ReflectionCoefficient

CURRENTLY ONLY FOR 1D PLANE WAVE SOLVES. Calculate power reflection coefficient for impinging wave on a surface. Assumes that wave of form F = F_incoming + R*F_reflected

Overview

This object is used within the 1D Reflection Benchmark in order to calculate the resulting reflection coefficient of the incoming wave. This assumes that the complex-valued solution wave at the domain boundary has the form

$var element = document.getElementById("moose-equation-e2f700d2-9c04-4218-b0d2-39d7fb488ae3");katex.render(" F_{boundary} = F_{incoming} + R F_{reflected}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-14241959-0c6d-4a47-a8ee-300e007132b7");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the reflection coefficient of the wave. As the wave is a complex-valued plane wave in the benchmark case, the incoming and reflected plane waves have the general forms

$var element = document.getElementById("moose-equation-4fae1487-6fad-4013-b2fc-6b531d97e979");katex.render(" F_{incoming} = C e^{jkL\\cos(\\theta \\pi / 180^{\\circ})} \\\\ F_{reflected} = C e^{-jkL\\cos(\\theta \\pi / 180^{\\circ})}", element, {displayMode:true,throwOnError:false});$

where

$var element = document.getElementById("moose-equation-ad9a320f-026d-49c8-a3a5-d450b8213f99");katex.render("C", element, {displayMode:false,throwOnError:false});$ is a constant coefficient representing the amplitude of the incoming wave,
$var element = document.getElementById("moose-equation-7a1bda1d-0db7-4135-9d8f-ed009c7466a8");katex.render("j = \\sqrt{-1}", element, {displayMode:false,throwOnError:false});$ ,
$var element = document.getElementById("moose-equation-00c97faf-f28e-4ac1-8c07-a31eb4814c30");katex.render("k", element, {displayMode:false,throwOnError:false});$ is the wave number ( $var element = document.getElementById("moose-equation-f85a2d6b-c30d-4edc-8f8e-9700b412fb64");katex.render("2 \\pi / \\lambda", element, {displayMode:false,throwOnError:false});$ where $var element = document.getElementById("moose-equation-6b269f50-30d1-4b9a-8ea0-6d654cca0648");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ is the wavelength),
$var element = document.getElementById("moose-equation-95496af4-45ef-440b-b420-e788c84c6c05");katex.render("L", element, {displayMode:false,throwOnError:false});$ is the length of the slab domain, and
$var element = document.getElementById("moose-equation-6b653035-2f12-46e2-ad5f-db1a67e97208");katex.render("\\theta", element, {displayMode:false,throwOnError:false});$ is the incident angle of the incoming wave, in degrees.

To calculate the percentage of reflected power, as required in the benchmark, the squared magnitude of $var element = document.getElementById("moose-equation-e079e07a-173a-40f1-bc8a-e64b6c9a69c7");katex.render("R", element, {displayMode:false,throwOnError:false});$ above is taken as the object output

var element = document.getElementById("moose-equation-0d6cd22b-c53a-4c84-89d7-5d3254e18ee7");katex.render("R_{power} = |R|^2", element, {displayMode:true,throwOnError:false});

Example Input File Syntax

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [reflection_coefficient]
    type = ReflectionCoefficient<<<{"description": "CURRENTLY ONLY FOR 1D PLANE WAVE SOLVES. Calculate power reflection coefficient for impinging wave on a surface. Assumes that wave of form F = F_incoming + R*F_reflected", "href": "ReflectionCoefficient.html"}>>>
    k<<<{"description": "Wave number"}>>> = ${k}
    length<<<{"description": "Domain length"}>>> = ${L}
    incoming_field_magnitude<<<{"description": "Incoming field magnitude"}>>> = ${E0}
    field_real<<<{"description": "The name of the real field variable this postprocessor operates on."}>>> = E_real
    field_imag<<<{"description": "Coupled imaginary field variable."}>>> = E_imag
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = vacuum
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = 'csv console'
  []
[]

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
field_imagCoupled imaginary field variable.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled imaginary field variable.
field_realThe name of the real field variable this postprocessor operates on.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the real field variable this postprocessor operates on.
kWave number
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Wave number
lengthDomain length
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Domain length
thetaWave incidence angle
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Wave incidence angle

Required Parameters

incoming_field_magnitude1Incoming field magnitude
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Incoming field magnitude

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
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

(moose/modules/electromagnetics/test/tests/benchmarks/slab_reflection/slab_reflection.i)

# 1D metal backed dielectric slab benchmark (electric field edition)
# Based on Section 3.4 of Jin, "The Finite Element Method in Electromagnetics, 3rd Ed."
# frequency = 20 MHz
# eps_R = 4 + (2 - j0.1)(1 - x/L)^2
# mu_R = 2 - j0.1
# L = 5 * wavelength

k =  0.41887902047863906 # 2 * pi * 20e6 / 3e8
L =  75 # = 5 * c / freq. (in m)
E0 = 1 # magnitude of the incident field (in V/m)
theta = 0 # wave incidence angle, in degrees

[GlobalParams]
  theta = ${theta}
[]

[Mesh]
  [slab]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 100
    xmin = 0
    xmax = ${L}
  []
  [rename]
    type = RenameBoundaryGenerator
    input = slab
    old_boundary = 'left right'
    new_boundary = 'metal vacuum'
  []
[]

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

[Functions]
  [coeff_real]
    type = JinSlabCoeffFunc
    k = ${k}
    length = ${L}
    component = real
  []
  [coeff_imag]
    type = JinSlabCoeffFunc
    k = ${k}
    length = ${L}
    component = imaginary
  []
  [negative_coeff_imag]
    type = JinSlabCoeffFunc
    k = ${k}
    length = ${L}
    coef = -1
    component = imaginary
  []
  [cosTheta]
    type = ParsedFunction
    expression = 'cos(${theta})'
  []
[]

[Materials]
  [coeff_real_material]
    type = ADGenericFunctionMaterial
    prop_names = coeff_real_material
    prop_values = coeff_real
  []
  [coeff_imag_material]
    type = ADGenericFunctionMaterial
    prop_names = coeff_imag_material
    prop_values = coeff_imag
  []
  [negative_coeff_imag_material]
    type = ADGenericFunctionMaterial
    prop_names = negative_coeff_imag_material
    prop_values = negative_coeff_imag
  []
[]

[Kernels]
  [diffusion_real]
    type = Diffusion
    variable = E_real
  []
  [field_real]
    type = ADMatReaction
    reaction_rate = coeff_real_material
    variable = E_real
  []
  [coupled_real]
    type = ADMatCoupledForce
    mat_prop_coef = negative_coeff_imag_material
    v = E_imag
    variable = E_real
  []
  [diffusion_imag]
    type = Diffusion
    variable = E_imag
  []
  [field_imag]
    type = ADMatReaction
    reaction_rate = coeff_real_material
    variable = E_imag
  []
  [coupled_imag]
    type = ADMatCoupledForce
    mat_prop_coef = coeff_imag_material
    v = E_real
    variable = E_imag
  []
[]

[BCs]
  [metal_real]
    type = DirichletBC
    value = 0
    variable = E_real
    boundary = metal
  []
  [metal_imag]
    type = DirichletBC
    value = 0
    variable = E_imag
    boundary = metal
  []
  [vacuum_real]
    type = EMRobinBC
    coeff_real = ${k}
    func_real = cosTheta
    profile_func_real = ${E0}
    boundary = vacuum
    component = real
    field_real = E_real
    field_imaginary = E_imag
    variable = E_real
    sign = negative
  []
  [vacuum_imag]
    type = EMRobinBC
    coeff_real = ${k}
    func_real = cosTheta
    profile_func_real = ${E0}
    boundary = vacuum
    component = imaginary
    field_real = E_real
    field_imaginary = E_imag
    variable = E_imag
    sign = negative
  []
[]

[Postprocessors]
  [reflection_coefficient]
    type = ReflectionCoefficient
    k = ${k}
    length = ${L}
    incoming_field_magnitude = ${E0}
    field_real = E_real
    field_imag = E_imag
    boundary = vacuum
    outputs = 'csv console'
  []
[]

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

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

[Outputs]
  exodus = false
  csv = true
  print_linear_residuals = true
[]

Overview
Example Input File Syntax
Input Parameters