat = 2000
  []
  [T_cond]
    type = HeatConduction
    variable = T
    diffusion_coefficient = 0.01
  []
  [T_source]
    type = HeatSource
    variable = T
    function = source
  []
[]

[BCs]
  [top]
    type = NeumannBC
    boundary = top
    variable = T
    value = -5
  []
  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = T
    value = 263.15
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  dt = 600 # 10 min
  end_time = 32400 # 9 hour
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/line.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 10
    xmax = 0.5
    xmin = -0.5
  []
  [left_line]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '-0.5 0 0'
    top_right = '0 0 0'
    block_id = 1
    block_name = 'left_line'
    location = INSIDE
  []
  [right_line]
    type = SubdomainBoundingBoxGenerator
    input = left_line
    bottom_left = '0 0 0'
    top_right = '0.5 0 0'
    block_id = 2
    block_name = 'right_line'
    location = INSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    # type = HeatConductionTimeDerivative
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
  []
  [heat_conduction]
    # type = HeatConduction
    type = TrussHeatConduction
    variable = temperature
    area = area
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.1
    execute_on = 'initial timestep_begin'
  []
[]

[Materials]
  [left_line]
    type = GenericConstantMaterial
    block = 'left_line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.1                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [right_line]
    type = GenericConstantMaterial
    block = 'right_line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '5.0e-3                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [center]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    num_points = 40
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_bar.i)

[Mesh]
  [whole]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 50
    nz = 1
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    zmin = -0.04
    zmax = 0.04
  []
  [bar]
    type = SubdomainBoundingBoxGenerator
    input = whole
    bottom_left = '-0.6 -0.05 -0.04'
    top_right = '0.6 0.05 0.04'
    block_id = 2
    block_name = 'bar'
    location = INSIDE
  []
  [block]
    type = SubdomainBoundingBoxGenerator
    input = bar
    bottom_left = '-0.6 -0.05 -0.04'
    top_right = '0.6 0.05 0.04'
    block_id = 1
    block_name = 'block'
    location = OUTSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'block'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'bar'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/block_w_bar'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/block_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 50
    nz = 1
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    zmin = -0.04
    zmax = 0.04
    boundary_name_prefix = block
  []
  [block_id]
    type = SubdomainIDGenerator
    input = block
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'block_id line_id'
  []
  [line_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'block line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'block'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'block'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.008
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'block'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'block'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'block_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/block_w_line'
    time_data = true
  []
[]

(modules/combined/test/tests/heat_convection/heat_convection_rz_test.i)

# Test cases for convective boundary conditions. TKLarson, 11/01/11, rev. 0.
# Input file for htc_2dtest1

# TKLarson
# 11/01/11
# Revision 0
#
# Goals of this test are:
#  1) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is based on an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004) (because I already had a version of the model).  While the
# Brazillian Cylinder test is for dynamic tensile testing of concrete, the model works for the present
# purposes.  The model is 2-d RZ coordinates.
#
# Brazillian Cylinder sample dimensions:
#       L = 20.3 cm, 0.203 m, (8 in)
#       r = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial cylinder temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a natural convection h (284 w/m^2-K (50 BTU/hr-ft^2-F)) on all faces of the cylinder.
# This is akin to putting the cylinder in an oven (nonconvection type) and turning the oven on.

# What we expect for this problem:
#  1) Use of h = 284 should cause the cylinder to slowly warm up
#  2) The fluid temperature should rise from initial (294 K) to final (477 K) in 600 s.
#  3) 1) and 2) should cause the cylinder to become soaked at 477.6 K after sufficient time(i.e. ~ 1/2 hr).
# This is a simple thermal soak problem.

[Mesh]    # Mesh Start
# 10cm x 20cm cylinder not so detailed mesh, 2 radial, 6 axial nodes
# Only one block (Block 1), all concrete
# Sideset 1 - top of cylinder, Sideset 2 - length of cylinder, Sideset 3 - bottom of cylinder
  file = heat_convection_rz_mesh.e
  coord_type = RZ
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial cylinder temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer cylinder radius and ends
  [./convective_clad_surface]    # Convective Start
         type = ConvectiveFluxBC  # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3'    # BC applied on top, along length, and bottom
         variable = temp
   rate = 284.      # (w/m^2-K)[50 BTU/hr/-ft^2-F]
          # the above h is a reasonable natural convection value
         initial = 294.26    # initial ambient (lab or oven) temperature (K)
         final = 477.6      # final ambient (lab or oven) temperature (K)
   duration = 600.    # length of time in seconds that it takes the ambient
          #   temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
#    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
#    thermal_conductivity = 19.37  # this makes alpha 9.74e-6 m^2/s
          # thermal conductivity arbitrarily increased by a decade to
          #    make the cylinder thermally soak faster (only for the purposes
          #    of this test problem
    thermal_conductivity = 193.7  # this makes alpha 9.74e-5 m^2/s
          # thermal conductivity arbitrarily increased by 2 decade to
          #    make the cylinder thermally soak faster (only for the purposes
          #    of this test problem

  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]

[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_rz
  exodus = true
[]      # Output END
#      # Input file END

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_force_step.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    data_file = blip.csv
    format = columns
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]


[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    incremental = true
    eigenstrain_names = thermal_expansion
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]


[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0
  num_steps = 50000

  end_time = 5.1e3
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e20
    force_step_every_function_point = true
    dt = 1e2
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/strip.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 1
    xmax = 0.5
    xmin = -0.5
    ymin = -0.05
    ymax = 0.05
  []
  [left_line]
    type = SubdomainBoundingBoxGenerator
    input = gmg
    bottom_left = '-0.5 0 0'
    top_right = '0 0 0'
    block_id = 1
    block_name = 'left_strip'
    location = INSIDE
  []
  [right_line]
    type = SubdomainBoundingBoxGenerator
    input = left_line
    bottom_left = '0 0 0'
    top_right = '0.5 0 0'
    block_id = 2
    block_name = 'right_strip'
    location = INSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [left_strip]
    type = GenericConstantMaterial
    block = 'left_strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.1                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [right_strip]
    type = GenericConstantMaterial
    block = 'right_strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '5.0e-3                  1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [center]
    type = LineValueSampler
    start_point = '-0.5 0 0'
    end_point = '0.5 0 0'
    num_points = 40
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/strip'
    time_data = true
  []
[]

(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/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'
  []
[]

(modules/heat_transfer/tutorials/introduction/therm_step03a.i)

#
# Single block thermal input with time derivative and volumetric heat source terms
# https://mooseframework.inl.gov/modules/heat_transfer/tutorials/introduction/therm_step03.html
#

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

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 1e4
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
[]

[Executioner]
  type = Transient
  end_time = 5
  dt = 1
[]

[VectorPostprocessors]
  [t_sampler]
    type = LineValueSampler
    variable = T
    start_point = '0 0.5 0'
    end_point = '2 0.5 0'
    num_points = 20
    sort_by = x
  []
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = therm_step03a_out
    execute_on = final
  []
[]

(modules/combined/test/tests/inelastic_strain/creep/creep_nl1.i)

#
# Test for effective strain calculation.
# Boundary conditions from NAFEMS test NL1
#
# This is not a verification test. This is the creep analog of the same test
# in the elas_plas directory. Instead of using the IsotropicPlasticity
# material model this test uses the PowerLawCreep material model.
#
[GlobalParams]
  temperature = temp
  order = FIRST
  family = LAGRANGE
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
[]

[Mesh]
  file = one_elem2.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./temp]
    initial_condition = 600.0
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pressure]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./elastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./tot_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./eff_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
    decomposition_method = EigenSolution
  [../]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
    execute_on = timestep_end
  [../]
  [./pressure]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = pressure
    scalar_type = Hydrostatic
    execute_on = timestep_end
  [../]
  [./elastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./elastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./creep_strain_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  [../]
  [./tot_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./tot_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./tot_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = tot_strain_zz
    index_i = 2
    index_j = 2
  [../]
  [./eff_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = eff_creep_strain
  [../]
[]

[Functions]
  [./appl_dispy]
    type = PiecewiseLinear
    x = '0     1.0     2.0'
    y = '0.0 0.25e-4 0.50e-4'
  [../]
[]

[BCs]
  [./side_x]
    type = DirichletBC
    variable = disp_x
    boundary = 101
    value = 0.0
  [../]
  [./origin_x]
    type = DirichletBC
    variable = disp_x
    boundary = 103
    value = 0.0
  [../]
  [./bot_y]
    type = DirichletBC
    variable = disp_y
    boundary = 102
    value = 0.0
  [../]
  [./origin_y]
    type = DirichletBC
    variable = disp_y
    boundary = 103
    value = 0.0
  [../]
  [./top_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1
    function = appl_dispy
  [../]
  [./temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2'
    value = 600.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 250e9
    poissons_ratio = 0.25
  [../]
  [./strain]
    type = ComputePlaneFiniteStrain
    block = 1
  [../]
  [./radial_return_stress]
    type = ComputeMultipleInelasticStress
    block = 1
    inelastic_models = 'powerlawcrp'
  [../]
  [./powerlawcrp]
    type = PowerLawCreepStressUpdate
    block = 1
    coefficient = 3.125e-14
    n_exponent = 5.0
    m_exponent = 0.0
    activation_energy = 0.0
  [../]
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  [../]
  [./density]
    type = Density
    block = 1
    density = 1.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12
  l_tol = 1e-6
  l_max_its = 100
  nl_max_its = 20

  dt = 1.0
  start_time = 0.0
  num_steps = 100
  end_time = 2.0
[]

[Postprocessors]
  [./stress_xx]
    type = ElementAverageValue
    variable = stress_xx
  [../]
  [./stress_yy]
    type = ElementAverageValue
    variable = stress_yy
  [../]
  [./stress_zz]
    type = ElementAverageValue
    variable = stress_zz
  [../]
  [./stress_xy]
    type = ElementAverageValue
    variable = stress_xy
  [../]
  [./vonmises]
    type = ElementAverageValue
    variable = vonmises
  [../]
  [./pressure]
    type = ElementAverageValue
    variable = pressure
  [../]
  [./el_strain_xx]
    type = ElementAverageValue
    variable = elastic_strain_xx
  [../]
  [./el_strain_yy]
    type = ElementAverageValue
    variable = elastic_strain_yy
  [../]
  [./el_strain_zz]
    type = ElementAverageValue
    variable = elastic_strain_zz
  [../]
  [./crp_strain_xx]
    type = ElementAverageValue
    variable = creep_strain_xx
  [../]
  [./crp_strain_yy]
    type = ElementAverageValue
    variable = creep_strain_yy
  [../]
  [./crp_strain_zz]
    type = ElementAverageValue
    variable = creep_strain_zz
  [../]
  [./eff_creep_strain]
    type = ElementAverageValue
    variable = eff_creep_strain
  [../]
  [./tot_strain_xx]
    type = ElementAverageValue
    variable = tot_strain_xx
  [../]
  [./tot_strain_yy]
    type = ElementAverageValue
    variable = tot_strain_yy
  [../]
  [./tot_strain_zz]
    type = ElementAverageValue
    variable = tot_strain_zz
  [../]
  [./disp_x1]
    type = NodalVariableValue
    nodeid = 0
    variable = disp_x
  [../]
  [./disp_x4]
    type = NodalVariableValue
    nodeid = 3
    variable = disp_x
  [../]
  [./disp_y1]
    type = NodalVariableValue
    nodeid = 0
    variable = disp_y
  [../]
  [./disp_y4]
    type = NodalVariableValue
    nodeid = 3
    variable = disp_y
  [../]
  [./_dt]
    type = TimestepSize
  [../]
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/functional_expansion_tools/examples/2D_interface_different_submesh/main.i)

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideDiffusiveFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  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
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

(modules/combined/tutorials/introduction/thermal_mechanical_contact/thermomech_cont_step02.i)

#
# Three shell thermo mechanical contact
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/step02.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  block = '0 1 2'
[]

[Mesh]
  # inner cylinder
  [inner]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmax = 1
    ymin = -1.75
    ymax = 1.75
    boundary_name_prefix = inner
  []

  # middle shell with subdomain ID 1
  [middle_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmin = 1.1
    xmax = 2.1
    ymin = -2.5
    ymax = 2.5
    boundary_name_prefix = middle
    boundary_id_offset = 4
  []
  [middle]
    type = SubdomainIDGenerator
    input = middle_elements
    subdomain_id = 1
  []

  # outer shell with subdomain ID 2
  [outer_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 48
    xmin = 2.2
    xmax = 3.2
    ymin = -3
    ymax = 3
    boundary_name_prefix = outer
    boundary_id_offset = 8
  []
  [outer]
    type = SubdomainIDGenerator
    input = outer_elements
    subdomain_id = 2
  []

  [collect_meshes]
    type = MeshCollectionGenerator
    inputs = 'inner middle outer'
  []

  # add set of 3 nodes to remove rigid body modes for y-translation in each block
  [pin]
    type = ExtraNodesetGenerator
    input = collect_meshes
    new_boundary = pin
    coord = '0 0 0; 1.6 0 0; 2.7 0 0'
  []

  patch_update_strategy = iteration

  # switch to an axisymmetric coordinate system
  coord_type = RZ
[]

[Variables]
  # temperature field variable (first order Lagrange by default)
  [T]
  []
  # temperature lagrange multipliers
  [Tlm1]
    block = 'inner_gap_secondary_subdomain'
  []
  [Tlm2]
    block = 'outer_gap_secondary_subdomain'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [dTdt]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    eigenstrain_names = thermal
    generate_output = 'vonmises_stress stress_xx strain_xx stress_yy strain_yy'
    volumetric_locking_correction = true
    temperature = T
  []
[]

[Contact]
  [inner_gap]
    primary = middle_left
    secondary = inner_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
  [outer_gap]
    primary = outer_left
    secondary = middle_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
[]

[Constraints]
  # thermal contact constraint
  [Tlm1]
    type = GapConductanceConstraint
    variable = Tlm1
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = middle_left
    primary_subdomain = inner_gap_secondary_subdomain
    secondary_boundary = inner_right
    secondary_subdomain = inner_gap_primary_subdomain
  []
  [Tlm2]
    type = GapConductanceConstraint
    variable = Tlm2
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = outer_left
    primary_subdomain = outer_gap_secondary_subdomain
    secondary_boundary = middle_right
    secondary_subdomain = outer_gap_primary_subdomain
  []
[]

[BCs]
  [center_axis_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 'inner_left'
    value = 0
  []
  [y_translation_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'pin'
    value = 0
  []
  [heat_center]
    type = FunctionDirichletBC
    variable = T
    boundary = 'inner_left'
    function = t*40
  []
  [cool_right]
    type = DirichletBC
    variable = T
    boundary = 'outer_right'
    value = 0
  []
[]

[Materials]
  [eigen_strain_inner]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-3
    stress_free_temperature = 0
    block = 0
  []
  [eigen_strain_middle]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 2e-4
    stress_free_temperature = 0
    block = 1
  []
  [eigen_strain_outer]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0
    block = 2
  []

  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  # thermal properties
  [thermal_conductivity_0]
    type = HeatConductionMaterial
    thermal_conductivity = 50
    specific_heat = 1
    block = 0
  []
  [thermal_conductivity_1]
    type = HeatConductionMaterial
    thermal_conductivity = 5
    specific_heat = 1
    block = 1
  []
  [thermal_conductivity_2]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    specific_heat = 1
    block = 2
  []
  [density]
    type = Density
    density = 1
  []
[]

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

# [Debug]
#   show_var_residual_norms = true
# []

[Executioner]
  type = Transient
  solve_type = PJFNK
  line_search = none
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero              '
  snesmf_reuse_base = false
  end_time = 7
  dt = 0.05

  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-50

  [Predictor]
    type = SimplePredictor
    scale = 0.5
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = 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
  [../]
[]

(tutorials/tutorial03_verification/app/test/tests/step03_analytical/1d_analytical.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    xmax = 0.03
    nx = 200
  []
[]

[Variables]
  [T]
  []
[]

[ICs]
  [T_O]
    type = ConstantIC
    variable = T
    value = 300
  []
[]

[Kernels]
  [T_time]
    type = HeatConductionTimeDerivative
    variable = T
    density_name = 7800
    specific_heat = 450
  []
  [T_cond]
    type = HeatConduction
    variable = T
    diffusion_coefficient = 80.2
  []
[]

[BCs]
  [left]
    type = NeumannBC
    variable = T
    boundary = left
    value = 7e5
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON
  dt = 0.01
  end_time = 1
[]

[Outputs]
  exodus = true
  csv = true
[]

[Functions]
  [T_exact]
    type = ParsedFunction
    symbol_names = 'k    rho  cp  T0  qs'
    symbol_values = '80.2 7800 450 300 7e5'
    expression = 'T0 + '
            'qs/k*(2*sqrt(k/(rho*cp)*t/pi)*exp(-x^2/(4*k/(rho*cp)*(t+1e-50))) - '
            'x*(1-erf(x/(2*sqrt(k/(rho*cp)*(t+1e-50))))))'
  []
[]

[Postprocessors]
  [error]
    type = NodalL2Error
    variable = T
    function = T_exact
  []
  [h]
    type = AverageElementSize
  []
[]


[VectorPostprocessors]
  [T_exact]
    type = LineFunctionSampler
    functions = T_exact
    start_point = '0 0 0'
    end_point = '0.03 0 0'
    num_points = 200
    sort_by = x
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [T_simulation]
    type = LineValueSampler
    variable = T
    start_point = '0 0 0'
    end_point = '0.03 0 0'
    num_points = 200
    sort_by = x
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(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
  [../]
[]

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

# Derived from the example '3D_volumetric_Cartesian' with the following differences:
#
#   1) The coupling is performed via BodyForce instead of the
#      FunctionSeriesToAux+CoupledForce approach
[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
  [../]
[]

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

[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/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    volumetric_locking_correction = true
    incremental = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
  [./bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 300
  [../]
  [./top_bottom_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = '1'
    value = 0
  [../]
  [./top_bottom_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0
  [../]
  [./top_bottom_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = '1'
    value = 0
  [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0
  num_steps = 50000
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

(modules/heat_transfer/test/tests/verify_against_analytical/1D_transient.i)

# This test solves a 1D transient heat equation
# The error is caclulated by comparing to the analytical solution
# The problem setup and analytical solution are taken from "Advanced Engineering
# Mathematics, 10th edition" by Erwin Kreyszig.
# http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364
# It is Example 1 in section 12.6 on page 561

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 160
  xmax = 80
[]

[Variables]
  [./T]
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '100*sin(pi*x/80)'
  [../]
[]

[Kernels]
  [./HeatDiff]
    type = HeatConduction
    variable = T
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = T
  [../]
[]

[BCs]
  [./sides]
    type = DirichletBC
    variable = T
    boundary = 'left right'
    value = 0
  [../]
[]

[Materials]
  [./k]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity'
    prop_values = '0.95' #copper in cal/(cm sec C)
  [../]
  [./cp]
    type = GenericConstantMaterial
    prop_names = 'specific_heat'
    prop_values = '0.092' #copper in cal/(g C)
  [../]
  [./rho]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = '8.92' #copper in g/(cm^3)
  [../]
[]

[Postprocessors]
  [./error]
    type = NodalL2Error
    function = '100*sin(pi*x/80)*exp(-0.95/(0.092*8.92)*pi^2/80^2*t)'
    variable = T
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  l_tol = 1e-6
  dt = 2
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_hex_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 5
  ny = 1
  nz = 1
  xmin = 0.0
  xmax = 0.1
  ymin = 0.0
  ymax = 0.01
  zmin = 0.0
  zmax = 0.01
  elem_type = HEX8
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 19
  [../]
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/transient_heat/transient_heat_derivatives.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 2
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

  [ie]
    type = HeatConductionTimeDerivative
    variable = temp
    specific_heat_dT = specific_heat_dT
    density_name_dT = density_dT
  []
[]

[Functions]
  [spheat]
    type = ParsedFunction
    expression = 't^4'
  []
  [thcond]
    type = ParsedFunction
    expression = 'exp(t)'
  []
[]

[BCs]
  [bottom]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 4
  []

  [top]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 1
  []
[]

[Materials]
  [constant]
    type = HeatConductionMaterial
    thermal_conductivity_temperature_function = thcond
    specific_heat_temperature_function = spheat
    temp = temp
  []
  [density]
    type = ParsedMaterial
    property_name = density
    coupled_variables = temp
    expression = 'temp^3 + 2/temp'
  []
  [density_dT]
    type = ParsedMaterial
    property_name = density_dT
    coupled_variables = temp
    expression = '3 * temp^2 - 2/temp/temp'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 1
  dt = .1
  nl_max_its = 10
  dtmin = .1
[]

[Postprocessors]
  [avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_line.i)

[Mesh]
  parallel_type = 'replicated'
  [rectangle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
    boundary_name_prefix = rectangle
  []
  [rectangle_id]
    type = SubdomainIDGenerator
    input = rectangle
    subdomain_id = 1
  []
  [line]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -0.5
    xmax = 0.5
    nx = 10
    boundary_name_prefix = line
    boundary_id_offset = 10
  []
  [line_id]
    type = SubdomainIDGenerator
    input = line
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'rectangle_id line_id'
  []
  [blcok_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'rectangle line'
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
    block = 'rectangle'
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 'rectangle'
  []
  [time_derivative_line]
    type = TrussHeatConductionTimeDerivative
    variable = temperature
    area = area
    block = 'line'
  []
  [heat_conduction_line]
    type = TrussHeatConduction
    variable = temperature
    area = area
    block = 'line'
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    variable = area
    value = 0.1 # strip thickness
    execute_on = 'initial timestep_begin'
  []
[]

[Constraints]
  [equalvalue]
    type = EqualValueEmbeddedConstraint
    secondary = 'line'
    primary = 'rectangle'
    penalty = 1e6
    formulation = kinematic
    primary_variable = temperature
    variable = temperature
  []
[]

[Materials]
  [rectangle]
    type = GenericConstantMaterial
    block = 'rectangle'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [line]
    type = GenericConstantMaterial
    block = 'line'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'rectangle_right line_right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/rectangle_w_line'
    time_data = true
  []
[]

(modules/heat_transfer/test/tests/truss_heat_conduction/rectangle_w_strip.i)

[Mesh]
  [rectangle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -1.25
    ymax = 1.25
  []
  [strip]
    type = SubdomainBoundingBoxGenerator
    input = rectangle
    bottom_left = '-0.5 -0.05 0'
    top_right = '0.5 0.05 0'
    block_id = 2
    block_name = 'strip'
    location = INSIDE
  []
  [top_bottom_layers]
    type = SubdomainBoundingBoxGenerator
    input = strip
    bottom_left = '-0.5 -0.05 0'
    top_right = '0.5 0.05 0'
    block_id = 1
    block_name = 'rectangle'
    location = OUTSIDE
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_conduction]
    type = HeatConduction
    variable = temperature
  []
[]

[Materials]
  [block]
    type = GenericConstantMaterial
    block = 'rectangle'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '1.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
  [strip]
    type = GenericConstantMaterial
    block = 'strip'
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '10.0                 1.0           1.0' # W/(cm K), J/(g K), g/cm^3
  []
[]

[BCs]
  [right]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'right'
    function = '10*t'
  []
[]

[VectorPostprocessors]
  [x_n0_25]
    type = LineValueSampler
    start_point = '-0.25 0 0'
    end_point = '-0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
  [x_0_25]
    type = LineValueSampler
    start_point = '0.25 0 0'
    end_point = '0.25 1.25 0'
    num_points = 100
    variable = 'temperature'
    sort_by = id
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 1
  end_time = 1
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'csv/rectangle_w_strip'
    time_data = true
  []
[]

(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/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/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change_restart2.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

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

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    volumetric_locking_correction = true
    incremental = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  num_steps = 50000
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
[]

[Problem]
  restart_file_base = adapt_tstep_function_change_restart1_checkpoint_cp/0065
[]

(modules/combined/test/tests/heat_convection/heat_convection_rz_tf_test.i)

# Test cases for convective boundary conditions. TKLarson, 11/01/11, rev. 0.
# Input file for htc_2dtest0

# TKLarson
# 11/01/11
# Revision 0
#
# Goals of this test are:
#  1) show that the 'fluid' temperature for convective boundary condition
#    is behaving as expected/desired
#  2) show that expected results ensue from application of convective boundary conditions
# Convective boundary condition:
#  q = h*A*(Tw - Tf)
#  where
#    q - heat transfer rate (w)
#    h - heat transfer coefficient (w/m^2-K)
#    A - surface area (m^2)
#    Tw - surface temperature (K)
#    Tf - fluid temperature adjacent to the surface (K)
# The heat transfer coefficient (h) is input as a variable called 'rate'
# Tf is a two valued function specified by 'initial' and 'final' along with a variable
#  called 'duration,' the length of time in seconds that it takes initial to linearly ramp
#  to 'final.'

# The mesh for this test case is based on an ASTM standard for the so-called Brazillian Cylinder test
# (ASTM International, Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete
# Specimens, C 496/C 496M-04, 2004) (because I already had a version of the model).  While the
# Brazillian Cylinder test is for dynamic tensile testing of concrete, the model works for the present
# purposes.  The model is 2-d RZ coordinates.
#
# Brazillian Cylinder sample dimensions:
#       L = 20.3 cm, 0.203 m, (8 in)
#       r = 5.08 cm, 0.0508 m, (2 in)

# Material properties are:
#   density = 2405.28 km/m^3
#   specific heat = 826.4 J/kg-K
#   thermal conductivity 1.937 w/m-K
#  alpha (thermal conductivity/(density*specific heat) is then 9.74e-7 m^2/s
#
# Initial cylinder temperature is room temperature 294.26 K (70 F)
# The initial fluid temperature is room temperature. We will ramp it to 477.6 K (400 F) in 10 minutes.
# We will use a very large h (1000000) to make the surface temperature mimick the fluid temperature.

# What we expect for this problem:
#  1) Use of h = 1000000 should cause the cylinder surface temperature to track the fluid temperature
#  2) The fluid temperature should rise from initial (294.26 K) to final (477.6 K) in 600 s.
#  3) 1) and 2) should prove that the Tf boundary condition is ramping as desired.
# Note, we do the above because there is no way to plot a variable that is not on a mesh node!

[Mesh]    # Mesh Start
# 10cm x 20cm cylinder not so detailed mesh, 2 radial, 6 axial nodes
# Only one block (Block 1), all concrete
# Sideset 1 - top of cylinder, Sideset 2 - length of cylinder, Sideset 3 - bottom of cylinder
  file = heat_convection_rz_mesh.e
  coord_type = RZ
[]    # Mesh END

[Variables]  # Variables Start
  [./temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 294.26 # Initial cylinder temperature
  [../]

[]    # Variables END


[Kernels]  # Kernels Start
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

[]    # Kernels END


[BCs]    # Boundary Conditions Start
# Heat transfer coefficient on outer cylinder radius and ends
  [./convective_clad_surface]    # Convective Start
         type = ConvectiveFluxBC        # Convective flux, e.g. q'' = h*(Tw - Tf)
         boundary = '1 2 3'    # BC applied on top, along length, and bottom
         variable = temp
   rate = 1000000.   # convective heat transfer coefficient (w/m^2-K)[176000 "]
#         #  the above h is ~ infinity for present purposes
         initial = 294.26         # initial ambient (lab or oven) temperature (K)
         final = 477.6            # final ambient (lab or oven) temperature (K)
   duration = 600.   # length of time in seconds that it takes the ambient
         #     temperature to ramp from initial to final
  [../]          # Convective End

[]    # BCs END

[Materials]    # Materials Start
  [./thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 826.4
    thermal_conductivity = 1.937  # this makes alpha 9.74e-7 m^2/s
  [../]
  [./density]
    type = Density
    block = 1
    density = 2405.28
  [../]
[]      # Materials END

[Executioner]    # Executioner Start
   type = Transient
#   type = Steady

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
  dt = 60.
  num_steps = 20  # Total run time 1200 s

[]      # Executioner END

[Outputs]    # Output Start
  # Output Start
  file_base = out_rz_tf
  exodus = true
[]      # Output END
#      # Input file END

(modules/heat_transfer/test/tests/thin_layer_heat_transfer/transient_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 10
    ny = 10
    nz = 2
    zmax = 0.2
    dim = 3
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    block_id = 1
    bottom_left = '0 0 0'
    top_right = '0.5 1 0.2'
    input = gen
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    block_id = 2
    bottom_left = '0.5 0 0'
    top_right = '1 1 0.2'
    input = block1
  []
  [breakmesh]
    input = block2
    type = BreakMeshByBlockGenerator
    block_pairs = '1 2'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [time]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [thermal_cond]
    type = HeatConduction
    variable = temperature
  []
[]

[InterfaceKernels]
  [thin_layer]
    type = ThinLayerHeatTransfer
    thermal_conductivity = thermal_conductivity_layer
    specific_heat = specific_heat_layer
    density = density_layer
    heat_source = heat_source_layer
    thickness = 0.01
    variable = temperature
    neighbor_var = temperature
    boundary = Block1_Block2
  []
[]

[BCs]
  [left_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = left
  []
  [right_temp]
    type = DirichletBC
    value = 0
    variable = temperature
    boundary = right
  []
[]

[Materials]
  [thermal_cond]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '1 1 1'
  []
  [thermal_cond_layer]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity_layer specific_heat_layer heat_source_layer density_layer'
    prop_values = '0.05 1 10000 1'
    boundary = Block1_Block2
  []
[]
[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10

  dt = 0.05
  num_steps = 2
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/functional_expansion_tools/examples/2D_interface_different_submesh/sub.i)

# Derived from the example '2D_interface' with the following differences:
#
#   1) The number of y divisions in the sub app is not the same as the master app
#   2) The subapp mesh is skewed in y
#   3) The Functional Expansion order for the flux term was increased to 7
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.4
  xmax = 2.4
  nx = 30
  ymin = 0.0
  ymax = 10.0
  ny = 23
  bias_y = 1.2
[]

[Variables]
  [./s]
  [../]
[]

[Kernels]
  [./diff_s]
    type = HeatConduction
    variable = s
  [../]
  [./time_diff_s]
    type = HeatConductionTimeDerivative
    variable = s
  [../]
[]

[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_s]
    type = ConstantIC
    value = 2
    variable = s
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = s
    boundary = bottom
    value = 0.1
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = left
    variable = s
    function = FX_Basis_Flux_Sub
  [../]
[]

[Functions]
  [./FX_Basis_Value_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Sub]
    type = FunctionSeries
    series_type = Cartesian
    orders = '7'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Value_UserObject_Sub]
    type = FXBoundaryValueUserObject
    function = FX_Basis_Value_Sub
    variable = s
    boundary = left
  [../]
  [./FX_Flux_UserObject_Sub]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Sub
    variable = s
    boundary = left
    diffusivity = thermal_conductivity
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_quad_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 5
  ny = 1
  xmin = 0.0
  xmax = 0.1
  ymin = 0.0
  ymax = 0.01
  elem_type = QUAD4
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 9
  [../]
[]

[Outputs]
  csv = true
[]

(modules/functional_expansion_tools/examples/2D_interface/main.i)

# Basic example coupling a master and sub app at an interface in a 2D model.
# The master app provides a flux term to the sub app via Functional Expansions, which then performs
# its calculations.  The sub app's interface conditions, both value and flux, are transferred back
# to the master app
[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0.0
  xmax = 0.4
  nx = 6
  ymin = 0.0
  ymax = 10.0
  ny = 20
[]

[Variables]
  [./m]
  [../]
[]

[Kernels]
  [./diff_m]
    type = HeatConduction
    variable = m
  [../]
  [./time_diff_m]
    type = HeatConductionTimeDerivative
    variable = m
  [../]
  [./source_m]
    type = BodyForce
    variable = m
    value = 100
  [../]
[]

[Materials]
  [./Impervium]
    type = GenericConstantMaterial
    prop_names =  'thermal_conductivity specific_heat density'
    prop_values = '0.00001              50.0          100.0' # W/(cm K), J/(g K), g/cm^3
  [../]
[]

[ICs]
  [./start_m]
    type = ConstantIC
    value = 2
    variable = m
  [../]
[]

[BCs]
  [./interface_value]
    type = FXValueBC
    variable = m
    boundary = right
    function = FX_Basis_Value_Main
  [../]
  [./interface_flux]
    type = FXFluxBC
    boundary = right
    variable = m
    function = FX_Basis_Flux_Main
  [../]
[]

[Functions]
  [./FX_Basis_Value_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '4'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
  [./FX_Basis_Flux_Main]
    type = FunctionSeries
    series_type = Cartesian
    orders = '5'
    physical_bounds = '0.0 10'
    y = Legendre
  [../]
[]

[UserObjects]
  [./FX_Flux_UserObject_Main]
    type = FXBoundaryFluxUserObject
    function = FX_Basis_Flux_Main
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
[]

[Postprocessors]
  [./average_interface_value]
    type = SideAverageValue
    variable = m
    boundary = right
  [../]
  [./total_flux]
    type = SideDiffusiveFluxIntegral
    variable = m
    boundary = right
    diffusivity = thermal_conductivity
  [../]
  [./picard_iterations]
    type = NumFixedPointIterations
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 1.0
  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
    sub_cycling = true
  [../]
[]

[Transfers]
  [./FluxToSub]
    type = MultiAppFXTransfer
    to_multi_app = FXTransferApp
    this_app_object_name = FX_Flux_UserObject_Main
    multi_app_object_name = FX_Basis_Flux_Sub
  [../]
  [./ValueToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Value_Main
    multi_app_object_name = FX_Value_UserObject_Sub
  [../]
  [./FluxToMe]
    type = MultiAppFXTransfer
    from_multi_app = FXTransferApp
    this_app_object_name = FX_Basis_Flux_Main
    multi_app_object_name = FX_Flux_UserObject_Sub
  [../]
[]

(modules/combined/tutorials/introduction/thermal_mechanical/thermomech_step01.i)

#
# Single block coupled thermal/mechanical
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/thermoech_step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
  [pin]
    type = ExtraNodesetGenerator
    input = generated
    new_boundary = pin
    coord = '0 0 0'
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 5e4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    automatic_eigenstrain_names = true
    generate_output = 'vonmises_stress'
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [expansion1]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.001
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
  [pin_x]
    type = DirichletBC
    variable = disp_x
    boundary = pin
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
[]

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

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/tutorials/introduction/thermal_mechanical_contact/thermomech_cont_step01.i)

#
# A first attempt at thermo mechanical contact
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  block = 0
[]

[Mesh]
  [generated1]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 15
    xmin = -0.6
    xmax = -0.1
    ymax = 5
    bias_y = 0.9
    boundary_name_prefix = pillar1
  []
  [generated2]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 6
    ny = 15
    xmin = 0.1
    xmax = 0.6
    ymax = 4.999
    bias_y = 0.9
    boundary_name_prefix = pillar2
    boundary_id_offset = 4
  []
  [collect_meshes]
    type = MeshCollectionGenerator
    inputs = 'generated1 generated2'
  []

  patch_update_strategy = iteration
[]

[Variables]
  # temperature field variable
  [T]
    # initialize to an average temperature
    initial_condition = 50
    order = FIRST
    family = LAGRANGE
  []
  # temperature lagrange multiplier
  [Tlm]
    block = 'pillars_secondary_subdomain'
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [dTdt]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    generate_output = 'vonmises_stress'
  []
[]

[Contact]
  [pillars]
    primary = pillar1_right
    secondary = pillar2_left
    model = frictionless
    formulation = mortar
  []
[]

[Constraints]
  # thermal contact constraint
  [Tlm]
    type = GapConductanceConstraint
    variable = Tlm
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = pillar1_right
    primary_subdomain = pillars_primary_subdomain
    secondary_boundary = pillar2_left
    secondary_subdomain = pillars_secondary_subdomain
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'pillar1_bottom pillar2_bottom'
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'pillar1_bottom pillar2_bottom'
    value = 0
  []
  [Pressure]
    [sides]
      boundary = 'pillar1_left pillar2_right'
      function = 1e4*t^2
    []
  []

  # thermal boundary conditions (pillars are heated/cooled from the bottom)
  [heat_left]
    type = DirichletBC
    variable = T
    boundary = pillar1_bottom
    value = 100
  []
  [cool_right]
    type = DirichletBC
    variable = T
    boundary = pillar2_bottom
    value = 0
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  # thermal properties
  [thermal_conductivity]
    type = HeatConductionMaterial
    thermal_conductivity = 100
    specific_heat = 1
  []
  [density]
    type = Density
    density = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  line_search = none
  # we deal with the saddle point structure of the system by adding a small shift
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero'
  end_time = 5
  dt = 0.1
  [Predictor]
    type = SimplePredictor
    scale = 1
  []
[]

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

(modules/combined/test/tests/adaptive_timestepping/adapt_tstep_function_change_restart1.i)

# This is a test designed to evaluate the cabability of the
# IterationAdaptiveDT TimeStepper to adjust time step size according to
# a function.  For example, if the power input function for a BISON
# simulation rapidly increases or decreases, the IterationAdaptiveDT
# TimeStepper should take time steps small enough to capture the
# oscillation.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  file = 1hex8_10mm_cube.e
[]

[Functions]
  [./Fiss_Function]
    type = PiecewiseLinear
    x = '0 1e6  2e6  2.001e6 2.002e6'
    y = '0 3e8  3e8  12e8    0'
  [../]
[]

[Variables]
  [./disp_x]
  [../]

  [./disp_y]
  [../]

  [./disp_z]
  [../]

  [./temp]
    initial_condition = 300.0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    incremental = true
    volumetric_locking_correction = true
    eigenstrain_names = thermal_expansion
    decomposition_method = EigenSolution
    add_variables  = true
    generate_output = 'vonmises_stress'
    temperature = temp
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]

  [./heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]

  [./heat_source]
     type = HeatSource
     variable = temp
     value = 1.0
     function = Fiss_Function
  [../]
[]

[BCs]
 [./bottom_temp]
   type = DirichletBC
   variable = temp
   boundary = 1
   value = 300
 [../]
 [./top_bottom_disp_x]
   type = DirichletBC
   variable = disp_x
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_y]
   type = DirichletBC
   variable = disp_y
   boundary = '1'
   value = 0
 [../]
 [./top_bottom_disp_z]
   type = DirichletBC
   variable = disp_z
   boundary = '1'
   value = 0
 [../]
[]

[Materials]
 [./thermal]
    type = HeatConductionMaterial
    temp = temp
    specific_heat = 1.0
    thermal_conductivity = 1.0
  [../]

  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 300e6
    poissons_ratio = .3
  [../]

  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]

  [./thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 5e-6
    stress_free_temperature = 300.0
    temperature = temp
    eigenstrain_name = thermal_expansion
  [../]

  [./density]
    type = Density
    density = 10963.0
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  verbose = true
  nl_abs_tol = 1e-10
  start_time = 0.0

  num_steps = 65
  end_time = 2.002e6
  [./TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = Fiss_Function
    max_function_change = 3e7
    dt = 1e6
  [../]
[]

[Postprocessors]
  [./Temperature_of_Block]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]

  [./vonMises]
    type = ElementAverageValue
    variable = vonmises_stress
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
  [./console]
    type = Console
    max_rows = 10
  [../]
  [./checkpoint]
    type = Checkpoint
    num_files = 1
  [../]
[]

(modules/heat_transfer/test/tests/NAFEMS/transient/T3/nafems_t3_edge_template.i)

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 5
  xmin = 0.0
  xmax = 0.1
  elem_type = EDGE2
[]

[Variables]
  [./temp]
    initial_condition = 0.0
  [../]
[]

[BCs]
  [./FixedTempLeft]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0.0
  [../]
  [./FunctionTempRight]
    type = FunctionDirichletBC
    variable = temp
    boundary = right
    function = '100.0 * sin(pi*t/40)'
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConduction
    variable = temp
  [../]
  [./HeatTdot]
    type = HeatConductionTimeDerivative
    variable = temp
  [../]
[]

[Materials]
  [./density]
    type = GenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '35.0 440.5 7200.0'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_tol = 1e-5
  nl_max_its = 50
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  dt = 1
  end_time = 32.0
[]

[Postprocessors]
  [./target_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 4
  [../]
[]

[Outputs]
  csv = true
[]

(modules/heat_transfer/include/kernels/TrussHeatConductionTimeDerivative.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 "HeatConductionTimeDerivative.h"
#include "Material.h"

class TrussHeatConductionTimeDerivative : public HeatConductionTimeDerivative
{
public:
  static InputParameters validParams();

  TrussHeatConductionTimeDerivative(const InputParameters & parameters);

protected:
  virtual Real computeQpResidual() override;

  virtual Real computeQpJacobian() override;

  /// Coupled variable for the cross-sectional area of truss element
  const VariableValue & _area;
};