VectorSecondTimeDerivative

The second time derivative operator for vector variables.

Overview

The VectorSecondTimeDerivative object implements the weak form inner product term associated with the second time derivative of a vector field variable with a function coefficient. The term is

$var element = document.getElementById("moose-equation-2cdf7ca7-fde8-4e44-9ebb-c2d9dc28949a");katex.render(" \\left(\\vec{\\psi}_i \\; , \\; a(\\mathbf{r}, t) \\frac{\\partial^2 \\vec{u}}{\\partial t^2}\\right)", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where

$var element = document.getElementById("moose-equation-195c5cc4-8364-40c5-b80d-b21ef72a3197");katex.render("\\vec{\\psi}_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a vector-valued test function,
$var element = document.getElementById("moose-equation-c2f09386-c394-4938-bc83-717888f9cf09");katex.render("\\vec{u}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the solution vector field variable, and
$var element = document.getElementById("moose-equation-3255b039-a2f8-4c78-ad3f-894187d4e4d0");katex.render("a(\\mathbf{r}, t)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a function coefficient (default = 1.0).

Example Input File Syntax

[Kernels]
  [time_derivative_real]
    type = VectorSecondTimeDerivative
    variable = E_real
    coefficient = '1/(3e8 * 3e8)' # 1/c^2 = mu_0 * eps_0
  []
[]

Input Parameters

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>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
coefficient1Coefficient function.
Default:1
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Coefficient function.
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
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
Unit:(no unit assumed)
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.

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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system, time
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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

Input Files

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

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

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

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = dipole_antenna_1G.msh
  []
[]

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

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [time_derivative_real]
    type = VectorSecondTimeDerivative
    variable = E_real
    coefficient = '1/(3e8 * 3e8)' # 1/c^2 = mu_0 * eps_0
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [time_derivative_imag]
    type = VectorSecondTimeDerivative
    variable = E_imag
    coefficient = '1/(3e8 * 3e8)' # 1/c^2 = mu_0 * eps_0
  []
[]

[BCs]
  [antenna_real]                          # Impose exact solution of E-field onto antenna surface.
    type = VectorCurlPenaltyDirichletBC   # Replace with proper antenna surface current condition.
    penalty = 1e5
    function_y = 'cos(2*pi*1e9*t)'
    boundary = antenna
    variable = E_real
  []
  [antenna_imag]
    type = VectorCurlPenaltyDirichletBC
    penalty = 1e5
    function_y = 'sin(2*pi*1e9*t)'
    boundary = antenna
    variable = E_imag
  []
  [radiation_condition_real]              # First order absorbing boundary condition
    type = VectorTransientAbsorbingBC
    variable = E_real
    coupled_field = E_imag
    boundary = boundary
    component = real
  []
  [radiation_condition_imag]
    type = VectorTransientAbsorbingBC
    variable = E_imag
    coupled_field = E_real
    boundary = boundary
    component = imaginary
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  num_steps = 150
  dt = 0.5e-10
  [TimeIntegrator]
    type = NewmarkBeta
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

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

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

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = dipole_antenna_1G.msh
  []
[]

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

[Kernels]
  [curl_curl_real]
    type = CurlCurlField
    variable = E_real
  []
  [time_derivative_real]
    type = VectorSecondTimeDerivative
    variable = E_real
    coefficient = '1/(3e8 * 3e8)' # 1/c^2 = mu_0 * eps_0
  []
  [curl_curl_imag]
    type = CurlCurlField
    variable = E_imag
  []
  [time_derivative_imag]
    type = VectorSecondTimeDerivative
    variable = E_imag
    coefficient = '1/(3e8 * 3e8)' # 1/c^2 = mu_0 * eps_0
  []
[]

[BCs]
  [antenna_real]                          # Impose exact solution of E-field onto antenna surface.
    type = VectorCurlPenaltyDirichletBC   # Replace with proper antenna surface current condition.
    penalty = 1e5
    function_y = 'cos(2*pi*1e9*t)'
    boundary = antenna
    variable = E_real
  []
  [antenna_imag]
    type = VectorCurlPenaltyDirichletBC
    penalty = 1e5
    function_y = 'sin(2*pi*1e9*t)'
    boundary = antenna
    variable = E_imag
  []
  [radiation_condition_real]              # First order absorbing boundary condition
    type = VectorTransientAbsorbingBC
    variable = E_real
    coupled_field = E_imag
    boundary = boundary
    component = real
  []
  [radiation_condition_imag]
    type = VectorTransientAbsorbingBC
    variable = E_imag
    coupled_field = E_real
    boundary = boundary
    component = imaginary
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  num_steps = 150
  dt = 0.5e-10
  [TimeIntegrator]
    type = NewmarkBeta
  []
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files