ConstantBounds

Provides constant bound of a variable for the PETSc's variational inequalities solver

Description

ConstantBounds is used for setting bounds on a nonlinear variable specified through the parameter bounded_variable. The bound type of upper or lower is set with bound_type parameter. The bound_value is used to specify the value of a bound. ConstantBounds expects a variable parameter to be set (as do all AuxKernels). This can be a dummy AuxVariable; the ConstantBounds actually operates on NumericVectors held by the nonlinear system and does nothing but return 0 for the value of the specified variable.

Note that in order for these bounds to have an effect, the user has to specify the PETSc options -snes_type vinewtonssls or -snes_type vinewtonrsls. A warning will be generated if neither options are specified. The PETSc manual pages for the vinewtonssls algorithm can be found here while the manual page for vinewtonrsls can be found here.

MOOSE users can also enforce constraints through MOOSE using UpperBoundNodalKernel and LowerBoundNodalKernel. However, using these objects requires introduction of Lagrange multiplier variables that increase the size of the nonlinear system as well as render some preconditioning methods like algebraic multi-grid ineffective. The number of nonlinear iterations required to solve a constrained PDE defined by this input file with the various constraint algorithms is summarized below:

vinewtonrsls and ConstantBounds: 22
vinewtonssls and ConstantBounds: 53
UpperBoundNodalKernel and LowerBoundNodalKernel: 25

Example Syntax

[Bounds]
  [u_upper_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = u
    bound_type = upper
    bound_value = 1
  []
  [u_lower_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  []

  [v_upper_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = v
    bound_type = upper
    bound_value = 3
  []
  [v_lower_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = v
    bound_type = lower
    bound_value = -1
  []
[]

Input Parameters

bound_valueThe value of bound for the variable
C++ Type:double
Controllable:No
Description:The value of bound for the variable
bounded_variableThe variable to be bounded
C++ Type:NonlinearVariableName
Controllable:No
Description:The variable to be bounded
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
bound_typeupperType of bound. 'upper' refers to the upper bound. 'lower' refers to the lower value.
Default:upper
C++ Type:MooseEnum
Options:upper, lower
Controllable:No
Description:Type of bound. 'upper' refers to the upper bound. 'lower' refers to the lower value.
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
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
Controllable:No
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

(moose/test/tests/nodalkernels/constraint_enforcement/upper-and-lower-bound.i)

l=10
nx=100
num_steps=10

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmax = ${l}
  nx = ${nx}
[]

[Variables]
  [u]
  []
  [lm_upper]
  []
  [lm_lower]
  []
[]

[ICs]
  [u]
    type = FunctionIC
    variable = u
    function = 'x'
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = u
  []
  [diff]
    type = Diffusion
    variable = u
  []
  [ffn]
    type = BodyForce
    variable = u
    function = 'if(x<5,-1,1)'
  []
[]

[NodalKernels]
  [upper_bound]
    type = UpperBoundNodalKernel
    variable = lm_upper
    v = u
    exclude_boundaries = 'left right'
    upper_bound = 10
  []
  [forces_from_upper]
    type = CoupledForceNodalKernel
    variable = u
    v = lm_upper
    coef = -1
  []
  [lower_bound]
    type = LowerBoundNodalKernel
    variable = lm_lower
    v = u
    exclude_boundaries = 'left right'
    lower_bound = 0
  []
  [forces_from_lower]
    type = CoupledForceNodalKernel
    variable = u
    v = lm_lower
    coef = 1
  []
[]


[BCs]
  [left]
    type = DirichletBC
    boundary = left
    value = 0
    variable = u
  []
  [right]
    type = DirichletBC
    boundary = right
    value = ${l}
    variable = u
  []
[]

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

[Executioner]
  type = Transient
  num_steps = ${num_steps}
  solve_type = NEWTON
  dtmin = 1
  petsc_options_iname = '-snes_max_linear_solve_fail -ksp_max_it -pc_type -sub_pc_factor_levels -snes_linesearch_type'
  petsc_options_value = '0                           30          asm      16                    basic'
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
  [dof]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Postprocessors]
  [active_upper_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_upper
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [upper_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = ${fparse 10+1e-8}
    comparator = 'greater'
  []
  [active_lower_lm]
    type = GreaterThanLessThanPostprocessor
    variable = lm_lower
    execute_on = 'nonlinear timestep_end'
    value = 1e-8
    comparator = 'greater'
  []
  [lower_violations]
    type = GreaterThanLessThanPostprocessor
    variable = u
    execute_on = 'nonlinear timestep_end'
    value = -1e-8
    comparator = 'less'
  []
  [nls]
    type = NumNonlinearIterations
  []
  [cum_nls]
    type = CumulativeValuePostprocessor
    postprocessor = nls
  []
[]

(moose/test/tests/bounds/constant_bounds.i)

[Mesh]
  type = GeneratedMesh

  dim = 2

  xmin = 0
  xmax = 1

  ymin = 0
  ymax = 1

  nx = 10
  ny = 10
[]

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

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

[AuxVariables]
  [bounds_dummy]
    order = FIRST
    family = LAGRANGE
  []
[]

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

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

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

  [right_u]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 1
  []

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

  [right_v]
    type = DirichletBC
    variable = v
    boundary = 1
    value = 1
  []
[]

[Bounds]
  [u_upper_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = u
    bound_type = upper
    bound_value = 1
  []
  [u_lower_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = u
    bound_type = lower
    bound_value = 0
  []

  [v_upper_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = v
    bound_type = upper
    bound_value = 3
  []
  [v_lower_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = v
    bound_type = lower
    bound_value = -1
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
  petsc_options_iname = '-snes_type'
  petsc_options_value = 'vinewtonrsls'
[]

[Outputs]
  exodus = true
[]