SwitchingFunctionConstraintLagrange

under construction:Undocumented Class

The SwitchingFunctionConstraintLagrange has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.


# SwitchingFunctionConstraintLagrange

!syntax description /Kernels/SwitchingFunctionConstraintLagrange

## Overview

!! Replace these lines with information regarding the SwitchingFunctionConstraintLagrange object.

## Example Input File Syntax

!! Describe and include an example of how to use the SwitchingFunctionConstraintLagrange object.

!syntax parameters /Kernels/SwitchingFunctionConstraintLagrange

!syntax inputs /Kernels/SwitchingFunctionConstraintLagrange

!syntax children /Kernels/SwitchingFunctionConstraintLagrange

Lagrange multiplier kernel to constrain the sum of all switching functions in a multiphase system. This kernel acts on the Lagrange multiplier variable.

Input Parameters

etaseta order parameters
C++ Type:std::vector
Options:
Description:eta order parameters
variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
epsilon1e-09Shift factor to avoid a zero pivot
Default:1e-09
C++ Type:double
Options:
Description:Shift factor to avoid a zero pivot
h_namesSwitching function materials
C++ Type:std::vector
Options:
Description:Switching function materials

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

modules/combined/examples/phase_field-mechanics/Pattern1.i
modules/phase_field/test/tests/MultiPhase/acmultiinterface_aux.i
modules/phase_field/test/tests/MultiPhase/acmultiinterface.i
modules/phase_field/test/tests/MultiPhase/lagrangemult.i

modules/combined/examples/phase_field-mechanics/Pattern1.i

#
# Pattern example 1
#
# Phase changes driven by a combination mechanical (elastic) and chemical
# driving forces. In this three phase system a matrix phase, an oversized and
# an undersized precipitate phase compete. The chemical free energy favors a
# phase separation into either precipitate phase. A mix of both precipitate
# emerges to balance lattice expansion and contraction.
#
# This example demonstrates the use of
# * ACMultiInterface
# * SwitchingFunctionConstraintEta and SwitchingFunctionConstraintLagrange
# * DerivativeParsedMaterial
# * ElasticEnergyMaterial
# * DerivativeMultiPhaseMaterial
# * MultiPhaseStressMaterial
# which are the components to se up a phase field model with an arbitrary number
# of phases
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 80
  ny = 80
  nz = 0
  xmin = -20
  xmax = 20
  ymin = -20
  ymax = 20
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[GlobalParams]
  # CahnHilliard needs the third derivatives
  derivative_order = 3
  enable_jit = true
  displacements = 'disp_x disp_y'
[]

# AuxVars to compute the free energy density for outputting
[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./cross_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./local_free_energy]
    type = TotalFreeEnergy
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
    additional_free_energy = cross_energy
  [../]
  [./cross_terms]
    type = CrossTermGradientFreeEnergy
    variable = cross_energy
    interfacial_vars = 'eta1 eta2 eta3'
    kappa_names = 'kappa11 kappa12 kappa13
                   kappa21 kappa22 kappa23
                   kappa31 kappa32 kappa33'
  [../]
[]

[Variables]
  # Solute concentration variable
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = RandomIC
      min = 0
      max = 0.8
      seed = 1235
    [../]
  [../]

  # Order parameter for the Matrix
  [./eta1]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.5
  [../]
  # Order parameters for the 2 different inclusion orientations
  [./eta2]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.1
  [../]

  # Mesh displacement
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]

  # Lagrange-multiplier
  [./lambda]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1.0
  [../]
[]

[Kernels]
  # Set up stress divergence kernels
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_res]
    type = CahnHilliard
    variable = c
    f_name = F
    args = 'eta1 eta2 eta3'
  [../]
  [./time]
    type = TimeDerivative
    variable = c
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulk1]
    type = AllenCahn
    variable = eta1
    args = 'eta2 eta3 c'
    mob_name = L1
    f_name = F
  [../]
  [./ACInterface1]
    type = ACMultiInterface
    variable = eta1
    etas = 'eta1 eta2 eta3'
    mob_name = L1
    kappa_names = 'kappa11 kappa12 kappa13'
  [../]
  [./lagrange1]
    type = SwitchingFunctionConstraintEta
    variable = eta1
    h_name   = h1
    lambda = lambda
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    args = 'eta1 eta3 c'
    mob_name = L2
    f_name = F
  [../]
  [./ACInterface2]
    type = ACMultiInterface
    variable = eta2
    etas = 'eta1 eta2 eta3'
    mob_name = L2
    kappa_names = 'kappa21 kappa22 kappa23'
  [../]
  [./lagrange2]
    type = SwitchingFunctionConstraintEta
    variable = eta2
    h_name   = h2
    lambda = lambda
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
  [./deta3dt]
    type = TimeDerivative
    variable = eta3
  [../]
  [./ACBulk3]
    type = AllenCahn
    variable = eta3
    args = 'eta1 eta2 c'
    mob_name = L3
    f_name = F
  [../]
  [./ACInterface3]
    type = ACMultiInterface
    variable = eta3
    etas = 'eta1 eta2 eta3'
    mob_name = L3
    kappa_names = 'kappa31 kappa32 kappa33'
  [../]
  [./lagrange3]
    type = SwitchingFunctionConstraintEta
    variable = eta3
    h_name   = h3
    lambda = lambda
  [../]

  # Lagrange-multiplier constraint kernel for lambda
  [./lagrange]
    type = SwitchingFunctionConstraintLagrange
    variable = lambda
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
    epsilon = 1e-6
  [../]
[]

[Materials]
  # declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c  L1 L2 L3  kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
    prop_values = '0.2 0        1  1  1   2.00    2.00    2.00    2.00    2.00    2.00    2.00    2.00    2.00   '
  [../]

  # We use this to output the level of constraint enforcement
  # ideally it should be 0 everywhere, if the constraint is fully enforced
  [./etasummat]
    type = ParsedMaterial
    f_name = etasum
    args = 'eta1 eta2 eta3'
    material_property_names = 'h1 h2 h3'
    function = 'h1+h2+h3-1'
    outputs = exodus
  [../]

  # This parsed material creates a single property for visualization purposes.
  # It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
  [./phasemap]
    type = ParsedMaterial
    f_name = phase
    args = 'eta2 eta3'
    function = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
    outputs = exodus
  [../]

  # matrix phase
  [./elasticity_tensor_1]
    type = ComputeElasticityTensor
    base_name = phase1
    C_ijkl = '3 3'
    fill_method = symmetric_isotropic
  [../]
  [./strain_1]
    type = ComputeSmallStrain
    base_name = phase1
    displacements = 'disp_x disp_y'
  [../]
  [./stress_1]
    type = ComputeLinearElasticStress
    base_name = phase1
  [../]

  # oversized phase
  [./elasticity_tensor_2]
    type = ComputeElasticityTensor
    base_name = phase2
    C_ijkl = '7 7'
    fill_method = symmetric_isotropic
  [../]
  [./strain_2]
    type = ComputeSmallStrain
    base_name = phase2
    displacements = 'disp_x disp_y'
    eigenstrain_names = eigenstrain
  [../]
  [./stress_2]
    type = ComputeLinearElasticStress
    base_name = phase2
  [../]
  [./eigenstrain_2]
    type = ComputeEigenstrain
    base_name = phase2
    eigen_base = '0.02'
    eigenstrain_name = eigenstrain
  [../]

  # undersized phase
  [./elasticity_tensor_3]
    type = ComputeElasticityTensor
    base_name = phase3
    C_ijkl = '7 7'
    fill_method = symmetric_isotropic
  [../]
  [./strain_3]
    type = ComputeSmallStrain
    base_name = phase3
    displacements = 'disp_x disp_y'
    eigenstrain_names = eigenstrain
  [../]
  [./stress_3]
    type = ComputeLinearElasticStress
    base_name = phase3
  [../]
  [./eigenstrain_3]
    type = ComputeEigenstrain
    base_name = phase3
    eigen_base = '-0.05'
    eigenstrain_name = eigenstrain
  [../]

  # switching functions
  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
  [../]
  [./switching3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
    h_order = SIMPLE
  [../]

  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
  [../]

  # chemical free energies
  [./chemical_free_energy_1]
    type = DerivativeParsedMaterial
    f_name = Fc1
    function = '4*c^2'
    args = 'c'
    derivative_order = 2
  [../]
  [./chemical_free_energy_2]
    type = DerivativeParsedMaterial
    f_name = Fc2
    function = '(c-0.9)^2-0.4'
    args = 'c'
    derivative_order = 2
  [../]
  [./chemical_free_energy_3]
    type = DerivativeParsedMaterial
    f_name = Fc3
    function = '(c-0.9)^2-0.5'
    args = 'c'
    derivative_order = 2
  [../]

  # elastic free energies
  [./elastic_free_energy_1]
    type = ElasticEnergyMaterial
    base_name = phase1
    f_name = Fe1
    derivative_order = 2
    args = 'c' # should be empty
  [../]
  [./elastic_free_energy_2]
    type = ElasticEnergyMaterial
    base_name = phase2
    f_name = Fe2
    derivative_order = 2
    args = 'c' # should be empty
  [../]
  [./elastic_free_energy_3]
    type = ElasticEnergyMaterial
    base_name = phase3
    f_name = Fe3
    derivative_order = 2
    args = 'c' # should be empty
  [../]

  # phase free energies (chemical + elastic)
  [./phase_free_energy_1]
    type = DerivativeSumMaterial
    f_name = F1
    sum_materials = 'Fc1 Fe1'
    args = 'c'
    derivative_order = 2
  [../]
  [./phase_free_energy_2]
    type = DerivativeSumMaterial
    f_name = F2
    sum_materials = 'Fc2 Fe2'
    args = 'c'
    derivative_order = 2
  [../]
  [./phase_free_energy_3]
    type = DerivativeSumMaterial
    f_name = F3
    sum_materials = 'Fc3 Fe3'
    args = 'c'
    derivative_order = 2
  [../]

  # global free energy
  [./free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = F
    fi_names = 'F1  F2  F3'
    hi_names = 'h1  h2  h3'
    etas     = 'eta1 eta2 eta3'
    args = 'c'
    W = 3
  [../]

  # Generate the global stress from the phase stresses
  [./global_stress]
    type = MultiPhaseStressMaterial
    phase_base = 'phase1 phase2 phase3'
    h          = 'h1     h2     h3'
  [../]
[]

[BCs]
  # the boundary conditions on the displacement enforce periodicity
  # at zero total shear and constant volume
  [./bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  [../]
  [./top_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'top'
    value = 0
  [../]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0
  [../]
  [./right_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  [../]

  [./Periodic]
    [./disp_x]
      auto_direction = 'y'
    [../]
    [./disp_y]
      auto_direction = 'x'
    [../]

    # all other phase field variables are fully periodic
    [./c]
      auto_direction = 'x y'
    [../]
    [./eta1]
      auto_direction = 'x y'
    [../]
    [./eta2]
      auto_direction = 'x y'
    [../]
    [./eta3]
      auto_direction = 'x y'
    [../]
    [./lambda]
      auto_direction = 'x y'
    [../]
  [../]
[]

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

# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    variable = c
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2

  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'asm      ilu'

  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10
  start_time = 0.0
  num_steps = 200

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.1
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

[Debug]
  # show_var_residual_norms = true
[]

modules/phase_field/test/tests/MultiPhase/acmultiinterface_aux.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 10
  nz = 0
  xmin = -10
  xmax = 10
  ymin = -5
  ymax = 5
  elem_type = QUAD4
[]

[AuxVariables]
  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = -3.5
      y1 =  0.0
      radius = 4.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 2.0
    [../]
  [../]
[]

[Variables]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 =  3.5
      y1 =  0.0
      radius = 4.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 2.0
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SpecifiedSmoothCircleIC
      x_positions = '-4.0 4.0'
      y_positions = ' 0.0 0.0'
      z_positions = ' 0.0 0.0'
      radii = '4.0 4.0'
      invalue = 0.1
      outvalue = 0.9
      int_width = 2.0
    [../]
  [../]

  [./lambda]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    args = 'eta1 eta3'
    mob_name = L2
    f_name = F
  [../]
  [./ACInterface2]
    type = ACMultiInterface
    variable = eta2
    etas = 'eta1 eta2 eta3'
    mob_name = L2
    kappa_names = 'kappa21 kappa22 kappa23'
  [../]
  [./lagrange2]
    type = SwitchingFunctionConstraintEta
    variable = eta2
    h_name   = h2
    lambda = lambda
  [../]

  [./deta3dt]
    type = TimeDerivative
    variable = eta3
  [../]
  [./ACBulk3]
    type = AllenCahn
    variable = eta3
    args = 'eta1 eta2'
    mob_name = L3
    f_name = F
  [../]
  [./ACInterface3]
    type = ACMultiInterface
    variable = eta3
    etas = 'eta1 eta2 eta3'
    mob_name = L3
    kappa_names = 'kappa31 kappa32 kappa33'
  [../]
  [./lagrange3]
    type = SwitchingFunctionConstraintEta
    variable = eta3
    h_name   = h3
    lambda = lambda
  [../]

  [./lagrange]
    type = SwitchingFunctionConstraintLagrange
    variable = lambda
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
    epsilon = 0
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'Fx  L1 L2 L3  kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
    prop_values = '0   1  1  1   1       1       1       1       1       1       1       1       1      '
  [../]

  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
  [../]
  [./switching3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
    h_order = SIMPLE
  [../]

  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
  [../]

  [./free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = F
    # we use a constant free energy (GeneriConstantmaterial property Fx)
    fi_names = 'Fx  Fx  Fx'
    hi_names = 'h1  h2  h3'
    etas     = 'eta1 eta2 eta3'
    # the free energy is given by the MultiBarrierFunctionMaterial only
    W = 1
    derivative_order = 2
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = 'bdf2'

  solve_type = 'PJFNK'
  #petsc_options = '-snes_ksp -snes_ksp_ew'
  #petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
  #petsc_options_iname = '-ksp_gmres_restart'
  #petsc_options_value = '1000              '

  l_max_its = 15
  l_tol = 1.0e-6

  nl_max_its = 50
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
  dt = 0.2
[]

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

modules/phase_field/test/tests/MultiPhase/acmultiinterface.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 10
  nz = 0
  xmin = -10
  xmax = 10
  ymin = -5
  ymax = 5
  elem_type = QUAD4
[]

[Variables]
  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = -3.5
      y1 =  0.0
      radius = 4.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 2.0
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 =  3.5
      y1 =  0.0
      radius = 4.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 2.0
    [../]
  [../]
  [./eta3]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SpecifiedSmoothCircleIC
      x_positions = '-4.0 4.0'
      y_positions = ' 0.0 0.0'
      z_positions = ' 0.0 0.0'
      radii = '4.0 4.0'
      invalue = 0.1
      outvalue = 0.9
      int_width = 2.0
    [../]
  [../]

  [./lambda]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulk1]
    type = AllenCahn
    variable = eta1
    args = 'eta2 eta3'
    mob_name = L1
    f_name = F
  [../]
  [./ACInterface1]
    type = ACMultiInterface
    variable = eta1
    etas = 'eta1 eta2 eta3'
    mob_name = L1
    kappa_names = 'kappa11 kappa12 kappa13'
  [../]
  [./lagrange1]
    type = SwitchingFunctionConstraintEta
    variable = eta1
    h_name   = h1
    lambda = lambda
  [../]

  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    args = 'eta1 eta3'
    mob_name = L2
    f_name = F
  [../]
  [./ACInterface2]
    type = ACMultiInterface
    variable = eta2
    etas = 'eta1 eta2 eta3'
    mob_name = L2
    kappa_names = 'kappa21 kappa22 kappa23'
  [../]
  [./lagrange2]
    type = SwitchingFunctionConstraintEta
    variable = eta2
    h_name   = h2
    lambda = lambda
  [../]

  [./deta3dt]
    type = TimeDerivative
    variable = eta3
  [../]
  [./ACBulk3]
    type = AllenCahn
    variable = eta3
    args = 'eta1 eta2'
    mob_name = L3
    f_name = F
  [../]
  [./ACInterface3]
    type = ACMultiInterface
    variable = eta3
    etas = 'eta1 eta2 eta3'
    mob_name = L3
    kappa_names = 'kappa31 kappa32 kappa33'
  [../]
  [./lagrange3]
    type = SwitchingFunctionConstraintEta
    variable = eta3
    h_name   = h3
    lambda = lambda
  [../]

  [./lagrange]
    type = SwitchingFunctionConstraintLagrange
    variable = lambda
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
    epsilon = 0
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'Fx  L1 L2 L3  kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
    prop_values = '0   1  1  1   1       1       1       1       1       1       1       1       1      '
  [../]

  [./etasummat]
    type = ParsedMaterial
    f_name = etasum
    args = 'eta1 eta2 eta3'
    material_property_names = 'h1 h2 h3'
    function = 'h1+h2+h3'
  [../]

  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
  [../]
  [./switching3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
    h_order = SIMPLE
  [../]

  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
  [../]

  [./free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = F
    # we use a constant free energy (GeneriConstantmaterial property Fx)
    fi_names = 'Fx  Fx  Fx'
    hi_names = 'h1  h2  h3'
    etas     = 'eta1 eta2 eta3'
    # the free energy is given by the MultiBarrierFunctionMaterial only
    W = 1
    derivative_order = 2
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = 'bdf2'

  solve_type = 'PJFNK'
  #petsc_options = '-snes_ksp -snes_ksp_ew'
  #petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
  #petsc_options_iname = '-ksp_gmres_restart'
  #petsc_options_value = '1000              '

  l_max_its = 15
  l_tol = 1.0e-6

  nl_max_its = 50
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
  dt = 0.2
[]

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

modules/phase_field/test/tests/MultiPhase/lagrangemult.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 14
  ny = 10
  nz = 0
  xmin = 10
  xmax = 40
  ymin = 15
  ymax = 35
  elem_type = QUAD4
[]

[Variables]
  [./c]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = 25.0
      y1 = 25.0
      radius = 6.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 3.0
    [../]
  [../]
  [./w]
    order = FIRST
    family = LAGRANGE
  [../]

  [./eta1]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = 30.0
      y1 = 25.0
      radius = 4.0
      invalue = 0.9
      outvalue = 0.1
      int_width = 2.0
    [../]
  [../]
  [./eta2]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.5
  [../]

  [./lambda]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1.0
  [../]
[]

[Kernels]
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulk1]
    type = AllenCahn
    variable = eta1
    args = 'c eta2'
    f_name = F
  [../]
  [./ACInterface1]
    type = ACInterface
    variable = eta1
    kappa_name = kappa_eta
  [../]
  [./lagrange1]
    type = SwitchingFunctionConstraintEta
    variable = eta1
    h_name   = h1
    lambda = lambda
  [../]

  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    args = 'c eta1'
    f_name = F
  [../]
  [./ACInterface2]
    type = ACInterface
    variable = eta2
    kappa_name = kappa_eta
  [../]
  [./lagrange2]
    type = SwitchingFunctionConstraintEta
    variable = eta2
    h_name   = h2
    lambda = lambda
  [../]

  [./lagrange]
    type = SwitchingFunctionConstraintLagrange
    variable = lambda
    etas    = 'eta1 eta2'
    h_names = 'h1   h2'
    epsilon = 0
  [../]

  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    args = 'eta1 eta2'
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
  [../]
  [./time1]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
[]

[BCs]
  [./Periodic]
    [./All]
      auto_direction = 'x y'
    [../]
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'L kappa_eta'
    prop_values = '1 1        '
  [../]
  [./consts2]
    type = GenericConstantMaterial
    prop_names  = 'M kappa_c'
    prop_values = '1 1'
  [../]

  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
    outputs = exodus
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
    outputs = exodus
  [../]

  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2'
  [../]

  [./free_energy_A]
    type = DerivativeParsedMaterial
    f_name = Fa
    args = 'c'
    function = '(c-0.1)^2'
    derivative_order = 2
    enable_jit = true
  [../]
  [./free_energy_B]
    type = DerivativeParsedMaterial
    f_name = Fb
    args = 'c'
    function = '(c-0.9)^2'
    derivative_order = 2
    enable_jit = true
  [../]

  [./free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = F
    fi_names = 'Fa   Fb'
    hi_names = 'h1   h2'
    etas     = 'eta1 eta2'
    args = 'c'
    derivative_order = 2
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = 'bdf2'

  solve_type = 'PJFNK'
  #petsc_options = '-snes_ksp -snes_ksp_ew'
  #petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
  #petsc_options_iname = '-ksp_gmres_restart'
  #petsc_options_value = '1000              '

  l_max_its = 15
  l_tol = 1.0e-6

  nl_max_its = 50
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 1
  dt = 0.01
  dtmin = 0.01
[]

[Debug]
  # show_var_residual_norms = true
[]

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

Input Parameters
Input Files

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