MFEMRWTE10IntegratedBC

Overview

Adds the frequency space integrator corresponding to the value upon a cross-sectional boundary of the TE10 mode of an electromagnetic wave traveling through an infinite rectangular waveguide. The physical system in question is explained in more detail here.

If the parameter "input_port" is set to false, corresponding to the output boundary of the waveguide, the following boundary integrator is applied:

var element = document.getElementById("moose-equation-45aaaff4-ee36-4ffe-b32b-f5ba15c4e2d8");katex.render("i\\mathrm{Im}[k]\\mu^{-1}(\\vec u, \\vec v)_{\\partial\\Omega} \\,\\,\\, \\forall \\vec v \\in V", 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 $var element = document.getElementById("moose-equation-c8fafd13-7f85-4b73-a90f-baa9103c1840");katex.render("\\vec u, \\vec v \\in H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-5d7af804-e40f-4ec9-ae18-b93170ce7f24");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-319ea6ad-4caa-4a62-a8fd-151d075f4d3d");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a complex scalar coefficient defined as follows:

var element = document.getElementById("moose-equation-fdad9735-6deb-4d0e-9713-aca3b1f94ea5");katex.render("k = i\\sqrt{(2\\pi\\nu)^2\\mu\\epsilon-\\frac{\\pi^2}{|\\vec a_1|^2}}", 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 $var element = document.getElementById("moose-equation-76e57055-a65d-4e89-9261-9ff64e00721a");katex.render("\\nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the "frequency" parameter, $var element = document.getElementById("moose-equation-67b99c30-8af0-4d14-8fa8-0bbf9f183057");katex.render("\\vec a_1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the port length vector, and $var element = document.getElementById("moose-equation-c446b341-2f5d-47e8-9e5a-e7f5e3aac137");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-c389a81e-adf6-44ee-904c-72377b559945");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the magnetic permeability and electric permittivity of the material in which the wave is propagating.

If the parameter "input_port" is set to true, corresponding to the input boundary of the waveguide, the following boundary integrator is applied:

var element = document.getElementById("moose-equation-76a418a3-9735-4895-950a-feeb66e3e6ac");katex.render("i\\mathrm{Im}[k]\\mu^{-1}(\\vec u, \\vec v)_{\\partial\\Omega} + 2\\mathrm{Im}[k]\\mu^{-1}(\\vec n \\times (\\mathrm{Im}[\\vec f]-i\\mathrm{Re}[\\vec f]), \\vec v)_{\\partial\\Omega} \\,\\,\\, \\forall \\vec v \\in V", 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 $var element = document.getElementById("moose-equation-4773d33f-9011-4c10-b4db-62b6639b2975");katex.render("\\vec f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is defined by

var element = document.getElementById("moose-equation-9e323eab-9b2d-4478-9751-d41a060846cd");katex.render("\\vec f=\\sqrt{\\frac{2\\omega\\mu}{|\\vec a_1||\\vec a_2|\\mathrm{Im}[k]}} \\sin(\\vec k_a \\cdot \\vec x)e^{-i\\vec k_c \\cdot \\vec x}\\hat e", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

with $var element = document.getElementById("moose-equation-4340a5ca-56af-48ca-b47d-d0fb51ef46d5");katex.render("\\vec a_2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ being the port width vector, $var element = document.getElementById("moose-equation-2fe80768-4125-45b7-a1a4-604302642a9a");katex.render("\\vec k_a=\\frac{\\pi}{|\\vec a_1|} \\frac{\\vec a_2 \\times \\vec k_c}{|\\vec a_2 \\times \\vec k_c|}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-f13638c2-8622-4285-a76c-14d5dce9546c");katex.render("\\vec k_c=k \\frac{\\vec a_1 \\times \\vec a_2}{|\\vec a_1 \\times \\vec a_2|}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . Lastly, $var element = document.getElementById("moose-equation-857afa3d-c332-47bf-b87b-cfb623c516a4");katex.render("\\hat e", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a unit vector in the direction of $var element = document.getElementById("moose-equation-64895d7d-8f3a-4eb3-8ae5-23f966da9293");katex.render("\\vec k_c \\times \\vec k_a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

Example Input File Syntax

[BCs<<<{"href": "../../../syntax/BCs/index.html"}>>>]
  [tangential_E]
    type = MFEMComplexVectorTangentialDirichletBC<<<{"description": "Applies a complex Dirichlet condition to the tangential components of a vector variable.", "href": "MFEMComplexVectorTangentialDirichletBC.html"}>>>
    variable<<<{"description": "Variable on which to apply the boundary condition"}>>> = E
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries."}>>> = '2 3 4'
  []
  [WaveguidePortIn]
    type = MFEMRWTE10IntegratedBC<<<{"description": "Adds the Robin boundary conditions for an electromagnetic problem with transverse waves in a rectangular waveguide.", "href": "MFEMRWTE10IntegratedBC.html"}>>>
    variable<<<{"description": "Variable on which to apply the boundary condition"}>>> = E
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries."}>>> = '5'
    input_port<<<{"description": "Whether the boundary attribute passed to this BC corresponds to the input port of the waveguide."}>>> = true
    port_length_vector<<<{"description": "Vector along the x-axis of the port, where its magnitude is the port length in meters."}>>> = "24.76e-2 0.0 0.0"
    port_width_vector<<<{"description": "Vector along the y-axis of the port, where its magnitude is the port width in meters."}>>> = "0.0 12.38e-2 0.0"
    frequency<<<{"description": "Mode frequency in Hz."}>>> = ${freq}
    epsilon<<<{"description": "Electric permittivity constant."}>>> = ${epsilon0}
    mu<<<{"description": "Magnetic permeability constant."}>>> = ${mu0}
  []
  [WaveguidePortOut]
    type = MFEMRWTE10IntegratedBC<<<{"description": "Adds the Robin boundary conditions for an electromagnetic problem with transverse waves in a rectangular waveguide.", "href": "MFEMRWTE10IntegratedBC.html"}>>>
    variable<<<{"description": "Variable on which to apply the boundary condition"}>>> = E
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries."}>>> = '6'
    input_port<<<{"description": "Whether the boundary attribute passed to this BC corresponds to the input port of the waveguide."}>>> = false
    port_length_vector<<<{"description": "Vector along the x-axis of the port, where its magnitude is the port length in meters."}>>> = "24.76e-2 0.0 0.0"
    port_width_vector<<<{"description": "Vector along the y-axis of the port, where its magnitude is the port width in meters."}>>> = "0.0 12.38e-2 0.0"
    frequency<<<{"description": "Mode frequency in Hz."}>>> = ${freq}
    epsilon<<<{"description": "Electric permittivity constant."}>>> = ${epsilon0}
    mu<<<{"description": "Magnetic permeability constant."}>>> = ${mu0}
  []
[]

Input Parameters

boundary-1 The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.
Default:-1
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.
epsilon1Electric permittivity constant.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Electric permittivity constant.
frequency1Mode frequency in Hz.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Mode frequency in Hz.
input_portFalseWhether the boundary attribute passed to this BC corresponds to the input port of the waveguide.
Default:False
C++ Type:bool
Controllable:No
Description:Whether the boundary attribute passed to this BC corresponds to the input port of the waveguide.
mu1Magnetic permeability constant.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Magnetic permeability constant.
port_length_vectorVector along the x-axis of the port, where its magnitude is the port length in meters.
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Vector along the x-axis of the port, where its magnitude is the port length in meters.
port_width_vectorVector along the y-axis of the port, where its magnitude is the port width in meters.
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Vector along the y-axis of the port, where its magnitude is the port width in meters.
variableVariable on which to apply the boundary condition
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Variable on which to apply the boundary condition

Optional 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:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/mfem/complex/complex_waveguide.i)

(test/tests/mfem/complex/complex_waveguide.i)

freq = 900e6
angfreq = ${fparse 2*pi*freq}
epsilon0 = 8.8541878176e-12
mu0 = ${fparse 4e-7*pi}
magnetic_reluctivity = ${fparse 1/mu0}
elec_cond_mouse = 0.97
elec_cond_air = 1e-323

[Mesh]
  type = MFEMMesh
  file = ../mesh/waveguide.g
  dim = 3
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

[FESpaces]
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
[]

[Variables]
  [E]
    type = MFEMComplexVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [mass_coef_mouse]
    type = ParsedFunction
    expression = -43*${epsilon0}*${angfreq}^2
  []
  [loss_coef_mouse]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_mouse}
  []
  [mass_coef_air]
    type = ParsedFunction
    expression = -${epsilon0}*${angfreq}^2
  []
  [loss_coef_air]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_air}
  []
[]

[FunctorMaterials]
  [Mouse]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_mouse loss_coef_mouse ${magnetic_reluctivity}'
    block = 1
  []
  [Air]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_air loss_coef_air ${magnetic_reluctivity}'
    block = 2
  []
[]

[BCs]
  [tangential_E]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = E
    boundary = '2 3 4'
  []
  [WaveguidePortIn]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '5'
    input_port = true
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
  [WaveguidePortOut]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '6'
    input_port = false
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = MagReluctivity
    []
  []
  [mass_loss]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMVectorFEMassKernel
      coefficient = massCoef
    []
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = lossCoef
    []
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [ObstructionAbsorption]
    type = MFEMComplexVectorPeriodAveragedPostprocessor
    coefficient = ${elec_cond_mouse}
    dual_variable = E
    primal_variable = E
    block = 1
  []
[]


[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/ComplexWaveguide
  []
[]

(test/tests/mfem/complex/complex_waveguide.i)

freq = 900e6
angfreq = ${fparse 2*pi*freq}
epsilon0 = 8.8541878176e-12
mu0 = ${fparse 4e-7*pi}
magnetic_reluctivity = ${fparse 1/mu0}
elec_cond_mouse = 0.97
elec_cond_air = 1e-323

[Mesh]
  type = MFEMMesh
  file = ../mesh/waveguide.g
  dim = 3
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

[FESpaces]
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
[]

[Variables]
  [E]
    type = MFEMComplexVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [mass_coef_mouse]
    type = ParsedFunction
    expression = -43*${epsilon0}*${angfreq}^2
  []
  [loss_coef_mouse]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_mouse}
  []
  [mass_coef_air]
    type = ParsedFunction
    expression = -${epsilon0}*${angfreq}^2
  []
  [loss_coef_air]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_air}
  []
[]

[FunctorMaterials]
  [Mouse]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_mouse loss_coef_mouse ${magnetic_reluctivity}'
    block = 1
  []
  [Air]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_air loss_coef_air ${magnetic_reluctivity}'
    block = 2
  []
[]

[BCs]
  [tangential_E]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = E
    boundary = '2 3 4'
  []
  [WaveguidePortIn]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '5'
    input_port = true
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
  [WaveguidePortOut]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '6'
    input_port = false
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = MagReluctivity
    []
  []
  [mass_loss]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMVectorFEMassKernel
      coefficient = massCoef
    []
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = lossCoef
    []
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [ObstructionAbsorption]
    type = MFEMComplexVectorPeriodAveragedPostprocessor
    coefficient = ${elec_cond_mouse}
    dual_variable = E
    primal_variable = E
    block = 1
  []
[]


[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/ComplexWaveguide
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files