VectorBodyForce

Description

VectorBodyForce is analogous to BodyForce except it is applied to vector finite element variables. Instead of taking one function parameter, the user can pass up to three functions representing the individual components of the vector variable. If not supplied by the user, function_x will default to '1', while function_y and function_z default to '0'.

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
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>
Controllable:No
Description:The displacements
functionA function that defines a vectorValue method. This cannot be supplied with the component parameters.
C++ Type:FunctionName
Controllable:No
Description:A function that defines a vectorValue method. This cannot be supplied with the component parameters.
function_x1A function that describes the x-component of the body force
Default:1
C++ Type:FunctionName
Controllable:No
Description:A function that describes the x-component of the body force
function_y0A function that describes the y-component of the body force
Default:0
C++ Type:FunctionName
Controllable:No
Description:A function that describes the y-component of the body force
function_z0A function that describes the z-component of the body force
Default:0
C++ Type:FunctionName
Controllable:No
Description:A function that describes the z-component of the body force
postprocessor1A postprocessor whose value is multiplied by the body force
Default:1
C++ Type:PostprocessorName
Controllable:No
Description:A postprocessor whose value is multiplied by the body force
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.
value1Coefficient to multiply by the body force term
Default:1
C++ Type:double
Controllable:Yes
Description:Coefficient to multiply by the body force term

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_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

Tagging 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>
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>
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
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

Input Files

(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/perpendicular.i)
(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/parallel.i)
(test/tests/preconditioners/fsp/vector-test.i)
(modules/electromagnetics/test/tests/auxkernels/current_density/em_current_density.i)
(test/tests/bcs/periodic/periodic_vector_bc_test.i)
(test/tests/kernels/vector_fe/lagrange_vec_1d.i)
(test/tests/kernels/vector_fe/ad_lagrange_vec.i)
(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/combined_default.i)
(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/combined_props.i)
(test/tests/materials/functor_properties/vector-magnitude/vector-test.i)
(test/tests/kernels/vector_fe/electromagnetic_coulomb_gauge.i)
(modules/electromagnetics/test/tests/bcs/vector_robin_bc/portbc_waves.i)
(test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i)
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_kernels.i)
(test/tests/kernels/vector_fe/lagrange_vec.i)

(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/perpendicular.i)

# Verification Test of PerpendicularElectricFieldInterface
# with default materials
#
# Imposes u_perpendicular = v_perpendicular on each interface
# between subdomain 0 and 1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 10
    xmax = 2
    ymax = 2
    zmax = 2
    elem_type = HEX20
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 1'
    block_id = 1
    input = gmg
  []
  [break_boundary]
    type = BreakBoundaryOnSubdomainGenerator
    input = subdomain1
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  []
[]

[Variables]
  [u]
    order = FIRST
    family = NEDELEC_ONE
    block = 0
  []
  [v]
    order = FIRST
    family = NEDELEC_ONE
    block = 1
  []
[]

[Kernels]
  [curl_u]
    type = CurlCurlField
    variable = u
    block = 0
  []
  [coeff_u]
    type = VectorFunctionReaction
    variable = u
    block = 0
  []
  [ffn_u]
    type = VectorBodyForce
    variable = u
    block = 0
    function_x = 1
    function_y = 1
    function_z = 1
  []
  [curl_v]
    type = CurlCurlField
    variable = v
    block = 1
  []
  [coeff_v]
    type = VectorFunctionReaction
    variable = v
    block = 1
  []
[]

[InterfaceKernels]
  [perpendicular]
    type = PerpendicularElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
  []
[]

[BCs]
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/parallel.i)

# Verification Test of ParallelElectricFieldInterface
# with default materials
#
# Imposes u_parallel = v_parallel on each interface
# between subdomain 0 and 1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 10
    xmax = 2
    ymax = 2
    zmax = 2
    elem_type = HEX20
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 1'
    block_id = 1
    input = gmg
  []
  [break_boundary]
    type = BreakBoundaryOnSubdomainGenerator
    input = subdomain1
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  []
[]


[Variables]
  [u]
    order = FIRST
    family = NEDELEC_ONE
    block = 0
  []
  [v]
    order = FIRST
    family = NEDELEC_ONE
    block = 1
  []
[]

[Kernels]
  [curl_u]
    type = CurlCurlField
    variable = u
    block = 0
  []
  [coeff_u]
    type = VectorFunctionReaction
    variable = u
    block = 0
  []
  [ffn_u]
    type = VectorBodyForce
    variable = u
    block = 0
    function_x = 1
    function_y = 1
    function_z = 1
  []
  [curl_v]
    type = CurlCurlField
    variable = v
    block = 1
  []
  [coeff_v]
    type = VectorFunctionReaction
    variable = v
    block = 1
  []
[]

[InterfaceKernels]
  [parallel]
    type = ParallelElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
  []
[]

[BCs]
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/preconditioners/fsp/vector-test.i)

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [u]
    family = LAGRANGE_VEC
  []
  [v]
    family = LAGRANGE_VEC
  []
[]

[Kernels]
  [time_u]
    type = VectorTimeDerivative
    variable = u
  []
  [fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  []
  [time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  []
  [diff_v]
    type = VectorDiffusion
    variable = v
  []
[]

[BCs]
  [left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  []
  [right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  []
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'uv'
    [uv]
      splitting = 'u v'
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      splitting_type  = symmetric_multiplicative
    []
    [u]
      vars = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      vars = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    []
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/electromagnetics/test/tests/auxkernels/current_density/em_current_density.i)

# This test is a modification of the vector_helmholtz.vector_kernels test
# to verify functionality of the current density auxkernel for the case of
# a vector field variable in electromagnetic mode.
# Manufactured solution: u = y * x_hat - x * y_hat

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    ymin = -1
    elem_type = QUAD9
  []
[]

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

[AuxVariables]
  [J]
    family = NEDELEC_ONE
    order = FIRST
  []
[]


[Kernels]
  [curl_curl]
    type = CurlCurlField
    variable = u
  []
  [coeff]
    type = VectorFunctionReaction
    variable = u
  []
  [rhs]
    type = VectorBodyForce
    variable = u
    function_x = 'y'
    function_y = '-x'
  []
[]

[BCs]
  [sides]
    type = VectorCurlPenaltyDirichletBC
    variable = u
    function_x = 'y'
    function_y = '-x'
    penalty = 1e8
    boundary = 'left right top bottom'
  []
[]

[AuxKernels]
  [current_density]
    type = ADCurrentDensity
    variable = J
    electrostatic = false
    electric_field = u
  []
[]

[Materials]                                 # THIS MATERIAL IS ONLY USED TO TEST THE CURRENT DENSITY CALCULATION
  [conductivity]                            # Electrical conductivity for graphite at 293.15 K in S/m
    type = ADGenericConstantMaterial        # perpendicular to basal plane
    prop_names = 'electrical_conductivity'  # Citation: H. Pierson, "Handbook of carbon, graphite,
    prop_values = 3.33e2                    #           diamond, and fullerenes: properties, processing,
  []                                        #           and applications," p. 61, William Andrew, 1993.
[]

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

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
[]

(test/tests/bcs/periodic/periodic_vector_bc_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  xmax = 40
  ymax = 40
  zmax = 0
  elem_type = QUAD4
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE_VEC
  [../]
[]

[Kernels]
  [./diff]
    type = VectorDiffusion
    variable = u
  [../]

  [./forcing]
    type = VectorBodyForce
    variable = u
    function_x = 'exp(-((x-5)^2+(y-5)^2))'
    function_y = 'exp(-((x-35)^2+(y-35)^2))'
  [../]

  [./dot]
    type = VectorTimeDerivative
    variable = u
  [../]
[]

[BCs]
  [./Periodic]
    [./x]
      variable = u
      primary = 3
      secondary = 1
      translation = '40 0 0'
    [../]

    [./y]
      variable = u
      primary = 0
      secondary = 2
      translation = '0 40 0'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 6
  solve_type = NEWTON
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = vector_out
  exodus = true
[]

(test/tests/kernels/vector_fe/lagrange_vec_1d.i)

# This example reproduces the libmesh vector_fe example 1 results

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 15
  xmin = -1
  elem_type = EDGE3
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
    order = SECOND
  [../]
[]

[Kernels]
  [./diff]
    type = VectorDiffusion
    variable = u
  [../]
  [./body_force]
    type = VectorBodyForce
    variable = u
    function_x = 'ffx'
  [../]
[]

[BCs]
  [./bnd]
    type = VectorFunctionDirichletBC
    variable = u
    function_x = 'x_exact_sln'
    boundary = 'left right'
  [../]
[]

[Functions]
  [./x_exact_sln]
    type = ParsedFunction
    expression = 'cos(.5*pi*x)'
  [../]
  [./ffx]
    type = ParsedFunction
    expression = '.25*pi*pi*cos(.5*pi*x)'
  [../]
[]

[Preconditioning]
  [./pre]
    type = SMP
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/vector_fe/ad_lagrange_vec.i)

# This example reproduces the libmesh vector_fe example 1 results

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -1
  ymin = -1
  elem_type = QUAD9
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
    order = SECOND
  [../]
[]

[Kernels]
  [./diff]
    type = ADVectorDiffusion
    variable = u
  [../]
  [./body_force]
    type = VectorBodyForce
    variable = u
    function_x = 'ffx'
    function_y = 'ffy'
  [../]
[]

[BCs]
  [./bnd]
    type = ADVectorFunctionDirichletBC
    variable = u
    function_x = 'x_exact_sln'
    function_y = 'y_exact_sln'
    boundary = 'left right top bottom'
  [../]
[]

[Functions]
  [./x_exact_sln]
    type = ParsedFunction
    expression = 'cos(.5*pi*x)*sin(.5*pi*y)'
  [../]
  [./y_exact_sln]
    type = ParsedFunction
    expression = 'sin(.5*pi*x)*cos(.5*pi*y)'
  [../]
  [./ffx]
    type = ParsedFunction
    expression = '.5*pi*pi*cos(.5*pi*x)*sin(.5*pi*y)'
  [../]
  [./ffy]
    type = ParsedFunction
    expression = '.5*pi*pi*sin(.5*pi*x)*cos(.5*pi*y)'
  [../]
[]

[Preconditioning]
  [./pre]
    type = SMP
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/combined_default.i)

# Verification Test of PerpendicularElectricFieldInterface and
# ParallelElectricFieldInterface with default materials
#
# Imposes u_perpendicular = v_perpendicular and u_parallel = v_parallel
# on each interface (equivalent to saying u = v for default parameters)
# between subdomain 0 and 1

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 10
    xmax = 2
    ymax = 2
    zmax = 2
    elem_type = HEX20
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 1'
    block_id = 1
    input = gmg
  []
  [break_boundary]
    type = BreakBoundaryOnSubdomainGenerator
    input = subdomain1
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  []
[]

[Variables]
  [u]
    order = FIRST
    family = NEDELEC_ONE
    block = 0
  []
  [v]
    order = FIRST
    family = NEDELEC_ONE
    block = 1
  []
[]

[Kernels]
  [curl_u]
    type = CurlCurlField
    variable = u
    block = 0
  []
  [coeff_u]
    type = VectorFunctionReaction
    variable = u
    block = 0
  []
  [ffn_u]
    type = VectorBodyForce
    variable = u
    block = 0
    function_x = 1
    function_y = 1
    function_z = 1
  []
  [curl_v]
    type = CurlCurlField
    variable = v
    block = 1
  []
  [coeff_v]
    type = VectorFunctionReaction
    variable = v
    block = 1
  []
[]

[InterfaceKernels]
  [perpendicular]
    type = PerpendicularElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
  []
  [parallel]
    type = ParallelElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
  []
[]

[BCs]
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(modules/electromagnetics/test/tests/interfacekernels/electromagnetic_interfaces/combined_props.i)

# Verification Test of PerpendicularElectricFieldInterface and
# ParallelElectricFieldInterface with user-defined materials
# and interface free charge
#
# Imposes epsilon_0 * u_perpendicular - epsilon_1 * v_perpendicular = free_charge
# and u_parallel = v_parallel on each interface between subdomain
# blocks 0 and 1
#
# epsilon_0 = 1.0
# epsilon_1 = 10.0
# free_charge = 1.0

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 10
    xmax = 2
    ymax = 2
    zmax = 2
    elem_type = HEX20
  []
  [subdomain1]
    type = SubdomainBoundingBoxGenerator
    bottom_left = '0 0 0'
    top_right = '1 1 1'
    block_id = 1
    input = gmg
  []
  [break_boundary]
    type = BreakBoundaryOnSubdomainGenerator
    input = subdomain1
  []
  [interface]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  []
[]

[Variables]
  [u]
    order = FIRST
    family = NEDELEC_ONE
    block = 0
  []
  [v]
    order = FIRST
    family = NEDELEC_ONE
    block = 1
  []
[]

[Kernels]
  [curl_u]
    type = CurlCurlField
    variable = u
    block = 0
  []
  [coeff_u]
    type = VectorFunctionReaction
    variable = u
    block = 0
  []
  [ffn_u]
    type = VectorBodyForce
    variable = u
    block = 0
    function_x = 1
    function_y = 1
    function_z = 1
  []
  [curl_v]
    type = CurlCurlField
    variable = v
    block = 1
  []
  [coeff_v]
    type = VectorFunctionReaction
    variable = v
    block = 1
  []
[]

[InterfaceKernels]
  [perpendicular]
    type = PerpendicularElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
    primary_epsilon = 1.0
    secondary_epsilon = 10.0
    free_charge = 1.0
  []
  [parallel]
    type = ParallelElectricFieldInterface
    variable = u
    neighbor_var = v
    boundary = primary0_interface
  []
[]

[BCs]
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/materials/functor_properties/vector-magnitude/vector-test.i)

# This example reproduces the libmesh vector_fe example 1 results

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -1
  ymin = -1
[]

[Variables]
  [u]
    family = LAGRANGE_VEC
  []
[]

[AuxVariables]
  [mag]
    order = FIRST
    family = MONOMIAL
  []
[]

[AuxKernels]
  [mag]
    type = FunctorAux
    variable = mag
    functor = mat_mag
  []
[]

[Kernels]
  [diff]
    type = VectorDiffusion
    variable = u
  []
  [body_force]
    type = VectorBodyForce
    variable = u
    function_x = 'ffx'
    function_y = 'ffy'
  []
[]

[BCs]
  [bnd]
    type = VectorFunctionDirichletBC
    variable = u
    function_x = 'x_exact_sln'
    function_y = 'y_exact_sln'
    function_z = '0'
    boundary = 'left right top bottom'
  []
[]

[Functions]
  [x_exact_sln]
    type = ParsedFunction
    expression = 'cos(.5*pi*x)*sin(.5*pi*y)'
  []
  [y_exact_sln]
    type = ParsedFunction
    expression = 'sin(.5*pi*x)*cos(.5*pi*y)'
  []
  [ffx]
    type = ParsedFunction
    expression = '.5*pi*pi*cos(.5*pi*x)*sin(.5*pi*y)'
  []
  [ffy]
    type = ParsedFunction
    expression = '.5*pi*pi*sin(.5*pi*x)*cos(.5*pi*y)'
  []
[]

[Materials]
  [functor]
    type = ADVectorMagnitudeFunctorMaterial
    vector_functor = u
    vector_magnitude_name = mat_mag
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/vector_fe/electromagnetic_coulomb_gauge.i)

# This is an MMS problem that demonstrates solution of Maxwell's equations in the
# Coulomb gauge potential form. The equations solved are:
# -\nabla^2 V = f_{V,mms}
# -\nabla^2 A - \omega^2 A + \nabla \frac{\partial V}{\partial t} = f_{A,mms}
# This tests the value and gradient of a VectorMooseVariable as well as the time
# derivative of the gradient of a standard MooseVariable
#
# This input file is subject to two tests:
# 1) An exodiff test of the physics
# 2) A Jacobian test to verify accuracy of hand-coded Jacobian routines

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -1
  ymin = -1
[]

[Variables]
  [./V]
  [../]
  [./A]
    family = LAGRANGE_VEC
    order = FIRST
    scaling = 1e-10
  [../]
[]

[Kernels]
  [./diff]
    type = CoefDiffusion
    variable = V
    coef = 5
  [../]
  [./V_frc]
    type = BodyForce
    function = 'V_forcing_function'
    variable = V
  [../]
  [./A_diff]
    type = VectorCoefDiffusion
    variable = A
    coef = 5
  [../]
  [./A_coeff_reaction]
    type = VectorCoeffReaction
    variable = A
    coefficient = -.09
  [../]
  [./A_coupled_grad_td]
    type = VectorCoupledGradientTimeDerivative
    variable = A
    v = V
  [../]
  [./A_frc]
    type = VectorBodyForce
    variable = A
    function_x = 'Ax_forcing_function'
    function_y = 'Ay_forcing_function'
    function_z = '0'
  [../]
[]

[BCs]
  [./bnd_V]
    type = FunctionDirichletBC
    variable = V
    boundary = 'left right top bottom'
    function = 'V_exact_sln'
  [../]
  [./bnd_A]
    type = VectorPenaltyDirichletBC
    variable = A
    x_exact_sln = 'Ax_exact_sln'
    y_exact_sln = 'Ay_exact_sln'
    z_exact_sln = '0'
    penalty = 1e10
    boundary = 'left right top bottom'
  [../]
[]

[Functions]
  [./V_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(1.1*x)*cos(1.2*y)'
  [../]
  [./Ax_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(0.4*x)*cos(0.5*y)'
  [../]
  [./Ay_exact_sln]
    type = ParsedFunction
    expression = 'cos(0.3*t)*cos(0.6*x)*cos(0.7*y)'
  [../]
  [./V_forcing_function]
    type = ParsedFunction
    expression = '0.33*sin(0.3*t)*sin(1.1*x)*cos(1.2*y) + 13.25*cos(0.3*t)*cos(1.1*x)*cos(1.2*y)'
  [../]
  [./Ax_forcing_function]
    type = ParsedFunction
    expression = '0.33*sin(0.3*t)*sin(1.1*x)*cos(1.2*y) + 1.96*cos(0.3*t)*cos(0.4*x)*cos(0.5*y)'
  [../]
  [./Ay_forcing_function]
    type = ParsedFunction
    expression = '0.36*sin(0.3*t)*sin(1.2*y)*cos(1.1*x) + 4.16*cos(0.3*t)*cos(0.6*x)*cos(0.7*y)'
  [../]
[]

[Preconditioning]
  [./pre]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  end_time = 3
  l_max_its = 100
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'asm 100'
  petsc_options = '-ksp_converged_reason -ksp_monitor_true_residual -ksp_monitor_singular_value -snes_linesearch_monitor'
  line_search = 'bt'
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/electromagnetics/test/tests/bcs/vector_robin_bc/portbc_waves.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    ymin = -1
    elem_type = QUAD9
  []
  uniform_refine = 1
[]

[Functions]
  [mms_real] # Manufactured solution, real component
    type = ParsedVectorFunction
    expression_x = 'cos(pi*x)*sin(pi*y)'
    expression_y = '-cos(pi*x)*sin(pi*y)'
    curl_z = 'pi*sin(pi*x)*sin(pi*y) - pi*cos(pi*x)*cos(pi*y)'
  []
  [mms_imaginary] # Manufactured solution, imaginary component
    type = ParsedVectorFunction
    expression_x = 'cos(pi*x + pi/2)*sin(pi*y)'
    expression_y = '-cos(pi*x + pi/2)*sin(pi*x)'
    curl_z = 'pi*sin(pi*x)*cos(pi*y) + pi*sin(pi*y)*cos(pi*x)'
  []
[]

[Variables]
  [u_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [u_imaginary]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = u_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = u_real
  []
  [rhs_real]
    type = VectorBodyForce
    variable = u_real
    function_x = 'pi*pi*sin(pi*x)*cos(pi*y) + sin(pi*y)*cos(pi*x) + pi*pi*sin(pi*y)*cos(pi*x)'
    function_y = '-pi*pi*sin(pi*x)*cos(pi*y) - pi*pi*sin(pi*y)*cos(pi*x) - sin(pi*y)*cos(pi*x)'
  []
  [curl_curl_imaginary]
    type = CurlCurlField
    variable = u_imaginary
  []
  [coeff_imaginary]
    type = VectorFunctionReaction
    variable = u_imaginary
  []
  [rhs_imaginary]
    type = VectorBodyForce
    variable = u_imaginary
    function_x = '-pi*pi*sin(pi*x)*sin(pi*y) - sin(pi*x)*sin(pi*y) + pi*pi*cos(pi*x)*cos(pi*y)'
    function_y = 'sin(pi*x)*sin(pi*y) + pi*pi*sin(pi*x)*sin(pi*y) - pi*pi*cos(pi*x)*cos(pi*y)'
  []
[]

[BCs]
  [sides_real]
    type = VectorEMRobinBC
    variable = u_real
    component = real
    coupled_field = u_imaginary
    imag_incoming = mms_imaginary
    real_incoming = mms_real
    boundary = 'left right top bottom'
  []
  [sides_imaginary]
    type = VectorEMRobinBC
    variable = u_imaginary
    component = imaginary
    coupled_field = u_real
    imag_incoming = mms_imaginary
    real_incoming = mms_real
    boundary = 'left right top bottom'
  []
[]

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

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i)

###########################################################
# This is a simple test of the VectorCoupledTimeDerivative kernel.
# The expected solution for the vector variable v is
# v_x(x) = 1/2 * (x^2 + x)
# v_y(x) = 1/2 * (x^2 + x)
###########################################################

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
  [../]
  [./v]
    family = LAGRANGE_VEC
  [../]
[]

[Kernels]
  [./time_u]
    type = VectorTimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  [../]
  [./time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_kernels.i)

# Test for EM module vector kernels CurlCurlField and VectorFunctionReaction
# Manufactured solution: u = y * x_hat - x * y_hat

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -1
    ymin = -1
    elem_type = QUAD9
  []
[]

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

[Kernels]
  [curl_curl]
    type = CurlCurlField
    variable = u
  []
  [coeff]
    type = VectorFunctionReaction
    variable = u
  []
  [rhs]
    type = VectorBodyForce
    variable = u
    function_x = 'y'
    function_y = '-x'
  []
[]

[BCs]
  [sides]
    type = VectorCurlPenaltyDirichletBC
    variable = u
    function_x = 'y'
    function_y = '-x'
    penalty = 1e8
    boundary = 'left right top bottom'
  []
[]

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

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/vector_fe/lagrange_vec.i)

# This example reproduces the libmesh vector_fe example 1 results

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -1
  ymin = -1
  elem_type = QUAD9
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
    order = SECOND
  [../]
[]

[Kernels]
  [./diff]
    type = VectorDiffusion
    variable = u
  [../]
  [./body_force]
    type = VectorBodyForce
    variable = u
    function_x = 'ffx'
    function_y = 'ffy'
  [../]
[]

[BCs]
  [./bnd]
    type = VectorFunctionDirichletBC
    variable = u
    function_x = 'x_exact_sln'
    function_y = 'y_exact_sln'
    function_z = '0'
    boundary = 'left right top bottom'
  [../]
[]

[Functions]
  [./x_exact_sln]
    type = ParsedFunction
    expression = 'cos(.5*pi*x)*sin(.5*pi*y)'
  [../]
  [./y_exact_sln]
    type = ParsedFunction
    expression = 'sin(.5*pi*x)*cos(.5*pi*y)'
  [../]
  [./ffx]
    type = ParsedFunction
    expression = '.5*pi*pi*cos(.5*pi*x)*sin(.5*pi*y)'
  [../]
  [./ffy]
    type = ParsedFunction
    expression = '.5*pi*pi*sin(.5*pi*x)*cos(.5*pi*y)'
  [../]
[]

[Preconditioning]
  [./pre]
    type = SMP
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

Description
Input Parameters
Input Files