VectorEMRobinBC

First order Robin-style Absorbing/Port BC for vector variables.

Overview

The VectorEMRobinBC object is an implementation of the first-order Robin-style boundary condition outlined in (Jin, 2014) Equation 9.60 and (Jin, 2010) Equation 9.3.51 for vector field variables.

General (vector field) form

The generic Jin condition is, in turn, based on the Sommerfeld radiation condition for scattered fields. Given that any scattered field can be made up of a combination of the scattered field and the incident field ( $var element = document.getElementById("moose-equation-5e7d5192-a7ff-42cb-811d-64fd099c3cd9");katex.render("\\vec{E} = \\vec{E}_{sc} + \\vec{E}_{inc}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ), then we have

$var element = document.getElementById("moose-equation-70c7f543-c4e1-46c4-9fb1-021297df9d17");katex.render(" \\hat{\\mathbf{n}} \\times \\left( \\frac{1}{\\mu_r} \\nabla \\times \\vec{E} \\right) + \\frac{j k_0}{\\eta_r} \\hat{\\mathbf{n}} \\times \\left( \\hat{\\mathbf{n}} \\times \\vec{E} \\right) = \\hat{\\mathbf{n}} \\times (\\nabla \\times \\vec{E}_{inc}) + \\frac{j k_0}{\\eta_r} \\hat{\\mathbf{n}} \\times \\left( \\hat{\\mathbf{n}} \\times \\vec{E}_{inc} \\right)", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where

$var element = document.getElementById("moose-equation-11aaeef2-c2d2-4447-b7e2-fc416a60bc11");katex.render("\\vec{E}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the total (i.e., the solution) electric field vector,
$var element = document.getElementById("moose-equation-8fb29235-285c-4587-8974-f0f0c099285c");katex.render("\\vec{E}_{inc}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the incoming electric field vector,
$var element = document.getElementById("moose-equation-06fe3d19-5762-4e7d-8323-63b7bec73eee");katex.render("\\mu_r", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the relative magnetic permeability,
$var element = document.getElementById("moose-equation-8107d581-556a-4bb3-ad37-402f9fdb3cf4");katex.render("j = \\sqrt{-1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ,
$var element = document.getElementById("moose-equation-44e61f31-9f8e-4bd2-99b1-ab6686ef56ac");katex.render("k_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the wave number ( $var element = document.getElementById("moose-equation-2fcbfe59-ee39-4667-b576-4df18acff515");katex.render("2 \\pi / \\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-5df149cb-0590-4dff-97c0-910891717f25");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the wavelength),
$var element = document.getElementById("moose-equation-a3b86953-ac30-46ed-a19f-3f533a6ab282");katex.render("\\eta_r", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a radiation condition parameter ( $var element = document.getElementById("moose-equation-1879b192-9d77-48e9-be68-43a62d0fb191");katex.render("\\eta_r = 1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ if the condition is applied in free space), and
$var element = document.getElementById("moose-equation-85f9c6a7-0046-4121-87aa-7e3bf20e2e63");katex.render("\\hat{\\mathbf{n}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the boundary normal vector.

Implemented form

In VectorEMRobinBC, this condition is slightly generalized. The ratio of $var element = document.getElementById("moose-equation-544e3546-4c0e-4273-86c8-e86ab6f3c018");katex.render("k_0 / \\eta_r", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is generalized to a coefficient function $var element = document.getElementById("moose-equation-ba6907fb-10e1-48da-826b-85c1d037eec9");katex.render("\\beta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and so the implemented form is

$var element = document.getElementById("moose-equation-b413b9bb-0808-4fff-9f17-56bfcae788b2");katex.render(" \\hat{\\mathbf{n}} \\times \\left( \\frac{1}{\\mu_r} \\nabla \\times \\vec{E} \\right) + j\\beta(\\mathbf{r}) \\hat{\\mathbf{n}} \\times \\left( \\hat{\\mathbf{n}} \\times \\vec{E} \\right) = \\hat{\\mathbf{n}} \\times (\\nabla \\times \\vec{E}_{inc}) + j\\beta(\\mathbf{r}) \\hat{\\mathbf{n}} \\times \\left( \\hat{\\mathbf{n}} \\times \\vec{E}_{inc} \\right)", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where

$var element = document.getElementById("moose-equation-5ec080bb-6a35-4f01-a8b1-a708cf13f528");katex.render("\\beta(\\mathbf{r})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a function containing the condition coefficients.

Note that $var element = document.getElementById("moose-equation-c7038fb4-efcf-4a1c-9dda-be0a993ef4fe");katex.render("\\beta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ generally is just the wavenumber $var element = document.getElementById("moose-equation-cdc06582-bd09-457f-8796-54754bcaffe4");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , since this condition is generally applied in free space, but any function can be applied through the "beta" parameter.

Usage notes

It is important to note that when used as an absorber (strictly absorbing means "mode" is set to absorbing and zero incoming wave but a port also has an absorbing component), care must be taken in setting the shape of the truncation boundary as well as the distance from the scattering object. Boundaries as close as $var element = document.getElementById("moose-equation-e6f380e4-e64a-4114-b9dc-30818c8fd40a");katex.render("0.3 \\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ away from the object was shown in (Jin, 2014), and several wavelengths were used in the Dipole Antenna Benchmark for VectorEMRobinBC. Also, this boundary condition is best applied on spherical boundaries (as a result of its origin from the Sommerfeld condition, which was derived for spherical boundaries). Of course, it is also valid on any non-spherical smooth surface with a trade-off in accuracy.

Example Input File Syntax

As a Port

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [sides_real]
    type = VectorEMRobinBC<<<{"description": "First order Robin-style Absorbing/Port BC for vector variables.", "href": "VectorEMRobinBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u_real
    component<<<{"description": "Variable field component (real or imaginary)."}>>> = real
    coupled_field<<<{"description": "Coupled field variable."}>>> = u_imaginary
    imag_incoming<<<{"description": "Imaginary incoming field vector."}>>> = mms_imaginary
    real_incoming<<<{"description": "Real incoming field vector."}>>> = mms_real
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left right top bottom'
  []
[]

As an Absorber

[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
  [radiation_condition_real]
    type = VectorEMRobinBC<<<{"description": "First order Robin-style Absorbing/Port BC for vector variables.", "href": "VectorEMRobinBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = E_real
    coupled_field<<<{"description": "Coupled field variable."}>>> = E_imag
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = boundary
    component<<<{"description": "Variable field component (real or imaginary)."}>>> = real
    mode<<<{"description": "Mode of operation for VectorEMRobinBC."}>>> = absorbing
    beta<<<{"description": "Scalar wave number."}>>> = 20.9439510239 # wave number at 1 GHz
  []
[]

Input Parameters

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

Required Parameters

beta1Scalar wave number.
Default:1
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Scalar wave number.
componentVariable field component (real or imaginary).
C++ Type:MooseEnum
Options:real, imaginary
Controllable:No
Description:Variable field component (real or imaginary).
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
imag_incoming0Imaginary incoming field vector.
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Imaginary incoming field vector.
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)
modeportMode of operation for VectorEMRobinBC.
Default:port
C++ Type:MooseEnum
Options:absorbing, port
Controllable:No
Description:Mode of operation for VectorEMRobinBC.
real_incoming0Real incoming field vector.
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Real incoming field vector.

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 BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
skip_execution_outside_variable_domainFalseWhether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(modules/electromagnetics/test/tests/benchmarks/dipole_antenna/dipole.i)
(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave.i)
(modules/electromagnetics/test/tests/bcs/vector_robin_bc/portbc_waves.i)
(modules/electromagnetics/test/tests/benchmarks/evanescent_wave/evanescent_wave_with_ADMaterials.i)

References

Jian-Ming Jin. Theory and Computation of Electromagnetic Fields. John Wiley & Sons, Hoboken, New Jersey, USA, 1st edition, 2010.

@book{jin-computation,
    author = "Jin, Jian-Ming",
    title = "Theory and Computation of Electromagnetic Fields",
    edition = "1st",
    year = "2010",
    publisher = "John Wiley \\& Sons",
    address = "Hoboken, New Jersey, USA"
}

Jian-Ming Jin. The Finite Element Method in Electromagnetics. John Wiley & Sons, Hoboken, New Jersey, USA, 3rd edition, 2014.

@book{jin-fem,
    author = "Jin, Jian-Ming",
    title = "The Finite Element Method in Electromagnetics",
    edition = "3rd",
    year = "2014",
    publisher = "John Wiley \\& Sons",
    address = "Hoboken, New Jersey, USA"
}

(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
[]

(modules/electromagnetics/test/tests/benchmarks/dipole_antenna/dipole.i)

# Verification Benchmark - Half-wave Dipole Antenna (Frequency Domain)
# Resonant Frequency = 1 GHz
# Wave Propagation Medium: Vacuum

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = dipole_antenna_1G.msh
  []
  [refine]
    type = RefineBlockGenerator
    input = file_mesh
    block = 'vacuum'
    refinement = 2
  []
[]

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

[Functions]
  [WaveNumberSquared]
    type = ParsedFunction
    expression = '(2*pi*1e9/3e8)*(2*pi*1e9/3e8)'
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = E_real
    function = WaveNumberSquared
    sign = negative
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = VectorFunctionReaction
    variable = E_imag
    function = WaveNumberSquared
    sign = negative
  []
[]

[BCs]
  [antenna_real]                          # Impose exact solution of electric field onto antenna surface.
    type = VectorCurlPenaltyDirichletBC   # Replace with proper antenna surface current condition.
    penalty = 1e5
    function_y = '1'
    boundary = antenna
    variable = E_real
  []
  [antenna_imag]
    type = VectorCurlPenaltyDirichletBC
    penalty = 1e5
    function_y = '1'
    boundary = antenna
    variable = E_imag
  []
  [radiation_condition_real]
    type = VectorEMRobinBC
    variable = E_real
    coupled_field = E_imag
    boundary = boundary
    component = real
    mode = absorbing
    beta = 20.9439510239  # wave number at 1 GHz
  []
  [radiation_condition_imag]
    type = VectorEMRobinBC
    variable = E_imag
    coupled_field = E_real
    boundary = boundary
    component = imaginary
    mode = absorbing
    beta = 20.9439510239  # wave number at 1 GHz
  []
[]

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

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

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/electromagnetics/test/tests/benchmarks/dipole_antenna/dipole.i)

# Verification Benchmark - Half-wave Dipole Antenna (Frequency Domain)
# Resonant Frequency = 1 GHz
# Wave Propagation Medium: Vacuum

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = dipole_antenna_1G.msh
  []
  [refine]
    type = RefineBlockGenerator
    input = file_mesh
    block = 'vacuum'
    refinement = 2
  []
[]

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

[Functions]
  [WaveNumberSquared]
    type = ParsedFunction
    expression = '(2*pi*1e9/3e8)*(2*pi*1e9/3e8)'
  []
[]

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [coeff_real]
    type = VectorFunctionReaction
    variable = E_real
    function = WaveNumberSquared
    sign = negative
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [coeff_imag]
    type = VectorFunctionReaction
    variable = E_imag
    function = WaveNumberSquared
    sign = negative
  []
[]

[BCs]
  [antenna_real]                          # Impose exact solution of electric field onto antenna surface.
    type = VectorCurlPenaltyDirichletBC   # Replace with proper antenna surface current condition.
    penalty = 1e5
    function_y = '1'
    boundary = antenna
    variable = E_real
  []
  [antenna_imag]
    type = VectorCurlPenaltyDirichletBC
    penalty = 1e5
    function_y = '1'
    boundary = antenna
    variable = E_imag
  []
  [radiation_condition_real]
    type = VectorEMRobinBC
    variable = E_real
    coupled_field = E_imag
    boundary = boundary
    component = real
    mode = absorbing
    beta = 20.9439510239  # wave number at 1 GHz
  []
  [radiation_condition_imag]
    type = VectorEMRobinBC
    variable = E_imag
    coupled_field = E_real
    boundary = boundary
    component = imaginary
    mode = absorbing
    beta = 20.9439510239  # wave number at 1 GHz
  []
[]

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

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

[Outputs]
  exodus = true
  perf_graph = 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/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
[]

(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
References