Bounds System

The Bounds system is designed to bound the value of a nonlinear variable. Whether the bound is an upper or lower bound depends on the parameters passed to the Bounds object. The bound may be spatially and time-dependent, and even depend on other simulation quantities, as implemented in the particular Bounds object used.

The auxiliary variable that serves as the variable parameter of a Bounds object is not actually used or even set in the computation. However, its type is used to decide if the Bounds loop will be 'nodal' (loop on all nodes) or 'elemental' (loop on quadrature points in elements). Its block restriction is used to define where the bounds is applied. It may be re-used for multiple bounds objects.

note

Only nodal and constant elemental variables are supported at this time.

The Bounds system supports both finite element and finite volume variables. Only elemental bounds should be used for finite volume variables.

Note that in order for 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 option is specified. The PETSc manual pages for the vinewtonssls algorithm can be found here while the manual page for vinewtonrsls can be found here.

Example syntax

In the following example, a lower and an upper bound are applied to two variables u and v using the same auxiliary variable bounds_dummy and four Bounds objects.

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

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

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

[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
  []
[]

Available Objects

Moose App
ConstantBoundsProvides constant bound of a variable for the PETSc's variational inequalities solver
ConstantBoundsAuxProvides constant bound of a variable for the PETSc's variational inequalities solver
VariableOldValueBoundsUses the old variable values as the bounds for the new solve.
VariableOldValueBoundsAuxUses the old variable values as the bounds for the new solve.

Available Actions

Moose App
AddBoundsVectorsActionAction to add vectors to nonlinear system when using the Bounds syntax.
AddBoundActionAdd a Kernel object to the simulation.

(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
[]

Example syntax
Available Objects
Available Actions