BoundaryIntegralValueConstraint

Enforces a prescribed average value for a finite element variable on a boundary using a scalar Lagrange multiplier.

Description

BoundaryIntegralValueConstraint enforces

var element = document.getElementById("moose-equation-7e4a52a8-2cd5-4cec-af46-a864606cb7ec");katex.render("\\int_{\\Gamma} \\left(u - \\phi_0\\right) \\, d\\Gamma = 0", element, {displayMode:true,throwOnError:false});

on a boundary $var element = document.getElementById("moose-equation-c97b03e8-b2a6-44ee-b78e-157bb2f851fb");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false});$ using a SCALAR Lagrange multiplier variable. This makes the average value of the finite element variable u on the specified boundary equal to phi0. The variable supplied to "lambda" must use family = SCALAR and order = FIRST.

The object assembles both the field-variable equation and the scalar Lagrange multiplier equation, so no separate ScalarKernel is required for the Lagrange multiplier variable. It is the finite element boundary analogue of FVBoundaryIntegralValueConstraint.

The scalar Lagrange multiplier $var element = document.getElementById("moose-equation-0704e1dd-7fb7-4099-b260-3ebcc35aa106");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ has the physical meaning of the uniform boundary loading needed to enforce the average value constraint. For example, in a mechanical problem where $var element = document.getElementById("moose-equation-27ae4ecf-f3dd-4dfd-a6a6-978c82a0116a");katex.render("u", element, {displayMode:false,throwOnError:false});$ is a displacement field, $var element = document.getElementById("moose-equation-7019c077-616e-47ed-adf5-27cf053c50e2");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ represents the uniform traction applied on $var element = document.getElementById("moose-equation-4bedb1cd-c02e-4021-8588-60503b9d5dda");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false});$ to enforce the prescribed average displacement. In a heat-conduction problem where $var element = document.getElementById("moose-equation-4fce1c89-6777-427e-91e6-10b2b3ce36ec");katex.render("u", element, {displayMode:false,throwOnError:false});$ is temperature, $var element = document.getElementById("moose-equation-a01ccc3a-a5cb-4a1e-9daf-b78cf2a607e3");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ represents the uniform boundary source term or flux needed to enforce the prescribed average temperature.

warning

This constraint introduces a saddle-point block with zero diagonal terms. Use a preconditioner that includes the field and scalar variables. SMP with full = true is required for the complete off-diagonal Jacobian block structure, and a suitable shift or factorization is typically needed for the indefinite matrix.

If phi0 is supplied as a postprocessor, set its execute_on to include LINEAR (or NONLINEAR) so the value is current during residual and Jacobian evaluation.

Example Input Syntax

The Lagrange multiplier variable is declared as a first-order scalar variable:

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [u]
  []
  [lambda_left]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
  [lambda_bottom]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
[]

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [left_average]
    type = BoundaryIntegralValueConstraint<<<{"description": "Enforces a prescribed average value for a finite element variable on a boundary using a scalar Lagrange multiplier.", "href": "BoundaryIntegralValueConstraint.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = left
    lambda<<<{"description": "Lagrange multiplier scalar variable"}>>> = lambda_left
    phi0<<<{"description": "The value that the constraint will enforce."}>>> = 0.25
  []
  [bottom_average]
    type = BoundaryIntegralValueConstraint<<<{"description": "Enforces a prescribed average value for a finite element variable on a boundary using a scalar Lagrange multiplier.", "href": "BoundaryIntegralValueConstraint.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = bottom
    lambda<<<{"description": "Lagrange multiplier scalar variable"}>>> = lambda_bottom
    phi0<<<{"description": "The value that the constraint will enforce."}>>> = 0.5
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
lambdaLagrange multiplier scalar variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Lagrange multiplier scalar variable
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
phi00The value that the constraint will enforce.
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The value that the constraint will enforce.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
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<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
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
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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.
diag_save_inThe name of auxiliary variables to save this BC'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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC'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
Controllable:Yes
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
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this BC'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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
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
skip_execution_outside_variable_domainFalseWhether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
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

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
Unit:(no unit assumed)
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.

Material Property Retrieval Parameters

(moose/test/tests/bcs/boundary_integral_value_constraint/boundary_integral_value_constraint.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 4
  ny = 4
  elem_type = QUAD4
[]

[Variables]
  [u]
  []
  [lambda_left]
    family = SCALAR
    order = FIRST
  []
  [lambda_bottom]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [source]
    type = BodyForce
    variable = u
    value = 1
  []
[]

[BCs]
  [left_average]
    type = BoundaryIntegralValueConstraint
    variable = u
    boundary = left
    lambda = lambda_left
    phi0 = 0.25
  []
  [bottom_average]
    type = BoundaryIntegralValueConstraint
    variable = u
    boundary = bottom
    lambda = lambda_bottom
    phi0 = 0.5
  []
[]

[Postprocessors]
  [left_average]
    type = SideAverageValue
    variable = u
    boundary = left
    execute_on = timestep_end
  []
  [bottom_average]
    type = SideAverageValue
    variable = u
    boundary = bottom
    execute_on = timestep_end
  []
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
[]

[Outputs]
  csv = true
  hide = 'lambda_left lambda_bottom'
[]

(moose/test/tests/bcs/boundary_integral_value_constraint/boundary_integral_value_constraint.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 4
  ny = 4
  elem_type = QUAD4
[]

[Variables]
  [u]
  []
  [lambda_left]
    family = SCALAR
    order = FIRST
  []
  [lambda_bottom]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
  [source]
    type = BodyForce
    variable = u
    value = 1
  []
[]

[BCs]
  [left_average]
    type = BoundaryIntegralValueConstraint
    variable = u
    boundary = left
    lambda = lambda_left
    phi0 = 0.25
  []
  [bottom_average]
    type = BoundaryIntegralValueConstraint
    variable = u
    boundary = bottom
    lambda = lambda_bottom
    phi0 = 0.5
  []
[]

[Postprocessors]
  [left_average]
    type = SideAverageValue
    variable = u
    boundary = left
    execute_on = timestep_end
  []
  [bottom_average]
    type = SideAverageValue
    variable = u
    boundary = bottom
    execute_on = timestep_end
  []
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_abs_tol = 1e-12
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
[]

[Outputs]
  csv = true
  hide = 'lambda_left lambda_bottom'
[]

Description
Example Input Syntax
Input Parameters