VectorCurrentSource

Kernel to calculate the current source term in the Helmholtz wave equation.

Overview

The VectorCurrentSource object implements the volumetric current source term in the electric field Helmholtz wave equation. This term, in general, is

$var element = document.getElementById("moose-equation-523e8a69-1318-4165-9a97-4ea03923e12f");katex.render(" j \\; f(\\mathbf{r}, t) \\; \\vec{J}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where

$var element = document.getElementById("moose-equation-8e2c275c-306c-4538-af31-ee7f3957d46f");katex.render("j = \\sqrt{-1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ,
$var element = document.getElementById("moose-equation-94952623-7014-450e-80e5-d0e8a2a1e293");katex.render("f(\\mathbf{r}, t)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a time- and spatially-varying coefficient function, and
$var element = document.getElementById("moose-equation-a3c1b736-a833-4867-929c-58ae143b4289");katex.render("\\vec{J}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the complex source vector field.

Note that $var element = document.getElementById("moose-equation-b58f1887-63f6-48ea-b837-e729c20baae0");katex.render("\\vec{J}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is provided via vector-valued functions, using the "source_real" and "source_imag" parameters for the real and imaginary components respectively.

Example Input File Syntax

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [current_real]
    type = VectorCurrentSource<<<{"description": "Kernel to calculate the current source term in the Helmholtz wave equation.", "href": "VectorCurrentSource.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u_real
    function_coefficient<<<{"description": "Function coefficient multiplier for current source (normally $\\omega$ or $\\omega \\cdot \\mu$)."}>>> = -1.0
    source_real<<<{"description": "Current Source vector, real component"}>>> = source_real
    source_imag<<<{"description": "Current Source vector, imaginary component"}>>> = source_imag
    component<<<{"description": "Component of field (real or imaginary)."}>>> = real
  []
[]

Input Parameters

source_imagCurrent Source vector, imaginary component
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Current Source vector, imaginary component
source_realCurrent Source vector, real component
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Current Source vector, real component
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
componentComponent of field (real or imaginary).
C++ Type:MooseEnum
Options:real, imaginary
Controllable:No
Description:Component of field (real or imaginary).
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
function_coefficient1Function coefficient multiplier for current source (normally $\omega$ or $\omega \cdot \mu$).
Default:1
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function coefficient multiplier for current source (normally $\omega$ or $\omega \cdot \mu$).
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)

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

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.)
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

Input Files

(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/vector_azim_magnetic_time_deriv.i)
(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/error_azim_magnetic_time_deriv.i)
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_current_source.i)
(modules/electromagnetics/test/tests/auxkernels/heating/aux_current_source_heating.i)
(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave.i)
(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/scalar_azim_magnetic_time_deriv.i)
(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave_with_ADMaterials.i)

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

# Test for VectorCurrentSource
# Manufactured solution: u_real = y^2 * x_hat - x^2 * y_hat
#                        u_imag = y^2 * x_hat - x^2 * y_hat

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

[Functions]
  [source_real]
    type = ParsedVectorFunction
    expression_x = 'y*y - 2'
    expression_y = '2 - x*x'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = '2 - y*y'
    expression_y = 'x*x - 2'
  []
[]

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

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = u_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = u_real
  []
  [current_real]
    type = VectorCurrentSource
    variable = u_real
    function_coefficient = -1.0
    source_real = source_real
    source_imag = source_imag
    component = real
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = u_imag
  []
  [coeff_imag]
    type = VectorFunctionReaction
    variable = u_imag
  []
  [current_imag]
    type = VectorCurrentSource
    variable = u_imag
    function_coefficient = -1.0
    source_real = source_real
    source_imag = source_imag
    component = imaginary
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = u_real
    function_x = 'y*y'
    function_y = '-x*x'
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = u_imag
    function_x = 'y*y'
    function_y = '-x*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
[]

(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/vector_azim_magnetic_time_deriv.i)

# Test for AzimuthMagneticTimeDerivRZ with a vector input
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
#                        E_imag = y^2 * x_hat - x^2 * y_hat
#                        dB_theta_real / dt = -(2*y + 2*x)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 1
    xmin = 0
    ymax = 1
    ymin = -1
    elem_type = QUAD9
  []
  coord_type = RZ
  rz_coord_axis = Y
[]

[Functions]
  #The exact solution for the heated species and electric field real and imag. component
  [exact_real]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []
  [exact_imag]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []

  #The forcing terms for the heated species and electric field real and imag. component
  [source_real]
    type = ParsedVectorFunction
    expression_x = '-y^2 - cos(pi*y) - 2'
    expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = '-y^2 + sin(pi*y) - 2'
    expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
  []

  [current_real]
    type = ParsedVectorFunction
    expression_x = 'sin(pi*y)'
    expression_y = '-sin(pi*x)'
  []
  [current_imag]
    type = ParsedVectorFunction
    expression_x = 'cos(pi*y)'
    expression_y = '-cos(pi*x)'
  []

  [azim_dB_dt_func]
    type = ParsedFunction
    expression = '-(2*y + 2*x)'
  []
[]

[Materials]
  [WaveCoeff]
    type = WaveEquationCoefficient
    eps_rel_real = 1.0
    eps_rel_imag = 0.0
    k_real = 1.0
    k_imag = 0.0
    mu_rel_real = 1.0
    mu_rel_imag = 0.0
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = ADMatWaveReaction
    variable = E_real
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = real
  []
  [current_real]
    type = VectorCurrentSource
    variable = E_real
    source_real = current_real
    source_imag = current_imag
    component = real
  []
  [body_force_real]
    type = VectorBodyForce
    variable = E_real
    function = source_real
  []

  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = ADMatWaveReaction
    variable = E_imag
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = imaginary
  []
  [current_imag]
    type = VectorCurrentSource
    variable = E_imag
    source_real = current_real
    source_imag = current_imag
    component = imaginary
  []
  [body_force_imag]
    type = VectorBodyForce
    variable = E_imag
    function = source_imag
  []
[]

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

[AuxKernels]
  [aux_azim_dB_dt_vector]
    type = AzimuthMagneticTimeDerivRZ
    Efield = E_real
    variable = azim_dB_dt_term_vector
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = E_real
    function = exact_real
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = E_imag
    function = exact_imag
    penalty = 1e8
    boundary = 'left right top bottom'
  []
[]

[Postprocessors]
  [error_real]
    type = ElementVectorL2Error
    variable = E_real
    function = exact_real
  []
  [error_imag]
    type = ElementVectorL2Error
    variable = E_imag
    function = exact_imag
  []

  [error_azim_dB_dt_vector]
    type = ElementL2Error
    variable = azim_dB_dt_term_vector
    function = azim_dB_dt_func
  []

  [h]
    type = AverageElementSize
  []
  [h_squared]
    type = ParsedPostprocessor
    pp_names = 'h'
    expression = 'h * h'
  []
[]

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

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

  nl_rel_tol = 1e-16
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/error_azim_magnetic_time_deriv.i)

# Test for AzimuthMagneticTimeDerivRZ with scalar inputs
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
#                        E_imag = y^2 * x_hat - x^2 * y_hat
#                        dB_theta_real / dt = -(2*y + 2*x)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 1
    xmin = 0
    ymax = 1
    ymin = -1
    elem_type = QUAD9
  []
  coord_type = RZ
  rz_coord_axis = Y
[]

[Functions]
  #The exact solution for the heated species and electric field real and imag. component
  [exact_real]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []
  [exact_imag]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []

  #The forcing terms for the heated species and electric field real and imag. component
  [source_real]
    type = ParsedVectorFunction
    expression_x = '-y^2 - cos(pi*y) - 2'
    expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = '-y^2 + sin(pi*y) - 2'
    expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
  []

  [current_real]
    type = ParsedVectorFunction
    expression_x = 'sin(pi*y)'
    expression_y = '-sin(pi*x)'
  []
  [current_imag]
    type = ParsedVectorFunction
    expression_x = 'cos(pi*y)'
    expression_y = '-cos(pi*x)'
  []

  [azim_dB_dt_func]
    type = ParsedFunction
    expression = '-(2*y + 2*x)'
  []
[]

[Materials]
  [WaveCoeff]
    type = WaveEquationCoefficient
    eps_rel_real = 1.0
    eps_rel_imag = 0.0
    k_real = 1.0
    k_imag = 0.0
    mu_rel_real = 1.0
    mu_rel_imag = 0.0
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = ADMatWaveReaction
    variable = E_real
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = real
  []
  [current_real]
    type = VectorCurrentSource
    variable = E_real
    source_real = current_real
    source_imag = current_imag
    component = real
  []
  [body_force_real]
    type = VectorBodyForce
    variable = E_real
    function = source_real
  []

  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = ADMatWaveReaction
    variable = E_imag
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = imaginary
  []
  [current_imag]
    type = VectorCurrentSource
    variable = E_imag
    source_real = current_real
    source_imag = current_imag
    component = imaginary
  []
  [body_force_imag]
    type = VectorBodyForce
    variable = E_imag
    function = source_imag
  []
[]

[AuxVariables]
  [aux_E_real_x]
    family = MONOMIAL
    order = FIRST
  []
  [aux_E_real_y]
    family = MONOMIAL
    order = FIRST
  []

  [azim_dB_dt_term]
    family = MONOMIAL
    order = FIRST
  []
[]

[AuxKernels]
  [aux_E_real_x]
    type = VectorVariableComponentAux
    variable = aux_E_real_x
    vector_variable = E_real
    component = X
  []
  [aux_E_real_y]
    type = VectorVariableComponentAux
    variable = aux_E_real_y
    vector_variable = E_real
    component = Y
  []

  [aux_azim_dB_dt]
    type = AzimuthMagneticTimeDerivRZ
    # Efield = E_real
    # Efield_X = aux_E_real_x
    # Efield_Y = aux_E_real_y
    variable = azim_dB_dt_term
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = E_real
    function = exact_real
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = E_imag
    function = exact_imag
    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'

  nl_rel_tol = 1e-16
[]

[Outputs]
  exodus = true
  csv = true
[]

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

# Test for VectorCurrentSource
# Manufactured solution: u_real = y^2 * x_hat - x^2 * y_hat
#                        u_imag = y^2 * x_hat - x^2 * y_hat

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

[Functions]
  [source_real]
    type = ParsedVectorFunction
    expression_x = 'y*y - 2'
    expression_y = '2 - x*x'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = '2 - y*y'
    expression_y = 'x*x - 2'
  []
[]

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

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = u_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = u_real
  []
  [current_real]
    type = VectorCurrentSource
    variable = u_real
    function_coefficient = -1.0
    source_real = source_real
    source_imag = source_imag
    component = real
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = u_imag
  []
  [coeff_imag]
    type = VectorFunctionReaction
    variable = u_imag
  []
  [current_imag]
    type = VectorCurrentSource
    variable = u_imag
    function_coefficient = -1.0
    source_real = source_real
    source_imag = source_imag
    component = imaginary
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = u_real
    function_x = 'y*y'
    function_y = '-x*x'
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = u_imag
    function_x = 'y*y'
    function_y = '-x*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
[]

(modules/electromagnetics/test/tests/auxkernels/heating/aux_current_source_heating.i)

# Test for SourceCurrentHeating
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
#                        E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
#                        heating = 'sin(x*pi)*cos(x*pi) + sin(y*pi)*cos(y*pi)'

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = -1
    ymin = -1
    elem_type = QUAD9
  []
[]

[Functions]
  #The exact solution for the heated species and electric field real and imag. component
  [exact_real]
    type = ParsedVectorFunction
    expression_x = 'cos(pi*y)'
    expression_y = '-cos(pi*x)'
  []
  [exact_imag]
    type = ParsedVectorFunction
    expression_x = 'sin(pi*y)'
    expression_y = '-sin(pi*x)'
  []

  #The forcing terms for the heated species and electric field real and imag. component
  [source_real]
    type = ParsedVectorFunction
    expression_x = '-2*cos(pi*y) + pi^2*cos(pi*y)'
    expression_y = '-pi^2*cos(pi*x) + 2*cos(pi*x)'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = 'pi^2*sin(pi*y)'
    expression_y = '-pi^2*sin(pi*x)'
  []

  [current_real]
    type = ParsedVectorFunction
    expression_x = 'sin(pi*y)'
    expression_y = '-sin(pi*x)'
  []
  [current_imag]
    type = ParsedVectorFunction
    expression_x = 'cos(pi*y)'
    expression_y = '-cos(pi*x)'
  []

  [heating_func]
    type = ParsedFunction
    expression = '1.0*sin(x*pi)*cos(x*pi) + 1.0*sin(y*pi)*cos(y*pi)'
  []
[]

[Materials]
  [WaveCoeff]
    type = WaveEquationCoefficient
    eps_rel_real = 1.0
    eps_rel_imag = 0.0
    k_real = 1.0
    k_imag = 0.0
    mu_rel_real = 1.0
    mu_rel_imag = 0.0
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = ADMatWaveReaction
    variable = E_real
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = real
  []
  [current_real]
    type = VectorCurrentSource
    variable = E_real
    source_real = current_real
    source_imag = current_imag
    component = real
  []
  [body_force_real]
    type = VectorBodyForce
    variable = E_real
    function = source_real
  []

  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = ADMatWaveReaction
    variable = E_imag
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = imaginary
  []
  [current_imag]
    type = VectorCurrentSource
    variable = E_imag
    source_real = current_real
    source_imag = current_imag
    component = imaginary
  []
  [body_force_imag]
    type = VectorBodyForce
    variable = E_imag
    function = source_imag
  []
[]

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

[AuxKernels]
  [aux_current_heating]
    type = SourceCurrentHeating
    variable = current_heating_term
    E_real = E_real
    E_imag = E_imag
    source_real = current_real
    source_imag = current_imag
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = E_real
    function = exact_real
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = E_imag
    function = exact_imag
    penalty = 1e8
    boundary = 'left right top bottom'
  []
[]

[Postprocessors]
  [error_real]
    type = ElementVectorL2Error
    variable = E_real
    function = exact_real
  []
  [error_imag]
    type = ElementVectorL2Error
    variable = E_imag
    function = exact_imag
  []

  [error_aux_heating]
    type = ElementL2Error
    variable = current_heating_term
    function = heating_func
  []

  [h]
    type = AverageElementSize
  []
  [h_squared]
    type = ParsedPostprocessor
    pp_names = 'h'
    expression = 'h * h'
  []
[]

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

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

  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave.i)

# Evanescent wave decay benchmark
# frequency = 20 GHz
# eps_R = 1.0
# mu_R = 1.0

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = waveguide_discontinuous.msh
  []
[]

[Functions]
  [waveNumberSquared]
    type = ParsedFunction
    expression = '(2*pi*20e9/3e8)^2'
  []
  [omegaMu]
    type = ParsedFunction
    expression = '2*pi*20e9*4*pi*1e-7'
  []
  [beta]
    type = ParsedFunction
    expression = '2*pi*20e9/3e8'
  []
  [curr_real]
    type = ParsedVectorFunction
    expression_y = 1.0
  []
  [curr_imag] # defaults to '0.0 0.0 0.0'
    type = ParsedVectorFunction
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curlCurl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = E_real
    function = waveNumberSquared
    sign = negative
  []
  [source_real]
    type = VectorCurrentSource
    variable = E_real
    component = real
    source_real = curr_real
    source_imag = curr_imag
    function_coefficient = omegaMu
    block = source
  []
  [curlCurl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = VectorFunctionReaction
    variable = E_imag
    function = waveNumberSquared
    sign = negative
  []
  [source_imaginary]
    type = VectorCurrentSource
    variable = E_imag
    component = imaginary
    source_real = curr_real
    source_imag = curr_imag
    function_coefficient = omegaMu
    block = source
  []
[]

[BCs]
  [absorbing_left_real]
    type = VectorEMRobinBC
    variable = E_real
    component = real
    beta = beta
    coupled_field = E_imag
    mode = absorbing
    boundary = 'port'
  []
  [absorbing_right_real]
    type = VectorEMRobinBC
    variable = E_real
    component = real
    beta = beta
    coupled_field = E_imag
    mode = absorbing
    boundary = 'exit'
  []
  [absorbing_left_imag]
    type = VectorEMRobinBC
    variable = E_imag
    component = imaginary
    beta = beta
    coupled_field = E_real
    mode = absorbing
    boundary = 'port'
  []
  [absorbing_right_imag]
    type = VectorEMRobinBC
    variable = E_imag
    component = imaginary
    beta = beta
    coupled_field = E_real
    mode = absorbing
    boundary = 'exit'
  []
[]

[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
[]

[Debug]
  show_var_residual_norms = true
[]

(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/scalar_azim_magnetic_time_deriv.i)

# Test for AzimuthMagneticTimeDerivRZ with scalar inputs
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
#                        E_imag = y^2 * x_hat - x^2 * y_hat
#                        dB_theta_real / dt = -(2*y + 2*x)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmax = 1
    xmin = 0
    ymax = 1
    ymin = -1
    elem_type = QUAD9
  []
  coord_type = RZ
  rz_coord_axis = Y
[]

[Functions]
  #The exact solution for the heated species and electric field real and imag. component
  [exact_real]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []
  [exact_imag]
    type = ParsedVectorFunction
    expression_x = 'y^2'
    expression_y = '-x^2'
  []

  #The forcing terms for the heated species and electric field real and imag. component
  [source_real]
    type = ParsedVectorFunction
    expression_x = '-y^2 - cos(pi*y) - 2'
    expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
  []
  [source_imag]
    type = ParsedVectorFunction
    expression_x = '-y^2 + sin(pi*y) - 2'
    expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
  []

  [current_real]
    type = ParsedVectorFunction
    expression_x = 'sin(pi*y)'
    expression_y = '-sin(pi*x)'
  []
  [current_imag]
    type = ParsedVectorFunction
    expression_x = 'cos(pi*y)'
    expression_y = '-cos(pi*x)'
  []

  [azim_dB_dt_func]
    type = ParsedFunction
    expression = '-(2*y + 2*x)'
  []
[]

[Materials]
  [WaveCoeff]
    type = WaveEquationCoefficient
    eps_rel_real = 1.0
    eps_rel_imag = 0.0
    k_real = 1.0
    k_imag = 0.0
    mu_rel_real = 1.0
    mu_rel_imag = 0.0
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = ADMatWaveReaction
    variable = E_real
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = real
  []
  [current_real]
    type = VectorCurrentSource
    variable = E_real
    source_real = current_real
    source_imag = current_imag
    component = real
  []
  [body_force_real]
    type = VectorBodyForce
    variable = E_real
    function = source_real
  []

  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = ADMatWaveReaction
    variable = E_imag
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = imaginary
  []
  [current_imag]
    type = VectorCurrentSource
    variable = E_imag
    source_real = current_real
    source_imag = current_imag
    component = imaginary
  []
  [body_force_imag]
    type = VectorBodyForce
    variable = E_imag
    function = source_imag
  []
[]

[AuxVariables]
  [aux_E_real_x]
    family = MONOMIAL
    order = FIRST
  []
  [aux_E_real_y]
    family = MONOMIAL
    order = FIRST
  []

  [azim_dB_dt_term_scalar]
    family = MONOMIAL
    order = FIRST
  []
[]

[AuxKernels]
  [aux_E_real_x]
    type = VectorVariableComponentAux
    variable = aux_E_real_x
    vector_variable = E_real
    component = X
  []
  [aux_E_real_y]
    type = VectorVariableComponentAux
    variable = aux_E_real_y
    vector_variable = E_real
    component = Y
  []

  [aux_azim_dB_dt_scalar]
    type = AzimuthMagneticTimeDerivRZ
    Efield_X = aux_E_real_x
    Efield_Y = aux_E_real_y
    variable = azim_dB_dt_term_scalar
  []
[]

[BCs]
  [sides_real]
    type = VectorCurlPenaltyDirichletBC
    variable = E_real
    function = exact_real
    penalty = 1e8
    boundary = 'left right top bottom'
  []
  [sides_imag]
    type = VectorCurlPenaltyDirichletBC
    variable = E_imag
    function = exact_imag
    penalty = 1e8
    boundary = 'left right top bottom'
  []
[]

[Postprocessors]
  [error_real]
    type = ElementVectorL2Error
    variable = E_real
    function = exact_real
  []
  [error_imag]
    type = ElementVectorL2Error
    variable = E_imag
    function = exact_imag
  []

  [error_azim_dB_dt_scalar]
    type = ElementL2Error
    variable = azim_dB_dt_term_scalar
    function = azim_dB_dt_func
  []

  [h]
    type = AverageElementSize
  []
  [h_squared]
    type = ParsedPostprocessor
    pp_names = 'h'
    expression = 'h * h'
  []
[]

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

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

  nl_rel_tol = 1e-16
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave_with_ADMaterials.i)

# This test is exactly the same as 'evanescent_wave/evanescent_wave.i'
# except it uses ADMatWaveReaction and WaveEquationCoefficient instead of VectorFunctionReaction

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = waveguide_discontinuous.msh
  []
[]

[Functions]
  [omegaMu]
    type = ParsedFunction
    expression = '2*pi*20e9*4*pi*1e-7'
  []
  [beta]
    type = ParsedFunction
    expression = '2*pi*20e9/3e8'
  []
  [curr_real]
    type = ParsedVectorFunction
    expression_y = 1.0
  []
  [curr_imag] # defaults to '0.0 0.0 0.0'
    type = ParsedVectorFunction
  []

  [eps_real_func]
    type = ParsedFunction
    expression = '1'
  []
  [mu_real_func]
    type = ParsedFunction
    expression = '(1 / 3e8)^2'
  []
  [k_real_func]
    type = ParsedFunction
    expression = '2*pi*20e9'
  []
[]

[Materials]
  [WaveCoeff]
    type = WaveEquationCoefficient
    eps_rel_imag = 0
    eps_rel_real = eps_real
    k_real = k_real
    mu_rel_imag = 0
    mu_rel_real = mu_real
  []
  [eps_real]
    type = ADGenericFunctionMaterial
    prop_names = eps_real
    prop_values = eps_real_func
  []
  [mu_real]
    type = ADGenericFunctionMaterial
    prop_names = mu_real
    prop_values = mu_real_func
  []
  [k_real]
    type = ADGenericFunctionMaterial
    prop_names = k_real
    prop_values = k_real_func
  []
[]

[Variables]
  [E_real]
    family = NEDELEC_ONE
    order = FIRST
  []
  [E_imag]
    family = NEDELEC_ONE
    order = FIRST
  []
[]

[Kernels]
  [curlCurl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = ADMatWaveReaction
    variable = E_real
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = real
  []
  [source_real]
    type = VectorCurrentSource
    variable = E_real
    component = real
    source_real = curr_real
    source_imag = curr_imag
    function_coefficient = omegaMu
    block = source
  []
  [curlCurl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = ADMatWaveReaction
    variable = E_imag
    field_real =  E_real
    field_imag =  E_imag
    wave_coef_real = wave_equation_coefficient_real
    wave_coef_imag = wave_equation_coefficient_imaginary
    component = imaginary
  []
  [source_imaginary]
    type = VectorCurrentSource
    variable = E_imag
    component = imaginary
    source_real = curr_real
    source_imag = curr_imag
    function_coefficient = omegaMu
    block = source
  []
[]

[BCs]
  [absorbing_left_real]
    type = VectorEMRobinBC
    variable = E_real
    component = real
    beta = beta
    coupled_field = E_imag
    mode = absorbing
    boundary = 'port'
  []
  [absorbing_right_real]
    type = VectorEMRobinBC
    variable = E_real
    component = real
    beta = beta
    coupled_field = E_imag
    mode = absorbing
    boundary = 'exit'
  []
  [absorbing_left_imag]
    type = VectorEMRobinBC
    variable = E_imag
    component = imaginary
    beta = beta
    coupled_field = E_real
    mode = absorbing
    boundary = 'port'
  []
  [absorbing_right_imag]
    type = VectorEMRobinBC
    variable = E_imag
    component = imaginary
    beta = beta
    coupled_field = E_real
    mode = absorbing
    boundary = 'exit'
  []
[]

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

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

[Outputs]
  exodus = true
  file_base = 'evanescent_wave_out'
  print_linear_residuals = true
[]

[Debug]
  show_var_residual_norms = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files