ADDisplacementRegularization

Adds a solid mechanics displacement regularization term using HuHu, LuLu, or HuHu-LuLu Hessian/Laplacian contractions. The Jacobian is computed using automatic differentiation.

Description

ADDisplacementRegularization is the automatic-differentiation version of DisplacementRegularization. It supports the same HuHu, LuLu, and HuHu-LuLu displacement regularization options and computes Jacobian contributions through MOOSE's AD infrastructure.

warning:Second-derivative FE data required

This kernel evaluates second derivatives of the trial and test functions. Use an FE family and order for which libMesh provides meaningful second derivatives on the selected elements; the example inputs use family = LAGRANGE and order = SECOND. Global $var element = document.getElementById("moose-equation-2b4a7bf5-417f-4e35-b2e7-2b54474707f5");katex.render("C^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ continuity is not required by this kernel, but variables whose second derivatives vanish will produce little or no regularization contribution.

The included tests and intended displacement-regularization use case run on $var element = document.getElementById("moose-equation-2c68ac9a-7287-4b0d-89bc-0d0f2c010e80");katex.render("C^0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ quadratic Lagrange elements. This is non-conforming for a standalone biharmonic solve, but the kernel is used as a regularization contribution rather than as a conforming biharmonic discretization.

For regularization = huhu_lulu, "lulu_factor" defaults to $var element = document.getElementById("moose-equation-e496ea75-511a-4f30-8361-fdb7f158358a");katex.render("1 / d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-054e23b0-37c3-4e65-9cc7-5a6534677016");katex.render("d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the mesh dimension. Values larger than $var element = document.getElementById("moose-equation-127be2b4-a9d3-4eaf-9c3f-ace20b2a27c0");katex.render("1 / d", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are accepted with a warning because they may cause negative strain-energy contributions.

The huhu_lulu option is rejected in one dimension because HuHu and LuLu are identical when the default LuLu factor is used. Use huhu or lulu directly for one-dimensional problems.

Example Input File Syntax

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  # The second-derivative regularization is tested on C0 quadratic Lagrange elements. The
  # diffusion term keeps this test problem well posed while the regularization block
  # exercises the HuHu/LuLu residual and Jacobian contributions.
  [diffusion]
    type = ADDiffusion<<<{"description": "Same as `Diffusion` in terms of physics/residual, but the Jacobian is computed using forward automatic differentiation", "href": "ADDiffusion.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
  []
  [regularization]
    type = ${reg_kernel}
    variable = u
    regularization = ${regularization_type}
    coefficient = 1
  []
  [body_force]
    type = BodyForce<<<{"description": "Demonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form $(\\psi_i, -f)$.", "href": "BodyForce.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    function<<<{"description": "A function that describes the body force"}>>> = forcing_func
  []
[]

Input Parameters

coefficientCoefficient multiplying the regularization term.
C++ Type:double
Unit:(no unit assumed)
Range:coefficient >= 0
Controllable:No
Description:Coefficient multiplying the regularization term.
regularizationRegularization type to apply: 'huhu' for Hessian-Hessian, 'lulu' for Laplacian-Laplacian, or 'huhu_lulu' for HuHu minus a scaled LuLu correction.
C++ Type:MooseEnum
Options:huhu, lulu, huhu_lulu
Controllable:No
Description:Regularization type to apply: 'huhu' for Hessian-Hessian, 'lulu' for Laplacian-Laplacian, or 'huhu_lulu' for HuHu minus a scaled LuLu correction.
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

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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
lulu_factorFactor multiplying the LuLu correction for 'huhu_lulu'. If omitted, defaults to 1 / dim, where dim is the mesh dimension.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor multiplying the LuLu correction for 'huhu_lulu'. If omitted, defaults to 1 / dim, where dim is the mesh dimension.

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 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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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 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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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.)
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
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

(modules/solid_mechanics/test/tests/displacement_regularization/ad_displacement_regularization_default_factor.i)

reg_kernel = ADDisplacementRegularization
regularization_type = huhu_lulu
forcing_scale = 0.5

[GlobalParams]
  symbol_names = 'c'
  symbol_values = '5'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD9
  xmin = -0.5
  xmax = 0.5
  ymin = -0.5
  ymax = 0.5
  nx = 4
  ny = 4
[]

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

[Kernels]
  # The second-derivative regularization is tested on C0 quadratic Lagrange elements. The
  # diffusion term keeps this test problem well posed while the regularization block
  # exercises the HuHu/LuLu residual and Jacobian contributions.
  [diffusion]
    type = ADDiffusion
    variable = u
  []
  [regularization]
    type = ${reg_kernel}
    variable = u
    regularization = ${regularization_type}
    coefficient = 1
  []
  [body_force]
    type = BodyForce
    variable = u
    function = forcing_func
  []
[]

[BCs]
  [boundary_value]
    type = FunctionPenaltyDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e8
  []
[]

[Functions]
  [u_func]
    type = ParsedFunction
    expression = 'exp(-c*(x^2+y^2))'
  []
  [forcing_func]
    type = ParsedFunction
    expression = '${forcing_scale} * 16*c^2*(c^2*(x^2+y^2)^2 - 4*c*(x^2+y^2) + 2)*exp(-c*(x^2+y^2))'
  []
[]

[Postprocessors]
  [l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  []
  [h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  []
[]

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

  [Quadrature]
    type = GAUSS
    order = ELEVENTH
  []
[]

[Outputs]
  csv = false
[]

Description
Example Input File Syntax
Input Parameters