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 (E=Esc+Einc\vec{E} = \vec{E}_{sc} + \vec{E}_{inc}), then we have

n^×(1μr×E)+jk0ηrn^×(n^×E)=n^×(×Einc)+jk0ηrn^×(n^×Einc) \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)

where

  • E\vec{E} is the total (i.e., the solution) electric field vector,

  • Einc\vec{E}_{inc} is the incoming electric field vector,

  • μr\mu_r is the relative magnetic permeability,

  • j=1j = \sqrt{-1},

  • k0k_0 is the wave number (2π/λ2 \pi / \lambda where λ\lambda is the wavelength),

  • ηr\eta_r is a radiation condition parameter (ηr=1\eta_r = 1 if the condition is applied in free space), and

  • n^\hat{\mathbf{n}} is the boundary normal vector.

Implemented form

In VectorEMRobinBC, this condition is slightly generalized. The ratio of k0/ηrk_0 / \eta_r is generalized to a coefficient function β\beta, and so the implemented form is

n^×(1μr×E)+jβ(r)n^×(n^×E)=n^×(×Einc)+jβ(r)n^×(n^×Einc) \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)

where

  • β(r)\beta(\mathbf{r}) is a function containing the condition coefficients.

Note that β\beta generally is just the wavenumber kk, 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 0.3λ0.3 \lambda 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]
  [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'
  []
[]
(modules/electromagnetics/test/tests/bcs/vector_robin_bc/portbc_waves.i)

As an Absorber

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

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

References

  1. Jian-Ming Jin. Theory and Computation of Electromagnetic Fields. John Wiley & Sons, Hoboken, New Jersey, USA, 1st edition, 2010.[BibTeX]
  2. Jian-Ming Jin. The Finite Element Method in Electromagnetics. John Wiley & Sons, Hoboken, New Jersey, USA, 3rd edition, 2014.[BibTeX]