- 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
- penaltyThe penalty coefficient
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The penalty coefficient
- 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
VectorCurlPenaltyDirichletBC
Enforces a Dirichlet boundary condition for the curl of vector nonlinear variables in a weak sense by applying a penalty to the difference in the current solution and the Dirichlet data.
Overview
VectorCurlPenaltyDirichletBC enforces a weak sense of the Dirichlet boundary condition of the curl of the nonlinear variable by setting the boundary as a penalty times the inner product of the test function crossed with the surface normal and the difference between the current solution and the Dirichlet data, also crossed with the surface normal. This is given by
where is a scalar defining the penalty value, is the test function, and is the vector difference between the current solution and Dirichlet data.
This boundary condition can be useful for problems where the mesh is not as refined and could potentially smooth out the problem data on a coarser mesh. It, however, has problems on refined meshes and leads to an ill-conditioned problem, which can be difficult to solve.
Users should instead use VectorPenaltyDirichletBC or VectorDivPenaltyDirichletBC if they wish to set a Dirichlet boundary condition via the penalty method on the vector variable itself or its divergence, respectively.
Example Input File Syntax
[BCs<<<{"href": "../../syntax/BCs/index.html"}>>>]
[bnd]
type = VectorCurlPenaltyDirichletBC<<<{"description": "Enforces a Dirichlet boundary condition for the curl of vector nonlinear variables in a weak sense by applying a penalty to the difference in the current solution and the Dirichlet data.", "href": "VectorCurlPenaltyDirichletBC.html"}>>>
boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'left right top bottom'
penalty<<<{"description": "The penalty coefficient"}>>> = 1e10
function<<<{"description": "The boundary condition vector function, use as an alternative to a component-wise specification"}>>> = sln
variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
[]
[]Input Parameters
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
- functionThe boundary condition vector function, use as an alternative to a component-wise specification
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The boundary condition vector function, use as an alternative to a component-wise specification
- function_x0The function for the x component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function for the x component
- function_y0The function for the y component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function for the y component
- function_z0The function for the z component
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function for the z component
- 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)
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/kernels/vector_helmholtz/vector_conduction_current.i)
- (modules/electromagnetics/test/tests/auxkernels/heating/aux_current_source_heating.i)
- (modules/combined/test/tests/electromagnetic_joule_heating/aux_microwave_heating.i)
- (modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/scalar_azim_magnetic_time_deriv.i)
- (modules/electromagnetics/test/tests/auxkernels/current_density/em_current_density.i)
- (modules/electromagnetics/test/tests/benchmarks/dipole_antenna/dipole.i)
- (test/tests/kernels/vector_fe/vector_kernel.i)
- (modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_kernels.i)
- (modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/vector_azim_magnetic_time_deriv.i)
- (test/tests/kernels/vector_fe/ad_coupled_curl_product.i)
- (test/tests/kernels/vector_fe/ad_vector_kernel.i)
- (modules/electromagnetics/test/tests/auxkernels/heating/aux_microwave_heating.i)
- (modules/electromagnetics/test/tests/benchmarks/dipole_antenna/dipole_transient.i)
- (modules/combined/test/tests/electromagnetic_joule_heating/microwave_heating.i)
- (test/tests/kernels/vector_fe/coupled_scalar_vector.i)
- (modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_ADmaterial_wave_reaction.i)
- (modules/electromagnetics/test/tests/kernels/vector_helmholtz/microwave_heating.i)
- (modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_current_source.i)
- (modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/error_azim_magnetic_time_deriv.i)
- (modules/electromagnetics/test/tests/kernels/vector_helmholtz/ad_vector_kernels.i)
(test/tests/kernels/vector_fe/vector_kernel.i)
# This example reproduces the libmesh vector_fe example 3 results
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[diff]
type = VectorFEWave
variable = u
x_forcing_func = x_ffn
y_forcing_func = y_ffn
[]
[]
[BCs]
[bnd]
type = VectorCurlPenaltyDirichletBC
boundary = 'left right top bottom'
penalty = 1e10
function = sln
variable = u
[]
[]
[Functions]
[x_ffn]
type = ParsedFunction
expression = '(2*pi*pi + 1)*cos(pi*x)*sin(pi*y)'
[]
[y_ffn]
type = ParsedFunction
expression = '-(2*pi*pi + 1)*sin(pi*x)*cos(pi*y)'
[]
[sln]
type = ParsedVectorFunction
expression_x = cos(pi*x)*sin(pi*y)
expression_y = -sin(pi*x)*cos(pi*y)
curl_z = -2*pi*cos(pi*x)*cos(pi*y)
[]
[]
[Postprocessors]
active = ''
[L2Error]
type = ElementVectorL2Error
variable = u
function = sln
[]
[HCurlSemiError]
type = ElementHCurlSemiError
variable = u
function = sln
[]
[HCurlError]
type = ElementHCurlError
variable = u
function = sln
[]
[]
[Preconditioning]
[pre]
type = SMP
[]
[]
[Executioner]
type = Steady
solve_type = LINEAR
petsc_options_iname = -pc_type
petsc_options_value = lu
[]
[Outputs]
exodus = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_conduction_current.i)
# Test for ADConductionCurrent
# Manufactured solution: field_real = y^2 * x_hat - x^2 * y_hat
# E_imag = y^2 * x_hat - x^2 * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for both the real and imag. component
[exact]
type = ParsedVectorFunction
expression_x = 'y*y'
expression_y = '-x*x'
[]
#The forcing terms for the real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*y^2 - 2*epsilon_i*mu_i*omega_i*omega_r*y^2 + epsilon_i*mu_i*omega_r^2*y^2 - epsilon_i*mu_r*omega_i^2*y^2 + 2*epsilon_i*mu_r*omega_i*omega_r*y^2 + epsilon_i*mu_r*omega_r^2*y^2 - epsilon_r*mu_i*omega_i^2*y^2 + 2*epsilon_r*mu_i*omega_i*omega_r*y^2 + epsilon_r*mu_i*omega_r^2*y^2 + epsilon_r*mu_r*omega_i^2*y^2 + 2*epsilon_r*mu_r*omega_i*omega_r*y^2 - epsilon_r*mu_r*omega_r^2*y^2 + mu_i*omega_i*sigma_i*y^2 + mu_i*omega_i*sigma_r*y^2 + mu_i*omega_r*sigma_i*y^2 - mu_i*omega_r*sigma_r*y^2 + mu_r*omega_i*sigma_i*y^2 - mu_r*omega_i*sigma_r*y^2 - mu_r*omega_r*sigma_i*y^2 - mu_r*omega_r*sigma_r*y^2 - 2'
expression_y = 'epsilon_i*mu_i*omega_i^2*x^2 + 2*epsilon_i*mu_i*omega_i*omega_r*x^2 - epsilon_i*mu_i*omega_r^2*x^2 + epsilon_i*mu_r*omega_i^2*x^2 - 2*epsilon_i*mu_r*omega_i*omega_r*x^2 - epsilon_i*mu_r*omega_r^2*x^2 + epsilon_r*mu_i*omega_i^2*x^2 - 2*epsilon_r*mu_i*omega_i*omega_r*x^2 - epsilon_r*mu_i*omega_r^2*x^2 - epsilon_r*mu_r*omega_i^2*x^2 - 2*epsilon_r*mu_r*omega_i*omega_r*x^2 + epsilon_r*mu_r*omega_r^2*x^2 - mu_i*omega_i*sigma_i*x^2 - mu_i*omega_i*sigma_r*x^2 - mu_i*omega_r*sigma_i*x^2 + mu_i*omega_r*sigma_r*x^2 - mu_r*omega_i*sigma_i*x^2 + mu_r*omega_i*sigma_r*x^2 + mu_r*omega_r*sigma_i*x^2 + mu_r*omega_r*sigma_r*x^2 + 2'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*y^2 + 2*epsilon_i*mu_i*omega_i*omega_r*y^2 + epsilon_i*mu_i*omega_r^2*y^2 + epsilon_i*mu_r*omega_i^2*y^2 + 2*epsilon_i*mu_r*omega_i*omega_r*y^2 - epsilon_i*mu_r*omega_r^2*y^2 + epsilon_r*mu_i*omega_i^2*y^2 + 2*epsilon_r*mu_i*omega_i*omega_r*y^2 - epsilon_r*mu_i*omega_r^2*y^2 + epsilon_r*mu_r*omega_i^2*y^2 - 2*epsilon_r*mu_r*omega_i*omega_r*y^2 - epsilon_r*mu_r*omega_r^2*y^2 + mu_i*omega_i*sigma_i*y^2 - mu_i*omega_i*sigma_r*y^2 - mu_i*omega_r*sigma_i*y^2 - mu_i*omega_r*sigma_r*y^2 - mu_r*omega_i*sigma_i*y^2 - mu_r*omega_i*sigma_r*y^2 - mu_r*omega_r*sigma_i*y^2 + mu_r*omega_r*sigma_r*y^2 - 2'
expression_y = 'epsilon_i*mu_i*omega_i^2*x^2 - 2*epsilon_i*mu_i*omega_i*omega_r*x^2 - epsilon_i*mu_i*omega_r^2*x^2 - epsilon_i*mu_r*omega_i^2*x^2 - 2*epsilon_i*mu_r*omega_i*omega_r*x^2 + epsilon_i*mu_r*omega_r^2*x^2 - epsilon_r*mu_i*omega_i^2*x^2 - 2*epsilon_r*mu_i*omega_i*omega_r*x^2 + epsilon_r*mu_i*omega_r^2*x^2 - epsilon_r*mu_r*omega_i^2*x^2 + 2*epsilon_r*mu_r*omega_i*omega_r*x^2 + epsilon_r*mu_r*omega_r^2*x^2 - mu_i*omega_i*sigma_i*x^2 + mu_i*omega_i*sigma_r*x^2 + mu_i*omega_r*sigma_i*x^2 + mu_i*omega_r*sigma_r*x^2 + mu_r*omega_i*sigma_i*x^2 + mu_r*omega_i*sigma_r*x^2 + mu_r*omega_r*sigma_i*x^2 - mu_r*omega_r*sigma_r*x^2 + 2'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[sigma]
type = ParsedFunction
expression = '4.0'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[cond_real]
type = ADGenericFunctionMaterial
prop_names = cond_real
prop_values = sigma
[]
[cond_imag]
type = ADGenericFunctionMaterial
prop_names = cond_imag
prop_values = sigma
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[conduction_real]
type = ADConductionCurrent
variable = E_real
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[conduction_imag]
type = ADConductionCurrent
variable = E_imag
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/auxkernels/heating/aux_current_source_heating.i)
# Test for SourceCurrentHeating
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
# E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
# heating = 'sin(x*pi)*cos(x*pi) + sin(y*pi)*cos(y*pi)'
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
expression_x = '-2*cos(pi*y) + pi^2*cos(pi*y)'
expression_y = '-pi^2*cos(pi*x) + 2*cos(pi*x)'
[]
[source_imag]
type = ParsedVectorFunction
expression_x = 'pi^2*sin(pi*y)'
expression_y = '-pi^2*sin(pi*x)'
[]
[current_real]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[current_imag]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[heating_func]
type = ParsedFunction
expression = '1.0*sin(x*pi)*cos(x*pi) + 1.0*sin(y*pi)*cos(y*pi)'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_real = 1.0
eps_rel_imag = 0.0
k_real = 1.0
k_imag = 0.0
mu_rel_real = 1.0
mu_rel_imag = 0.0
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[current_real]
type = VectorCurrentSource
variable = E_real
source_real = current_real
source_imag = current_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[current_imag]
type = VectorCurrentSource
variable = E_imag
source_real = current_real
source_imag = current_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[AuxVariables]
[current_heating_term]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_current_heating]
type = SourceCurrentHeating
variable = current_heating_term
E_real = E_real
E_imag = E_imag
source_real = current_real
source_imag = current_imag
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_aux_heating]
type = ElementL2Error
variable = current_heating_term
function = heating_func
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-12
[]
[Outputs]
exodus = true
csv = true
[]
(modules/combined/test/tests/electromagnetic_joule_heating/aux_microwave_heating.i)
# Test for JouleHeatingHeatGeneratedAux
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
# E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
# n = x^2*y^2
# heating = '0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[exact_n]
type = ParsedFunction
expression = 'x^2*y^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*cos(pi*y) - 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*y) + epsilon_i*mu_i*omega_r^2*cos(pi*y) - epsilon_i*mu_r*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_r*omega_r^2*sin(pi*y) - epsilon_r*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_r*mu_i*omega_r^2*sin(pi*y) + epsilon_r*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_r*omega_r^2*cos(pi*y) + mu_i*omega_i*sigma_i*cos(pi*y) + mu_i*omega_i*sigma_r*sin(pi*y) + mu_i*omega_r*sigma_i*sin(pi*y) - mu_i*omega_r*sigma_r*cos(pi*y) + mu_r*omega_i*sigma_i*sin(pi*y) - mu_r*omega_i*sigma_r*cos(pi*y) - mu_r*omega_r*sigma_i*cos(pi*y) - mu_r*omega_r*sigma_r*sin(pi*y) + pi^2*cos(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*cos(pi*x) + 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*x) - epsilon_i*mu_i*omega_r^2*cos(pi*x) + epsilon_i*mu_r*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_r*omega_r^2*sin(pi*x) + epsilon_r*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_r*mu_i*omega_r^2*sin(pi*x) - epsilon_r*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_r*omega_r^2*cos(pi*x) - mu_i*omega_i*sigma_i*cos(pi*x) - mu_i*omega_i*sigma_r*sin(pi*x) - mu_i*omega_r*sigma_i*sin(pi*x) + mu_i*omega_r*sigma_r*cos(pi*x) - mu_r*omega_i*sigma_i*sin(pi*x) + mu_r*omega_i*sigma_r*cos(pi*x) + mu_r*omega_r*sigma_i*cos(pi*x) + mu_r*omega_r*sigma_r*sin(pi*x) - pi^2*cos(pi*x)'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_i*omega_r^2*sin(pi*y) + epsilon_i*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_i*mu_r*omega_r^2*cos(pi*y) + epsilon_r*mu_i*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_i*omega_r^2*cos(pi*y) + epsilon_r*mu_r*omega_i^2*sin(pi*y) - 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*y) - epsilon_r*mu_r*omega_r^2*sin(pi*y) + mu_i*omega_i*sigma_i*sin(pi*y) - mu_i*omega_i*sigma_r*cos(pi*y) - mu_i*omega_r*sigma_i*cos(pi*y) - mu_i*omega_r*sigma_r*sin(pi*y) - mu_r*omega_i*sigma_i*cos(pi*y) - mu_r*omega_i*sigma_r*sin(pi*y) - mu_r*omega_r*sigma_i*sin(pi*y) + mu_r*omega_r*sigma_r*cos(pi*y) + pi^2*sin(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_i*omega_r^2*sin(pi*x) - epsilon_i*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_i*mu_r*omega_r^2*cos(pi*x) - epsilon_r*mu_i*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_i*omega_r^2*cos(pi*x) - epsilon_r*mu_r*omega_i^2*sin(pi*x) + 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*x) + epsilon_r*mu_r*omega_r^2*sin(pi*x) - mu_i*omega_i*sigma_i*sin(pi*x) + mu_i*omega_i*sigma_r*cos(pi*x) + mu_i*omega_r*sigma_i*cos(pi*x) + mu_i*omega_r*sigma_r*sin(pi*x) + mu_r*omega_i*sigma_i*cos(pi*x) + mu_r*omega_i*sigma_r*sin(pi*x) + mu_r*omega_r*sigma_i*sin(pi*x) - mu_r*omega_r*sigma_r*cos(pi*x) - pi^2*sin(pi*x)'
[]
[source_n]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '-2*x^2 - 2*y^2 - 0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
[heating_func]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[sigma]
type = ParsedFunction
expression = '4.0'
#expression = 'x^2*y^2'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[cond_real]
type = ADGenericFunctionMaterial
prop_names = cond_real
prop_values = sigma
[]
[cond_imag]
type = ADGenericFunctionMaterial
prop_names = cond_imag
prop_values = sigma
[]
[ElectromagneticMaterial]
type = ElectromagneticHeatingMaterial
electric_field = E_real
complex_electric_field = E_imag
electric_field_heating_name = electric_field_heating
electrical_conductivity = cond_real
formulation = FREQUENCY
solver = ELECTROMAGNETIC
[]
[]
[Variables]
[n]
family = LAGRANGE
order = FIRST
[]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[conduction_real]
type = ADConductionCurrent
variable = E_real
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[conduction_imag]
type = ADConductionCurrent
variable = E_imag
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[n_diffusion]
type = Diffusion
variable = n
[]
[microwave_heating]
type = ADJouleHeatingSource
variable = n
heating_term = 'electric_field_heating'
[]
[body_force_n]
type = BodyForce
variable = n
function = source_n
[]
[]
[AuxVariables]
[heating_term]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_microwave_heating]
type = JouleHeatingHeatGeneratedAux
variable = heating_term
heating_term = 'electric_field_heating'
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_n]
type = FunctorDirichletBC
variable = n
boundary = 'left right top bottom'
functor = exact_n
preset = false
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_n]
type = ElementL2Error
variable = n
function = exact_n
[]
[error_aux_heating]
type = ElementL2Error
variable = heating_term
function = heating_func
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-12
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/auxkernels/azimuthal_Faradays_law/scalar_azim_magnetic_time_deriv.i)
# Test for AzimuthMagneticTimeDerivRZ with scalar inputs
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
# E_imag = y^2 * x_hat - x^2 * y_hat
# dB_theta_real / dt = -(2*y + 2*x)
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmax = 1
xmin = 0
ymax = 1
ymin = -1
elem_type = QUAD9
[]
coord_type = RZ
rz_coord_axis = Y
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
expression_x = '-y^2 - cos(pi*y) - 2'
expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
[]
[source_imag]
type = ParsedVectorFunction
expression_x = '-y^2 + sin(pi*y) - 2'
expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
[]
[current_real]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[current_imag]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[azim_dB_dt_func]
type = ParsedFunction
expression = '-(2*y + 2*x)'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_real = 1.0
eps_rel_imag = 0.0
k_real = 1.0
k_imag = 0.0
mu_rel_real = 1.0
mu_rel_imag = 0.0
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[current_real]
type = VectorCurrentSource
variable = E_real
source_real = current_real
source_imag = current_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[current_imag]
type = VectorCurrentSource
variable = E_imag
source_real = current_real
source_imag = current_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[AuxVariables]
[aux_E_real_x]
family = MONOMIAL
order = FIRST
[]
[aux_E_real_y]
family = MONOMIAL
order = FIRST
[]
[azim_dB_dt_term_scalar]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_E_real_x]
type = VectorVariableComponentAux
variable = aux_E_real_x
vector_variable = E_real
component = X
[]
[aux_E_real_y]
type = VectorVariableComponentAux
variable = aux_E_real_y
vector_variable = E_real
component = Y
[]
[aux_azim_dB_dt_scalar]
type = AzimuthMagneticTimeDerivRZ
Efield_X = aux_E_real_x
Efield_Y = aux_E_real_y
variable = azim_dB_dt_term_scalar
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_azim_dB_dt_scalar]
type = ElementL2Error
variable = azim_dB_dt_term_scalar
function = azim_dB_dt_func
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-16
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/auxkernels/current_density/em_current_density.i)
# This test is a modification of the vector_helmholtz.vector_kernels test
# to verify functionality of the current density auxkernel for the case of
# a vector field variable in electromagnetic mode.
# Manufactured solution: u = y * x_hat - x * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[AuxVariables]
[J]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl]
type = CurlCurlField
variable = u
[]
[coeff]
type = VectorFunctionReaction
variable = u
[]
[rhs]
type = VectorBodyForce
variable = u
function_x = 'y'
function_y = '-x'
[]
[]
[BCs]
[sides]
type = VectorCurlPenaltyDirichletBC
variable = u
function_x = 'y'
function_y = '-x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[AuxKernels]
[current_density]
type = ADCurrentDensity
variable = J
electrostatic = false
electric_field = u
[]
[]
[Materials] # THIS MATERIAL IS ONLY USED TO TEST THE CURRENT DENSITY CALCULATION
[conductivity] # Electrical conductivity for graphite at 293.15 K in S/m
type = ADGenericConstantMaterial # perpendicular to basal plane
prop_names = 'electrical_conductivity' # Citation: H. Pierson, "Handbook of carbon, graphite,
prop_values = 3.33e2 # diamond, and fullerenes: properties, processing,
[] # and applications," p. 61, William Andrew, 1993.
[]
[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
[]
(test/tests/kernels/vector_fe/vector_kernel.i)
# This example reproduces the libmesh vector_fe example 3 results
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[diff]
type = VectorFEWave
variable = u
x_forcing_func = x_ffn
y_forcing_func = y_ffn
[]
[]
[BCs]
[bnd]
type = VectorCurlPenaltyDirichletBC
boundary = 'left right top bottom'
penalty = 1e10
function = sln
variable = u
[]
[]
[Functions]
[x_ffn]
type = ParsedFunction
expression = '(2*pi*pi + 1)*cos(pi*x)*sin(pi*y)'
[]
[y_ffn]
type = ParsedFunction
expression = '-(2*pi*pi + 1)*sin(pi*x)*cos(pi*y)'
[]
[sln]
type = ParsedVectorFunction
expression_x = cos(pi*x)*sin(pi*y)
expression_y = -sin(pi*x)*cos(pi*y)
curl_z = -2*pi*cos(pi*x)*cos(pi*y)
[]
[]
[Postprocessors]
active = ''
[L2Error]
type = ElementVectorL2Error
variable = u
function = sln
[]
[HCurlSemiError]
type = ElementHCurlSemiError
variable = u
function = sln
[]
[HCurlError]
type = ElementHCurlError
variable = u
function = sln
[]
[]
[Preconditioning]
[pre]
type = SMP
[]
[]
[Executioner]
type = Steady
solve_type = LINEAR
petsc_options_iname = -pc_type
petsc_options_value = lu
[]
[Outputs]
exodus = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_kernels.i)
# Test for EM module vector kernels CurlCurlField and VectorFunctionReaction
# Manufactured solution: u = y * x_hat - x * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl]
type = CurlCurlField
variable = u
[]
[coeff]
type = VectorFunctionReaction
variable = u
[]
[rhs]
type = VectorBodyForce
variable = u
function_x = 'y'
function_y = '-x'
[]
[]
[BCs]
[sides]
type = VectorCurlPenaltyDirichletBC
variable = u
function_x = 'y'
function_y = '-x'
penalty = 1e8
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/auxkernels/azimuthal_Faradays_law/vector_azim_magnetic_time_deriv.i)
# Test for AzimuthMagneticTimeDerivRZ with a vector input
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
# E_imag = y^2 * x_hat - x^2 * y_hat
# dB_theta_real / dt = -(2*y + 2*x)
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmax = 1
xmin = 0
ymax = 1
ymin = -1
elem_type = QUAD9
[]
coord_type = RZ
rz_coord_axis = Y
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
expression_x = '-y^2 - cos(pi*y) - 2'
expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
[]
[source_imag]
type = ParsedVectorFunction
expression_x = '-y^2 + sin(pi*y) - 2'
expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
[]
[current_real]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[current_imag]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[azim_dB_dt_func]
type = ParsedFunction
expression = '-(2*y + 2*x)'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_real = 1.0
eps_rel_imag = 0.0
k_real = 1.0
k_imag = 0.0
mu_rel_real = 1.0
mu_rel_imag = 0.0
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[current_real]
type = VectorCurrentSource
variable = E_real
source_real = current_real
source_imag = current_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[current_imag]
type = VectorCurrentSource
variable = E_imag
source_real = current_real
source_imag = current_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[AuxVariables]
[azim_dB_dt_term_vector]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_azim_dB_dt_vector]
type = AzimuthMagneticTimeDerivRZ
Efield = E_real
variable = azim_dB_dt_term_vector
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_azim_dB_dt_vector]
type = ElementL2Error
variable = azim_dB_dt_term_vector
function = azim_dB_dt_func
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-16
[]
[Outputs]
exodus = true
csv = true
[]
(test/tests/kernels/vector_fe/ad_coupled_curl_product.i)
# This example couples the product of the curl of a variable vector
# and a supplied field into a diffusion problem of a Lagrange variable
# using automatic differentiation
[Mesh]
type = GeneratedMesh
dim = 3
nx = 5
ny = 5
nz = 5
xmin = -1
ymin = -1
zmin = -1
elem_type = HEX20
[]
[Variables]
[u]
[]
[v]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[coupled_curl_supplied_field_product]
type = ADCoupledCurlSuppliedFieldProduct
variable = u
vector = v
supplied_field_x = '0'
supplied_field_y = '0'
supplied_field_z = '1'
[]
[u_diff]
type = Diffusion
variable = u
[]
[u_body_force]
type = BodyForce
variable = u
function = u_body_force_ffn
[]
[diff]
type = ADVectorFEWave
variable = v
x_forcing_func = x_ffn
y_forcing_func = y_ffn
[]
[]
[BCs]
[v_bnd]
type = VectorCurlPenaltyDirichletBC
boundary = 'left right top bottom front back'
penalty = 1e10
function = v_sln
variable = v
[]
[u_bnd]
type = ADFunctionPenaltyDirichletBC
boundary = 'left right top bottom front back'
penalty = 1e10
function = u_sln
variable = u
[]
[]
[Functions]
[x_ffn]
type = ParsedFunction
expression = '(2*pi*pi + 1)*cos(pi*x)*sin(pi*y)'
[]
[y_ffn]
type = ParsedFunction
expression = '-(2*pi*pi + 1)*sin(pi*x)*cos(pi*y)'
[]
[u_body_force_ffn]
type = ParsedFunction
expression = '-2*pi*cos(pi*x)*cos(pi*y) + pi^2*cos(z*pi)'
[]
[u_sln]
type = ParsedFunction
expression = 'cos(z*pi)'
[]
[v_sln]
type = ParsedVectorFunction
expression_x = 'cos(pi*x)*sin(pi*y)'
expression_y = '-sin(pi*x)*cos(pi*y)'
curl_z = '-2*pi*cos(pi*x)*cos(pi*y)'
[]
[]
[Postprocessors]
[v_L2Error]
type = ElementVectorL2Error
variable = v
function = v_sln
[]
[HCurlSemiError]
type = ElementHCurlSemiError
variable = v
function = v_sln
[]
[HCurlError]
type = ElementHCurlError
variable = v
function = v_sln
[]
[u_L2Error]
type = ElementL2Error
variable = u
function = u_sln
[]
[]
[Preconditioning]
[pre]
type = SMP
[]
[]
[Executioner]
type = Steady
solve_type = NEWTON
petsc_options_iname = -pc_type
petsc_options_value = lu
[]
[Outputs]
exodus = true
csv = true
[]
(test/tests/kernels/vector_fe/ad_vector_kernel.i)
# This example reproduces the libmesh vector_fe example 3 results
# using automatic differentiation
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[diff]
type = ADVectorFEWave
variable = u
x_forcing_func = x_ffn
y_forcing_func = y_ffn
[]
[]
[BCs]
[bnd]
type = VectorCurlPenaltyDirichletBC
boundary = 'left right top bottom'
penalty = 1e10
function = sln
variable = u
[]
[]
[Functions]
[x_ffn]
type = ParsedFunction
expression = '(2*pi*pi + 1)*cos(pi*x)*sin(pi*y)'
[]
[y_ffn]
type = ParsedFunction
expression = '-(2*pi*pi + 1)*sin(pi*x)*cos(pi*y)'
[]
[sln]
type = ParsedVectorFunction
expression_x = 'cos(pi*x)*sin(pi*y)'
expression_y = '-sin(pi*x)*cos(pi*y)'
curl_z = '-2*pi*cos(pi*x)*cos(pi*y)'
[]
[]
[Postprocessors]
active = ''
[L2Error]
type = ElementVectorL2Error
variable = u
function = sln
[]
[HCurlSemiError]
type = ElementHCurlSemiError
variable = u
function = sln
[]
[HCurlError]
type = ElementHCurlError
variable = u
function = sln
[]
[]
[Preconditioning]
[pre]
type = SMP
[]
[]
[Executioner]
type = Steady
solve_type = LINEAR
petsc_options_iname = -pc_type
petsc_options_value = lu
[]
[Outputs]
exodus = true
[]
(modules/electromagnetics/test/tests/auxkernels/heating/aux_microwave_heating.i)
# Test for EMJouleHeatingHeatGeneratedAux
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
# E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
# n = x^2*y^2
# heating = '0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[exact_n]
type = ParsedFunction
expression = 'x^2*y^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*cos(pi*y) - 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*y) + epsilon_i*mu_i*omega_r^2*cos(pi*y) - epsilon_i*mu_r*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_r*omega_r^2*sin(pi*y) - epsilon_r*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_r*mu_i*omega_r^2*sin(pi*y) + epsilon_r*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_r*omega_r^2*cos(pi*y) + mu_i*omega_i*sigma_i*cos(pi*y) + mu_i*omega_i*sigma_r*sin(pi*y) + mu_i*omega_r*sigma_i*sin(pi*y) - mu_i*omega_r*sigma_r*cos(pi*y) + mu_r*omega_i*sigma_i*sin(pi*y) - mu_r*omega_i*sigma_r*cos(pi*y) - mu_r*omega_r*sigma_i*cos(pi*y) - mu_r*omega_r*sigma_r*sin(pi*y) + pi^2*cos(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*cos(pi*x) + 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*x) - epsilon_i*mu_i*omega_r^2*cos(pi*x) + epsilon_i*mu_r*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_r*omega_r^2*sin(pi*x) + epsilon_r*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_r*mu_i*omega_r^2*sin(pi*x) - epsilon_r*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_r*omega_r^2*cos(pi*x) - mu_i*omega_i*sigma_i*cos(pi*x) - mu_i*omega_i*sigma_r*sin(pi*x) - mu_i*omega_r*sigma_i*sin(pi*x) + mu_i*omega_r*sigma_r*cos(pi*x) - mu_r*omega_i*sigma_i*sin(pi*x) + mu_r*omega_i*sigma_r*cos(pi*x) + mu_r*omega_r*sigma_i*cos(pi*x) + mu_r*omega_r*sigma_r*sin(pi*x) - pi^2*cos(pi*x)'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_i*omega_r^2*sin(pi*y) + epsilon_i*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_i*mu_r*omega_r^2*cos(pi*y) + epsilon_r*mu_i*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_i*omega_r^2*cos(pi*y) + epsilon_r*mu_r*omega_i^2*sin(pi*y) - 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*y) - epsilon_r*mu_r*omega_r^2*sin(pi*y) + mu_i*omega_i*sigma_i*sin(pi*y) - mu_i*omega_i*sigma_r*cos(pi*y) - mu_i*omega_r*sigma_i*cos(pi*y) - mu_i*omega_r*sigma_r*sin(pi*y) - mu_r*omega_i*sigma_i*cos(pi*y) - mu_r*omega_i*sigma_r*sin(pi*y) - mu_r*omega_r*sigma_i*sin(pi*y) + mu_r*omega_r*sigma_r*cos(pi*y) + pi^2*sin(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_i*omega_r^2*sin(pi*x) - epsilon_i*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_i*mu_r*omega_r^2*cos(pi*x) - epsilon_r*mu_i*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_i*omega_r^2*cos(pi*x) - epsilon_r*mu_r*omega_i^2*sin(pi*x) + 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*x) + epsilon_r*mu_r*omega_r^2*sin(pi*x) - mu_i*omega_i*sigma_i*sin(pi*x) + mu_i*omega_i*sigma_r*cos(pi*x) + mu_i*omega_r*sigma_i*cos(pi*x) + mu_i*omega_r*sigma_r*sin(pi*x) + mu_r*omega_i*sigma_i*cos(pi*x) + mu_r*omega_i*sigma_r*sin(pi*x) + mu_r*omega_r*sigma_i*sin(pi*x) - mu_r*omega_r*sigma_r*cos(pi*x) - pi^2*sin(pi*x)'
[]
[source_n]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '-2*x^2 - 2*y^2 - 0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
[heating_func]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[sigma]
type = ParsedFunction
expression = '4.0'
#expression = 'x^2*y^2'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[cond_real]
type = ADGenericFunctionMaterial
prop_names = cond_real
prop_values = sigma
[]
[cond_imag]
type = ADGenericFunctionMaterial
prop_names = cond_imag
prop_values = sigma
[]
[]
[Variables]
[n]
family = LAGRANGE
order = FIRST
[]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[conduction_real]
type = ADConductionCurrent
variable = E_real
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[conduction_imag]
type = ADConductionCurrent
variable = E_imag
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[n_diffusion]
type = Diffusion
variable = n
[]
[microwave_heating]
type = EMJouleHeatingSource
variable = n
E_imag = E_imag
E_real = E_real
conductivity = cond_real
[]
[body_force_n]
type = BodyForce
variable = n
function = source_n
[]
[]
[AuxVariables]
[heating_term]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_microwave_heating]
type = EMJouleHeatingHeatGeneratedAux
variable = heating_term
E_imag = E_imag
E_real = E_real
conductivity = cond_real
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_n]
type = FunctorDirichletBC
variable = n
boundary = 'left right top bottom'
functor = exact_n
preset = false
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_n]
type = ElementL2Error
variable = n
function = exact_n
[]
[error_aux_heating]
type = ElementL2Error
variable = heating_term
function = heating_func
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-12
[]
[Outputs]
exodus = true
csv = 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 electric 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/combined/test/tests/electromagnetic_joule_heating/microwave_heating.i)
# Test for ADJouleHeatingSource
#
# This test utilizes the method of manufactured solutions, such that
# all terms of the PDE's and all supplied parameter are are non-zero.
# The exact PDE's are the following:
#
# curl(curl(E)) - mu*omega^2*epsilon*E + j*mu*omega*sigma*E = F_E_supplied
# div(-grad(n)) - 0.5*Re(sigma*E * E^*) = F_n_supplied
#
# Where:
# - E is the electric field
# - mu is the permeability
# - omega is the angular frequency of the system
# - epsilon is the permittivity
# - j is the sqrt(-1)
# - sigma is the electric conductivity
# - F_E_supplied is the forcing term of the electric field MMS
# - n is the energy density of a species
# (this is analogous to the electron energy density in plasma physics)
# - E^* is the complex conjugate of the electric field
# - F_n_supplied is the forcing term of the energy density MMS
#
# All boundary conditions in this test are Dirichlet BCs. The manufactured
# solutions are as follow:
#
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
# E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
# n = x^2*y^2
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[exact_n]
type = ParsedFunction
expression = 'x^2*y^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*cos(pi*y) - 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*y) + epsilon_i*mu_i*omega_r^2*cos(pi*y) - epsilon_i*mu_r*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_r*omega_r^2*sin(pi*y) - epsilon_r*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_r*mu_i*omega_r^2*sin(pi*y) + epsilon_r*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_r*omega_r^2*cos(pi*y) + mu_i*omega_i*sigma_i*cos(pi*y) + mu_i*omega_i*sigma_r*sin(pi*y) + mu_i*omega_r*sigma_i*sin(pi*y) - mu_i*omega_r*sigma_r*cos(pi*y) + mu_r*omega_i*sigma_i*sin(pi*y) - mu_r*omega_i*sigma_r*cos(pi*y) - mu_r*omega_r*sigma_i*cos(pi*y) - mu_r*omega_r*sigma_r*sin(pi*y) + pi^2*cos(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*cos(pi*x) + 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*x) - epsilon_i*mu_i*omega_r^2*cos(pi*x) + epsilon_i*mu_r*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_r*omega_r^2*sin(pi*x) + epsilon_r*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_r*mu_i*omega_r^2*sin(pi*x) - epsilon_r*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_r*omega_r^2*cos(pi*x) - mu_i*omega_i*sigma_i*cos(pi*x) - mu_i*omega_i*sigma_r*sin(pi*x) - mu_i*omega_r*sigma_i*sin(pi*x) + mu_i*omega_r*sigma_r*cos(pi*x) - mu_r*omega_i*sigma_i*sin(pi*x) + mu_r*omega_i*sigma_r*cos(pi*x) + mu_r*omega_r*sigma_i*cos(pi*x) + mu_r*omega_r*sigma_r*sin(pi*x) - pi^2*cos(pi*x)'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_i*omega_r^2*sin(pi*y) + epsilon_i*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_i*mu_r*omega_r^2*cos(pi*y) + epsilon_r*mu_i*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_i*omega_r^2*cos(pi*y) + epsilon_r*mu_r*omega_i^2*sin(pi*y) - 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*y) - epsilon_r*mu_r*omega_r^2*sin(pi*y) + mu_i*omega_i*sigma_i*sin(pi*y) - mu_i*omega_i*sigma_r*cos(pi*y) - mu_i*omega_r*sigma_i*cos(pi*y) - mu_i*omega_r*sigma_r*sin(pi*y) - mu_r*omega_i*sigma_i*cos(pi*y) - mu_r*omega_i*sigma_r*sin(pi*y) - mu_r*omega_r*sigma_i*sin(pi*y) + mu_r*omega_r*sigma_r*cos(pi*y) + pi^2*sin(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_i*omega_r^2*sin(pi*x) - epsilon_i*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_i*mu_r*omega_r^2*cos(pi*x) - epsilon_r*mu_i*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_i*omega_r^2*cos(pi*x) - epsilon_r*mu_r*omega_i^2*sin(pi*x) + 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*x) + epsilon_r*mu_r*omega_r^2*sin(pi*x) - mu_i*omega_i*sigma_i*sin(pi*x) + mu_i*omega_i*sigma_r*cos(pi*x) + mu_i*omega_r*sigma_i*cos(pi*x) + mu_i*omega_r*sigma_r*sin(pi*x) + mu_r*omega_i*sigma_i*cos(pi*x) + mu_r*omega_i*sigma_r*sin(pi*x) + mu_r*omega_r*sigma_i*sin(pi*x) - mu_r*omega_r*sigma_r*cos(pi*x) - pi^2*sin(pi*x)'
[]
[source_n]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '-2*x^2 - 2*y^2 - 0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[sigma]
type = ParsedFunction
expression = '4.0'
#expression = 'x^2*y^2'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[cond_real]
type = ADGenericFunctionMaterial
prop_names = cond_real
prop_values = sigma
[]
[cond_imag]
type = ADGenericFunctionMaterial
prop_names = cond_imag
prop_values = sigma
[]
[ElectromagneticMaterial]
type = ElectromagneticHeatingMaterial
electric_field = E_real
complex_electric_field = E_imag
electric_field_heating_name = electric_field_heating
electrical_conductivity = cond_real
formulation = FREQUENCY
solver = ELECTROMAGNETIC
[]
[]
[Variables]
[n]
family = LAGRANGE
order = FIRST
[]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[conduction_real]
type = ADConductionCurrent
variable = E_real
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[conduction_imag]
type = ADConductionCurrent
variable = E_imag
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[n_diffusion]
type = Diffusion
variable = n
[]
[microwave_heating]
type = ADJouleHeatingSource
variable = n
heating_term = 'electric_field_heating'
[]
[body_force_n]
type = BodyForce
variable = n
function = source_n
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_n]
type = FunctorDirichletBC
variable = n
boundary = 'left right top bottom'
functor = exact_n
preset = false
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_n]
type = ElementL2Error
variable = n
function = exact_n
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-12
[]
[Outputs]
exodus = true
csv = true
[]
(test/tests/kernels/vector_fe/coupled_scalar_vector.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[Variables]
[./u]
family = NEDELEC_ONE
order = FIRST
[../]
[./v]
[../]
[]
[Kernels]
[./wave]
type = VectorFEWave
variable = u
x_forcing_func = 'x_ffn'
y_forcing_func = 'y_ffn'
[../]
[./diff]
type = Diffusion
variable = v
[../]
[./source]
type = BodyForce
variable = v
[../]
[./advection]
type = EFieldAdvection
variable = v
efield = u
charge = 'positive'
mobility = 100
[../]
[]
[BCs]
[./bnd]
type = VectorCurlPenaltyDirichletBC
boundary = 'left right top bottom'
penalty = 1e10
function_x = 'x_sln'
function_y = 'y_sln'
variable = u
[../]
[./bnd_v]
type = DirichletBC
boundary = 'left right top bottom'
value = 0
variable = v
[../]
[]
[Functions]
[./x_ffn]
type = ParsedFunction
expression = '(2*pi*pi + 1)*cos(pi*x)*sin(pi*y)'
[../]
[./y_ffn]
type = ParsedFunction
expression = '-(2*pi*pi + 1)*sin(pi*x)*cos(pi*y)'
[../]
[./x_sln]
type = ParsedFunction
expression = 'cos(pi*x)*sin(pi*y)'
[../]
[./y_sln]
type = ParsedFunction
expression = '-sin(pi*x)*cos(pi*y)'
[../]
[]
[Preconditioning]
[./pre]
type = SMP
full = true
[../]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'asm'
petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
[]
[Outputs]
exodus = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_ADmaterial_wave_reaction.i)
# Test for ADMatWaveReaction
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
# E_imag = y^2 * x_hat - x^2 * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for both the real and imag. component
[exact]
type = ParsedVectorFunction
expression_x = 'y*y'
expression_y = '-x*x'
[]
#The forcing terms for the real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r omega_i mu_i epsilon_i'
symbol_values = 'omega mu epsilon omega mu epsilon'
expression_x = '-epsilon_i*mu_i*omega_i^2*y^2 - 2*epsilon_i*mu_i*omega_i*omega_r*y^2 + epsilon_i*mu_i*omega_r^2*y^2 - epsilon_i*mu_r*omega_i^2*y^2 + 2*epsilon_i*mu_r*omega_i*omega_r*y^2 + epsilon_i*mu_r*omega_r^2*y^2 - epsilon_r*mu_i*omega_i^2*y^2 + 2*epsilon_r*mu_i*omega_i*omega_r*y^2 + epsilon_r*mu_i*omega_r^2*y^2 + epsilon_r*mu_r*omega_i^2*y^2 + 2*epsilon_r*mu_r*omega_i*omega_r*y^2 - epsilon_r*mu_r*omega_r^2*y^2 - 2'
expression_y = 'epsilon_i*mu_i*omega_i^2*x^2 + 2*epsilon_i*mu_i*omega_i*omega_r*x^2 - epsilon_i*mu_i*omega_r^2*x^2 + epsilon_i*mu_r*omega_i^2*x^2 - 2*epsilon_i*mu_r*omega_i*omega_r*x^2 - epsilon_i*mu_r*omega_r^2*x^2 + epsilon_r*mu_i*omega_i^2*x^2 - 2*epsilon_r*mu_i*omega_i*omega_r*x^2 - epsilon_r*mu_i*omega_r^2*x^2 - epsilon_r*mu_r*omega_i^2*x^2 - 2*epsilon_r*mu_r*omega_i*omega_r*x^2 + epsilon_r*mu_r*omega_r^2*x^2 + 2'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r omega_i mu_i epsilon_i'
symbol_values = 'omega mu epsilon omega mu epsilon'
expression_x = '-epsilon_i*mu_i*omega_i^2*y^2 + 2*epsilon_i*mu_i*omega_i*omega_r*y^2 + epsilon_i*mu_i*omega_r^2*y^2 + epsilon_i*mu_r*omega_i^2*y^2 + 2*epsilon_i*mu_r*omega_i*omega_r*y^2 - epsilon_i*mu_r*omega_r^2*y^2 + epsilon_r*mu_i*omega_i^2*y^2 + 2*epsilon_r*mu_i*omega_i*omega_r*y^2 - epsilon_r*mu_i*omega_r^2*y^2 + epsilon_r*mu_r*omega_i^2*y^2 - 2*epsilon_r*mu_r*omega_i*omega_r*y^2 - epsilon_r*mu_r*omega_r^2*y^2 - 2'
expression_y = 'epsilon_i*mu_i*omega_i^2*x^2 - 2*epsilon_i*mu_i*omega_i*omega_r*x^2 - epsilon_i*mu_i*omega_r^2*x^2 - epsilon_i*mu_r*omega_i^2*x^2 - 2*epsilon_i*mu_r*omega_i*omega_r*x^2 + epsilon_i*mu_r*omega_r^2*x^2 - epsilon_r*mu_i*omega_i^2*x^2 - 2*epsilon_r*mu_i*omega_i*omega_r*x^2 + epsilon_r*mu_i*omega_r^2*x^2 - epsilon_r*mu_r*omega_i^2*x^2 + 2*epsilon_r*mu_r*omega_i*omega_r*x^2 + epsilon_r*mu_r*omega_r^2*x^2 + 2'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/microwave_heating.i)
# Test for EMJouleHeatingSource
# Manufactured solution: E_real = cos(pi*y) * x_hat - cos(pi*x) * y_hat
# E_imag = sin(pi*y) * x_hat - sin(pi*x) * y_hat
# n = x^2*y^2
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 5
ny = 5
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[exact_n]
type = ParsedFunction
expression = 'x^2*y^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*cos(pi*y) - 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*y) + epsilon_i*mu_i*omega_r^2*cos(pi*y) - epsilon_i*mu_r*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_r*omega_r^2*sin(pi*y) - epsilon_r*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_r*mu_i*omega_r^2*sin(pi*y) + epsilon_r*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_r*omega_r^2*cos(pi*y) + mu_i*omega_i*sigma_i*cos(pi*y) + mu_i*omega_i*sigma_r*sin(pi*y) + mu_i*omega_r*sigma_i*sin(pi*y) - mu_i*omega_r*sigma_r*cos(pi*y) + mu_r*omega_i*sigma_i*sin(pi*y) - mu_r*omega_i*sigma_r*cos(pi*y) - mu_r*omega_r*sigma_i*cos(pi*y) - mu_r*omega_r*sigma_r*sin(pi*y) + pi^2*cos(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*cos(pi*x) + 2*epsilon_i*mu_i*omega_i*omega_r*sin(pi*x) - epsilon_i*mu_i*omega_r^2*cos(pi*x) + epsilon_i*mu_r*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_r*omega_r^2*sin(pi*x) + epsilon_r*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_r*mu_i*omega_r^2*sin(pi*x) - epsilon_r*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_r*omega_r^2*cos(pi*x) - mu_i*omega_i*sigma_i*cos(pi*x) - mu_i*omega_i*sigma_r*sin(pi*x) - mu_i*omega_r*sigma_i*sin(pi*x) + mu_i*omega_r*sigma_r*cos(pi*x) - mu_r*omega_i*sigma_i*sin(pi*x) + mu_r*omega_i*sigma_r*cos(pi*x) + mu_r*omega_r*sigma_i*cos(pi*x) + mu_r*omega_r*sigma_r*sin(pi*x) - pi^2*cos(pi*x)'
[]
[source_imag]
type = ParsedVectorFunction
symbol_names = 'omega_r mu_r epsilon_r sigma_r omega_i mu_i epsilon_i sigma_i'
symbol_values = 'omega mu epsilon sigma omega mu epsilon sigma'
expression_x = '-epsilon_i*mu_i*omega_i^2*sin(pi*y) + 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*y) + epsilon_i*mu_i*omega_r^2*sin(pi*y) + epsilon_i*mu_r*omega_i^2*cos(pi*y) + 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*y) - epsilon_i*mu_r*omega_r^2*cos(pi*y) + epsilon_r*mu_i*omega_i^2*cos(pi*y) + 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*y) - epsilon_r*mu_i*omega_r^2*cos(pi*y) + epsilon_r*mu_r*omega_i^2*sin(pi*y) - 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*y) - epsilon_r*mu_r*omega_r^2*sin(pi*y) + mu_i*omega_i*sigma_i*sin(pi*y) - mu_i*omega_i*sigma_r*cos(pi*y) - mu_i*omega_r*sigma_i*cos(pi*y) - mu_i*omega_r*sigma_r*sin(pi*y) - mu_r*omega_i*sigma_i*cos(pi*y) - mu_r*omega_i*sigma_r*sin(pi*y) - mu_r*omega_r*sigma_i*sin(pi*y) + mu_r*omega_r*sigma_r*cos(pi*y) + pi^2*sin(pi*y)'
expression_y = 'epsilon_i*mu_i*omega_i^2*sin(pi*x) - 2*epsilon_i*mu_i*omega_i*omega_r*cos(pi*x) - epsilon_i*mu_i*omega_r^2*sin(pi*x) - epsilon_i*mu_r*omega_i^2*cos(pi*x) - 2*epsilon_i*mu_r*omega_i*omega_r*sin(pi*x) + epsilon_i*mu_r*omega_r^2*cos(pi*x) - epsilon_r*mu_i*omega_i^2*cos(pi*x) - 2*epsilon_r*mu_i*omega_i*omega_r*sin(pi*x) + epsilon_r*mu_i*omega_r^2*cos(pi*x) - epsilon_r*mu_r*omega_i^2*sin(pi*x) + 2*epsilon_r*mu_r*omega_i*omega_r*cos(pi*x) + epsilon_r*mu_r*omega_r^2*sin(pi*x) - mu_i*omega_i*sigma_i*sin(pi*x) + mu_i*omega_i*sigma_r*cos(pi*x) + mu_i*omega_r*sigma_i*cos(pi*x) + mu_i*omega_r*sigma_r*sin(pi*x) + mu_r*omega_i*sigma_i*cos(pi*x) + mu_r*omega_i*sigma_r*sin(pi*x) + mu_r*omega_r*sigma_i*sin(pi*x) - mu_r*omega_r*sigma_r*cos(pi*x) - pi^2*sin(pi*x)'
[]
[source_n]
type = ParsedFunction
symbol_names = 'sigma_r'
symbol_values = 'sigma'
expression = '-2*x^2 - 2*y^2 - 0.5*sigma_r*(sin(x*pi)^2 + sin(y*pi)^2 + cos(x*pi)^2 + cos(y*pi)^2)'
[]
#Material Coefficients
[omega]
type = ParsedFunction
expression = '2.0'
[]
[mu]
type = ParsedFunction
expression = '1.0'
[]
[epsilon]
type = ParsedFunction
expression = '3.0'
[]
[sigma]
type = ParsedFunction
expression = '4.0'
#expression = 'x^2*y^2'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_imag = eps_imag
eps_rel_real = eps_real
k_real = k_real
k_imag = k_imag
mu_rel_imag = mu_imag
mu_rel_real = mu_real
[]
[eps_real]
type = ADGenericFunctionMaterial
prop_names = eps_real
prop_values = epsilon
[]
[eps_imag]
type = ADGenericFunctionMaterial
prop_names = eps_imag
prop_values = epsilon
[]
[mu_real]
type = ADGenericFunctionMaterial
prop_names = mu_real
prop_values = mu
[]
[mu_imag]
type = ADGenericFunctionMaterial
prop_names = mu_imag
prop_values = mu
[]
[k_real]
type = ADGenericFunctionMaterial
prop_names = k_real
prop_values = omega
[]
[k_imag]
type = ADGenericFunctionMaterial
prop_names = k_imag
prop_values = omega
[]
[cond_real]
type = ADGenericFunctionMaterial
prop_names = cond_real
prop_values = sigma
[]
[cond_imag]
type = ADGenericFunctionMaterial
prop_names = cond_imag
prop_values = sigma
[]
[]
[Variables]
[n]
family = LAGRANGE
order = FIRST
[]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[conduction_real]
type = ADConductionCurrent
variable = E_real
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[conduction_imag]
type = ADConductionCurrent
variable = E_imag
field_imag = E_imag
field_real = E_real
conductivity_real = cond_real
conductivity_imag = cond_imag
ang_freq_real = k_real
ang_freq_imag = k_imag
permeability_real = mu_real
permeability_imag = mu_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[n_diffusion]
type = Diffusion
variable = n
[]
[microwave_heating]
type = EMJouleHeatingSource
variable = n
E_imag = E_imag
E_real = E_real
conductivity = cond_real
[]
[body_force_n]
type = BodyForce
variable = n
function = source_n
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_n]
type = FunctorDirichletBC
variable = n
boundary = 'left right top bottom'
functor = exact_n
preset = false
[]
[]
[Postprocessors]
[error_real]
type = ElementVectorL2Error
variable = E_real
function = exact_real
[]
[error_imag]
type = ElementVectorL2Error
variable = E_imag
function = exact_imag
[]
[error_n]
type = ElementL2Error
variable = n
function = exact_n
[]
[h]
type = AverageElementSize
[]
[h_squared]
type = ParsedPostprocessor
pp_names = 'h'
expression = 'h * h'
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Steady
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
nl_rel_tol = 1e-12
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/vector_current_source.i)
# Test for VectorCurrentSource
# Manufactured solution: u_real = y^2 * x_hat - x^2 * y_hat
# u_imag = y^2 * x_hat - x^2 * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Functions]
[source_real]
type = ParsedVectorFunction
expression_x = 'y*y - 2'
expression_y = '2 - x*x'
[]
[source_imag]
type = ParsedVectorFunction
expression_x = '2 - y*y'
expression_y = 'x*x - 2'
[]
[]
[Variables]
[u_real]
family = NEDELEC_ONE
order = FIRST
[]
[u_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_real]
type = CurlCurlField
variable = u_real
[]
[coeff_real]
type = VectorFunctionReaction
variable = u_real
[]
[current_real]
type = VectorCurrentSource
variable = u_real
function_coefficient = -1.0
source_real = source_real
source_imag = source_imag
component = real
[]
[curl_curl_imag]
type = CurlCurlField
variable = u_imag
[]
[coeff_imag]
type = VectorFunctionReaction
variable = u_imag
[]
[current_imag]
type = VectorCurrentSource
variable = u_imag
function_coefficient = -1.0
source_real = source_real
source_imag = source_imag
component = imaginary
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = u_real
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = u_imag
function_x = 'y*y'
function_y = '-x*x'
penalty = 1e8
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/auxkernels/azimuthal_Faradays_law/error_azim_magnetic_time_deriv.i)
# Test for AzimuthMagneticTimeDerivRZ with scalar inputs
# Manufactured solution: E_real = y^2 * x_hat - x^2 * y_hat
# E_imag = y^2 * x_hat - x^2 * y_hat
# dB_theta_real / dt = -(2*y + 2*x)
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmax = 1
xmin = 0
ymax = 1
ymin = -1
elem_type = QUAD9
[]
coord_type = RZ
rz_coord_axis = Y
[]
[Functions]
#The exact solution for the heated species and electric field real and imag. component
[exact_real]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
[exact_imag]
type = ParsedVectorFunction
expression_x = 'y^2'
expression_y = '-x^2'
[]
#The forcing terms for the heated species and electric field real and imag. component
[source_real]
type = ParsedVectorFunction
expression_x = '-y^2 - cos(pi*y) - 2'
expression_y = 'x^2 + cos(pi*x) + 4 + 2*y/x'
[]
[source_imag]
type = ParsedVectorFunction
expression_x = '-y^2 + sin(pi*y) - 2'
expression_y = 'x^2 - sin(pi*x) + 4 + 2*y/x'
[]
[current_real]
type = ParsedVectorFunction
expression_x = 'sin(pi*y)'
expression_y = '-sin(pi*x)'
[]
[current_imag]
type = ParsedVectorFunction
expression_x = 'cos(pi*y)'
expression_y = '-cos(pi*x)'
[]
[azim_dB_dt_func]
type = ParsedFunction
expression = '-(2*y + 2*x)'
[]
[]
[Materials]
[WaveCoeff]
type = WaveEquationCoefficient
eps_rel_real = 1.0
eps_rel_imag = 0.0
k_real = 1.0
k_imag = 0.0
mu_rel_real = 1.0
mu_rel_imag = 0.0
[]
[]
[Variables]
[E_real]
family = NEDELEC_ONE
order = FIRST
[]
[E_imag]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl_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
[]
[current_real]
type = VectorCurrentSource
variable = E_real
source_real = current_real
source_imag = current_imag
component = real
[]
[body_force_real]
type = VectorBodyForce
variable = E_real
function = source_real
[]
[curl_curl_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
[]
[current_imag]
type = VectorCurrentSource
variable = E_imag
source_real = current_real
source_imag = current_imag
component = imaginary
[]
[body_force_imag]
type = VectorBodyForce
variable = E_imag
function = source_imag
[]
[]
[AuxVariables]
[aux_E_real_x]
family = MONOMIAL
order = FIRST
[]
[aux_E_real_y]
family = MONOMIAL
order = FIRST
[]
[azim_dB_dt_term]
family = MONOMIAL
order = FIRST
[]
[]
[AuxKernels]
[aux_E_real_x]
type = VectorVariableComponentAux
variable = aux_E_real_x
vector_variable = E_real
component = X
[]
[aux_E_real_y]
type = VectorVariableComponentAux
variable = aux_E_real_y
vector_variable = E_real
component = Y
[]
[aux_azim_dB_dt]
type = AzimuthMagneticTimeDerivRZ
# Efield = E_real
# Efield_X = aux_E_real_x
# Efield_Y = aux_E_real_y
variable = azim_dB_dt_term
[]
[]
[BCs]
[sides_real]
type = VectorCurlPenaltyDirichletBC
variable = E_real
function = exact_real
penalty = 1e8
boundary = 'left right top bottom'
[]
[sides_imag]
type = VectorCurlPenaltyDirichletBC
variable = E_imag
function = exact_imag
penalty = 1e8
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'
nl_rel_tol = 1e-16
[]
[Outputs]
exodus = true
csv = true
[]
(modules/electromagnetics/test/tests/kernels/vector_helmholtz/ad_vector_kernels.i)
# Test for EM module vector kernels ADCurlCurlField and VectorFunctionReaction
# Manufactured solution: u = y * x_hat - x * y_hat
[Mesh]
[gmg]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmin = -1
ymin = -1
elem_type = QUAD9
[]
[]
[Variables]
[u]
family = NEDELEC_ONE
order = FIRST
[]
[]
[Kernels]
[curl_curl]
type = ADCurlCurlField
variable = u
[]
[coeff]
type = VectorFunctionReaction
variable = u
[]
[rhs]
type = VectorBodyForce
variable = u
function_x = 'y'
function_y = '-x'
[]
[]
[BCs]
[sides]
type = VectorCurlPenaltyDirichletBC
variable = u
function_x = 'y'
function_y = '-x'
penalty = 1e8
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
[]