ScalarLMKernel

This Kernel demonstrates the usage of the scalar augmentation class described in KernelScalarBase. This single kernel is an alternative to the combination of ScalarLagrangeMultiplier, AverageValueConstraint, and an Elemental Integral Postprocessor. All terms from the spatial and scalar variables are handled by this object.

This Kernel enforces the constraint of

$var element = document.getElementById("moose-equation-114168a4-8928-4f81-b23a-1a0f8cf328ed");katex.render(" \\int_{\\Omega} \\phi = V_0", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-8141c0cb-0c67-48fc-af67-4663799a52a5");katex.render("V_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a given constant, using a Lagrange multiplier approach. Since this is a single constraint, a single scalar variable $var element = document.getElementById("moose-equation-da715129-c039-4344-abd2-efe1cc51d1e1");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is required, as shown below.


[Variables]
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

The residual of $var element = document.getElementById("moose-equation-7230c0e4-a580-4810-b70e-13e616f9d0f9");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ related to the Lagrange multiplier is given as:

$(1)var element = document.getElementById("moose-equation-492e9bcf-6c9d-46d4-9fd0-5244d15efc26");katex.render(" F^{(\\phi)}_i \\equiv \\lambda^h \\int_{\\Omega} \\varphi_i \\;\\text{d}\\Omega ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The residual of the Lagrange multiplier $var element = document.getElementById("moose-equation-f5c7406f-32ac-4ce3-bc28-9fd9dde41cd8");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is given as:

$(2)var element = document.getElementById("moose-equation-45fba07b-abc9-4d9e-9389-aa451b4dbad8");katex.render(" F^{(\\lambda)} \\equiv \\int_{\\Omega} \\phi^h \\;\\text{d}\\Omega - V_0 = 0 ", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

This Kernel implements the residual and Jacobian contributions to the spatial variable $var element = document.getElementById("moose-equation-3fe92fbd-be07-49ce-92ff-34930ddcd53b");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ equation from the $var element = document.getElementById("moose-equation-fd8d5731-9a02-43cc-977b-9df8717d0c16");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ in Eq. (1). Also, it implements the residual and Jacobian contributions to the scalar Lagrange multiplier $var element = document.getElementById("moose-equation-d64a0514-f095-45fd-a3bd-dd92f6e317c1");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ constraint equation from the spatial variable $var element = document.getElementById("moose-equation-3a1e918f-87fe-419c-a653-376825ae4ebf");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ in Eq. (2).

So that the input syntax matches with ScalarLagrangeMultiplier, a Postprocessor is required that computes the total volume of the domain, assigned to the parameter pp_name.

Currently, a NullScalarKernel is required to activate the dependency of the scalar variable within the block or subdomain of this object. See one of the example files listed below.

The detailed description of the derivation of the weak form can be found at scalar_constraint_kernel.

Input Parameters

pp_nameName of the Postprocessor containing the volume of the domain.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Name of the Postprocessor containing the volume of the domain.
valueGiven (constant) which we want the integral of the solution variable to match.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Given (constant) which we want the integral of the solution variable to match.
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>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
compute_field_residualsTrueWhether to compute residuals for the field variable.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute residuals for the field variable.
compute_scalar_residualsTrueWhether to compute scalar residuals
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute scalar residuals
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
kappaPrimary coupled scalar variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Primary coupled scalar variable
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
Unit:(no unit assumed)
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

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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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

Input Files

(test/tests/kernels/scalar_kernel_constraint/diffusion_override_scalar.i)
(test/tests/kernels/scalar_kernel_constraint/scalar_constraint_kernel.i)
(test/tests/kernels/ad_scalar_kernel_constraint/diffusion_bipass_scalar.i)
(test/tests/kernels/ad_scalar_kernel_constraint/scalar_constraint_together.i)
(test/tests/kernels/ad_scalar_kernel_constraint/scalar_constraint_kernel_RJ.i)
(test/tests/kernels/scalar_kernel_constraint/diffusion_bipass_scalar.i)
(test/tests/kernels/ad_scalar_kernel_constraint/diffusion_override_scalar.i)

(test/tests/kernels/scalar_kernel_constraint/diffusion_override_scalar.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  # Make sure that we can derive from the scalar base class
  # but actually not assign a scalar variable
  [diff]
    type = DiffusionNoScalar
    variable = u
    scalar_variable = lambda
  []

  [ffnk]
    type = BodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = FunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = FunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = FunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = FunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  nl_max_its = 10
  # This example builds an indefinite matrix, so "-pc_type hypre -pc_hypre_type boomeramg" cannot
  # be used reliably on this problem. ILU(0) seems to do OK in both serial and parallel in my testing,
  # I have not seen any zero pivot issues.
  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'bjacobi  ilu'
  # This is a linear problem, so we don't need to recompute the
  # Jacobian. This isn't a big deal for a Steady problems, however, as
  # there is only one solve.
  solve_type = 'LINEAR'
[]

[Outputs]
#  exodus = true
  csv = true
  hide = lambda
[]

(test/tests/kernels/scalar_kernel_constraint/scalar_constraint_kernel.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

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

  [ffnk]
    type = BodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = FunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = FunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = FunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = FunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  nl_max_its = 10
  # This example builds an indefinite matrix, so "-pc_type hypre -pc_hypre_type boomeramg" cannot
  # be used reliably on this problem
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  # This is a linear problem, so we don't need to recompute the
  # Jacobian. This isn't a big deal for a Steady problems, however, as
  # there is only one solve.
  solve_type = 'LINEAR'
[]

[Outputs]
  exodus = true
  hide = lambda
[]

(test/tests/kernels/ad_scalar_kernel_constraint/diffusion_bipass_scalar.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  # Make sure that we can derive from the scalar base class
  # but actually not assign a scalar variable
  [diff]
    type = ADDiffusionNoScalar
    variable = u
  []

  [ffnk]
    type = ADBodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ADScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  residual_and_jacobian_together = true
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  nl_max_its = 10
  # This example builds an indefinite matrix, so "-pc_type hypre -pc_hypre_type boomeramg" cannot
  # be used reliably on this problem
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  # This is a linear problem, so we don't need to recompute the
  # Jacobian. This isn't a big deal for a Steady problems, however, as
  # there is only one solve.
  solve_type = 'LINEAR'
[]

[Outputs]
#  exodus = true
  csv = true
  hide = lambda
[]

(test/tests/kernels/ad_scalar_kernel_constraint/scalar_constraint_together.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  [diff]
    type = ADDiffusion
    variable = u
  []

  [ffnk]
    type = ADBodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ADScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = ADFunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Steady
  residual_and_jacobian_together = true
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  solve_type = NEWTON
[]

[Outputs]
#  exodus = true
  csv = true
  hide = lambda
[]

(test/tests/kernels/ad_scalar_kernel_constraint/scalar_constraint_kernel_RJ.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  [diff]
    type = ADDiffusion
    variable = u
  []

  [sk_lm]
    type = ADScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = ADDirichletBC
    variable = u
    boundary = 'bottom'
    value = 0
  []
  [right]
    type = ADDirichletBC
    variable = u
    boundary = 'right'
    value = 0
  []
  [top]
    type = ADDirichletBC
    variable = u
    boundary = 'top'
    value = 0
  []
  [left]
    type = ADDirichletBC
    variable = u
    boundary = 'left'
    value = 0
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
[]

# Force LU decomposition, nonlinear iterations, to check Jacobian terms with single factorization
[Executioner]
  type = Steady
  residual_and_jacobian_together = true
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
  hide = lambda
[]

(test/tests/kernels/scalar_kernel_constraint/diffusion_bipass_scalar.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  # Make sure that we can derive from the scalar base class
  # but actually not assign a scalar variable
  [diff]
    type = DiffusionNoScalar
    variable = u
  []

  [ffnk]
    type = BodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = FunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = FunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = FunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = FunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  nl_max_its = 10
  # This example builds an indefinite matrix, so "-pc_type hypre -pc_hypre_type boomeramg" cannot
  # be used reliably on this problem
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  # This is a linear problem, so we don't need to recompute the
  # Jacobian. This isn't a big deal for a Steady problems, however, as
  # there is only one solve.
  solve_type = 'LINEAR'
[]

[Outputs]
#  exodus = true
  csv = true
  hide = lambda
[]

(test/tests/kernels/ad_scalar_kernel_constraint/diffusion_override_scalar.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD9
[]

[Functions]
  [exact_fn]
    type = ParsedFunction
    value = 'x*x+y*y'
  []

  [ffn]
    type = ParsedFunction
    value = -4
  []

  [bottom_bc_fn]
    type = ParsedFunction
    value = -2*y
  []

  [right_bc_fn]
    type = ParsedFunction
    value =  2*x
  []

  [top_bc_fn]
    type = ParsedFunction
    value =  2*y
  []

  [left_bc_fn]
    type = ParsedFunction
    value = -2*x
  []
[]

[Variables]
  [u]
    family = LAGRANGE
    order = SECOND
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Kernels]
  # Make sure that we can derive from the scalar base class
  # but actually not assign a scalar variable
  [diff]
    type = ADDiffusionNoScalar
    variable = u
    scalar_variable = lambda
  []

  [ffnk]
    type = ADBodyForce
    variable = u
    function = ffn
  []

  [sk_lm]
    type = ADScalarLMKernel
    variable = u
    kappa = lambda
    pp_name = pp
    value = 2.666666666666666
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [bottom]
    type = FunctionNeumannBC
    variable = u
    boundary = 'bottom'
    function = bottom_bc_fn
  []
  [right]
    type = FunctionNeumannBC
    variable = u
    boundary = 'right'
    function = right_bc_fn
  []
  [top]
    type = FunctionNeumannBC
    variable = u
    boundary = 'top'
    function = top_bc_fn
  []
  [left]
    type = FunctionNeumannBC
    variable = u
    boundary = 'left'
    function = left_bc_fn
  []
[]

[Postprocessors]
  # integrate the volume of domain since original objects set
  # int(phi)=V0, rather than int(phi-V0)=0
  [pp]
    type = FunctionElementIntegral
    function = 1
    execute_on = initial
  []
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
    execute_on = 'initial timestep_end'
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-9
  l_tol = 1.e-10
  nl_max_its = 10
  # This example builds an indefinite matrix, so "-pc_type hypre -pc_hypre_type boomeramg" cannot
  # be used reliably on this problem. ILU(0) seems to do OK in both serial and parallel in my testing,
  # I have not seen any zero pivot issues.
  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'bjacobi  ilu'
  # This is a linear problem, so we don't need to recompute the
  # Jacobian. This isn't a big deal for a Steady problems, however, as
  # there is only one solve.
  solve_type = 'LINEAR'
[]

[Outputs]
#  exodus = true
  csv = true
  hide = lambda
[]

Input Parameters
Input Files