MFEMCurlAux

Overview

AuxKernel for calculating the curl of an $var element = document.getElementById("moose-equation-8552da45-478d-4342-b0f5-b4f99601f373");katex.render("H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ conforming source variable defined on a 3D Nédélec finite element space and storing it in an $var element = document.getElementById("moose-equation-02b21897-d2a7-4261-8b1e-09ce34176d95");katex.render("H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ conforming result variable defined on a Raviart-Thomas finite element space.

The result may be scaled by an optional (global) scalar factor.

var element = document.getElementById("moose-equation-159920bd-9472-4fcf-af05-9f548db38441");katex.render("\\vec v = \\lambda \\vec\\nabla \\times \\vec u", 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 $var element = document.getElementById("moose-equation-11caa69f-3473-401a-a4fa-e5975736aa5b");katex.render("\\vec u \\in H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-71412558-557f-4118-a1bc-a4c88fdf4ac9");katex.render("\\vec v \\in H(\\mathrm{div})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-f3c4e39d-9daf-485e-aa34-476cf04071c9");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar constant.

Example Input File Syntax

[AuxKernels<<<{"href": "../../../syntax/AuxKernels/index.html"}>>>]
  [curl]
    type = MFEMCurlAux<<<{"description": "Calculates the curl of an H(curl) conforming ND source variable and stores the result on an H(div) conforming RT result auxvariable", "href": "MFEMCurlAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = db_dt_field
    source<<<{"description": "Vector H(curl) MFEMVariable to take the curl of."}>>> = e_field
    scale_factor<<<{"description": "Factor to scale result auxvariable by."}>>> = -1.0
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
[]

Input Parameters

sourceVector H(curl) MFEMVariable to take the curl of.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Vector H(curl) MFEMVariable to take the curl of.
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
scale_factor1Factor to scale result auxvariable by.
Default:1
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Factor to scale result auxvariable by.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/mfem/submeshes/hphi_magnetodynamic.i)
(test/tests/mfem/submeshes/magnetostatic.i)
(test/tests/mfem/kernels/curlcurl.i)
(test/tests/mfem/submeshes/av_magnetostatic.i)
(test/tests/mfem/submeshes/nl_hphi_magnetodynamic.i)

(test/tests/mfem/kernels/curlcurl.i)

# Definite Maxwell problem solved with Nedelec elements of the first kind
# based on MFEM Example 3.

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/small_fichera.mesh
[]

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxVariables]
  [db_dt_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [curl]
    type = MFEMCurlAux
    variable = db_dt_field
    source = e_field
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [exact_e_field]
    type = ParsedVectorFunction
    expression_x = 'sin(kappa * y)'
    expression_y = 'sin(kappa * z)'
    expression_z = 'sin(kappa * x)'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []

  [forcing_field]
    type = ParsedVectorFunction
    expression_x = '(1. + kappa * kappa) * sin(kappa * y)'
    expression_y = '(1. + kappa * kappa) * sin(kappa * z)'
    expression_z = '(1. + kappa * kappa) * sin(kappa * x)'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
[]

[BCs]
  [tangential_E_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = e_field
    vector_coefficient = exact_e_field
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = e_field
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = e_field
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = e_field
    vector_coefficient = forcing_field
  []
[]


[Solvers]
  active = 'gmres ams'
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
  [matrix_free_ams]
    type = MFEMMatrixFreeAMS
  []
  [gmres]
    type = MFEMHypreGMRES
    preconditioner = ams
    l_tol = 1e-12
  []
  [cg]
    type = MFEMCGSolver
    preconditioner = matrix_free_ams
    l_tol = 1e-12
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[VectorPostprocessors]
  [line_sample_e_field]
    type = MFEMVariableLineValueSampler
    variable = 'e_field'
    start_point = '-0.99 -0.99 0.99'
    end_point = '0.99 0.99 -0.99'
    num_points = 114
  []
  [line_sample_db_dt_field]
    type = MFEMVariableLineValueSampler
    variable = 'db_dt_field'
    start_point = '-0.99 -0.99 0.99'
    end_point = '0.99 0.99 -0.99'
    num_points = 114
  []
[]

[Outputs]
  [CSV]
    type = CSV
    execute_on = 'timestep_end'
    file_base = OutputData/CurlCurl/curlcurl
  []
[]

(test/tests/mfem/submeshes/hphi_magnetodynamic.i)

# Solve for the magnetic field around a closed conductor subject to
# global current constraint.

conductor_domains = 'TorusCore TorusSheath'
conductor_resistivity = 1.0
vacuum_permeability = 1.0

[Problem]
  type = MFEMProblem
[]

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/split_embedded_concentric_torus.e
[]

[FunctorMaterials]
  [Conductor]
    type = MFEMGenericFunctorMaterial
    prop_names = 'resistivity'
    prop_values = ${conductor_resistivity}
    block = ${conductor_domains}
  []
  [Vacuum]
    type = MFEMGenericFunctorMaterial
    prop_names = 'permeability'
    prop_values = '${vacuum_permeability}'
  []
[]

[SubMeshes]
  [conductor]
    type = MFEMDomainSubMesh
    block = ${conductor_domains}
    submesh_boundary = conductor_surface
  []
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [CoilHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = conductor
  []
[]

[Variables]
  [coil_induced_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
[]

[AuxVariables]
  [h_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [coil_external_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
  [j_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [update_j_field]
    type = MFEMCurlAux
    variable = j_field
    source = h_field
    scale_factor = 1.0
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  [conductor_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = coil_induced_h_field
    vector_coefficient = coil_external_h_field
    boundary = conductor_surface
  []
[]

[Kernels]
  [dBdt]
    type = MFEMTimeDerivativeVectorFEMassKernel
    variable = coil_induced_h_field
    coefficient = permeability
  []
  [curlE]
    type = MFEMCurlCurlKernel
    variable = coil_induced_h_field
    coefficient = resistivity
  []
[]


[Solvers]
  [ams]
    type = MFEMHypreAMS
    fespace = CoilHCurlFESpace
  []
  [main]
    type = MFEMHyprePCG
    preconditioner = ams
    l_tol = 1e-9
    l_max_its = 100
  []
[]

[Executioner]
  type = MFEMTransient
  dt = 0.5
  start_time = 0.0
  end_time = 2.0
[]

[MultiApps]
  [hphi_magnetostatic]
    type = FullSolveMultiApp
    input_files = hphi_magnetostatic.i
    execute_on = INITIAL
  []
[]

[Transfers]
  [from_external_field]
    type = MultiAppMFEMCopyTransfer
    source_variables = h_field
    variables = h_field
    from_multi_app = hphi_magnetostatic
  []
  [submesh_transfer_to_coil]
    type = MFEMSubMeshTransfer
    from_variable = h_field
    to_variable = coil_external_h_field
    execute_on = TIMESTEP_BEGIN
  []
  [submesh_transfer_from_coil]
    type = MFEMSubMeshTransfer
    from_variable = coil_induced_h_field
    to_variable = h_field
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [CoilPower]
    type = MFEMVectorFEInnerProductIntegralPostprocessor
    coefficient = resistivity
    dual_variable = j_field
    primal_variable = j_field
    block = 'TorusCore TorusSheath'
  []
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/HPhiMagnetodynamicClosedCoilCSV
  []
  [VacuumParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HPhiMagnetodynamicClosedCoil
    vtk_format = ASCII
  []
[]

(test/tests/mfem/submeshes/magnetostatic.i)

# Definite Maxwell problem solved with Nedelec elements of the first kind
# based on MFEM Example 3.

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/cylinder-hex-q2.gen
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
[]

[Variables]
  [a_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [electric_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [b_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [curl]
    type = MFEMCurlAux
    variable = b_field
    source = a_field
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  [tangential_a_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = a_field
    boundary = '1 2 3'
  []
[]

[Kernels]
  inactive = coefficient_source
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = a_field
  []
  [auxvar_source]
    type = MFEMMixedVectorGradientKernel
    trial_variable = electric_potential
    variable = a_field
    block = 1
  []
  [coefficient_source]
    type = MFEMVectorFEDomainLFKernel
    vector_coefficient = electric_potential_grad
    variable = a_field
    block = 1
  []
[]


[Solvers]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
    singular = true
  []
  [main]
    type = MFEMHypreGMRES
    preconditioner = ams
    l_tol = 1e-12
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [subapp]
    type = FullSolveMultiApp
    input_files = open_coil_source.i
    execute_on = INITIAL
  []
[]

[Transfers]
  [from_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = electric_potential
    variables = electric_potential
    from_multi_app = subapp
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Magnetostatic
    vtk_format = ASCII
  []
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMVariableLineValueSampler
    variable = 'electric_potential'
    start_point = '0 0.5 -0.5'
    end_point = '0 0.5 0.5'
    num_points = 101
  []
[]

[Outputs]
  [CSV]
    type = CSV
    execute_on = 'timestep_end'
    file_base = OutputData/electric_potential
  []
[]

(test/tests/mfem/kernels/curlcurl.i)

# Definite Maxwell problem solved with Nedelec elements of the first kind
# based on MFEM Example 3.

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/small_fichera.mesh
[]

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxVariables]
  [db_dt_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [curl]
    type = MFEMCurlAux
    variable = db_dt_field
    source = e_field
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [exact_e_field]
    type = ParsedVectorFunction
    expression_x = 'sin(kappa * y)'
    expression_y = 'sin(kappa * z)'
    expression_z = 'sin(kappa * x)'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []

  [forcing_field]
    type = ParsedVectorFunction
    expression_x = '(1. + kappa * kappa) * sin(kappa * y)'
    expression_y = '(1. + kappa * kappa) * sin(kappa * z)'
    expression_z = '(1. + kappa * kappa) * sin(kappa * x)'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
[]

[BCs]
  [tangential_E_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = e_field
    vector_coefficient = exact_e_field
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = e_field
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = e_field
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = e_field
    vector_coefficient = forcing_field
  []
[]


[Solvers]
  active = 'gmres ams'
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
  [matrix_free_ams]
    type = MFEMMatrixFreeAMS
  []
  [gmres]
    type = MFEMHypreGMRES
    preconditioner = ams
    l_tol = 1e-12
  []
  [cg]
    type = MFEMCGSolver
    preconditioner = matrix_free_ams
    l_tol = 1e-12
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[VectorPostprocessors]
  [line_sample_e_field]
    type = MFEMVariableLineValueSampler
    variable = 'e_field'
    start_point = '-0.99 -0.99 0.99'
    end_point = '0.99 0.99 -0.99'
    num_points = 114
  []
  [line_sample_db_dt_field]
    type = MFEMVariableLineValueSampler
    variable = 'db_dt_field'
    start_point = '-0.99 -0.99 0.99'
    end_point = '0.99 0.99 -0.99'
    num_points = 114
  []
[]

[Outputs]
  [CSV]
    type = CSV
    execute_on = 'timestep_end'
    file_base = OutputData/CurlCurl/curlcurl
  []
[]

(test/tests/mfem/submeshes/av_magnetostatic.i)

# Magnetostatic problem solved on a closed conductor subject to
# global loop voltage constraint.

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/embedded_concentric_torus.e
[]

[Problem]
  type = MFEMProblem
[]

[SubMeshes]
  inactive = 'fluxcut'
  [fluxcut]
    type = MFEMCutTransitionSubMesh
    cut_boundary = 'MeasurementPlane'
    block = 'TorusCore TorusSheath'
    transition_subdomain = transition_dom
    transition_subdomain_boundary = transition_bdr
    closed_subdomain = coil_dom
  []
[]

[FESpaces]
  inactive = 'FluxFESpace'
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [FluxFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = fluxcut
  []
[]

[Variables]
  [a_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxVariables]
  inactive = 'flux_e_field'
  [b_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [flux_e_field]
    type = MFEMVariable
    fespace = FluxFESpace
  []
[]

[AuxKernels]
  [curl]
    type = MFEMCurlAux
    variable = b_field
    source = a_field
    scale_factor = 1.0
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  [tangential_a_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = a_field
    boundary = 'Exterior'
  []
[]

[FunctorMaterials]
  inactive = 'ConductorBoundary'
  [Vacuum]
    type = MFEMGenericFunctorMaterial
    prop_names = reluctivity
    prop_values = 1.0
  []
  [Conductor]
    type = MFEMGenericFunctorMaterial
    prop_names = conductivity
    prop_values = 1.0
    block = 'TorusCore TorusSheath'
  []
  [ConductorBoundary]
    type = MFEMGenericFunctorMaterial
    prop_names = conductivity_boundary
    prop_values = 1.0
    boundary = 'MeasurementPlane'
  []
[]

[Kernels]
  [mass]
    type = MFEMVectorFEMassKernel
    variable = a_field
    coefficient = 1e-10
  []
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = a_field
    coefficient = reluctivity
  []
  [source]
    type = MFEMMixedVectorMassKernel
    variable = a_field
    trial_variable = e_field
    coefficient = conductivity
    block = 'TorusCore TorusSheath'
  []
[]


[Solvers]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
  [main]
    type = MFEMHyprePCG
    preconditioner = ams
    l_tol = 1e-14
    l_max_its = 1000
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [coil]
    type = FullSolveMultiApp
    input_files = cut_closed_coil.i
    execute_on = INITIAL
  []
[]

[Transfers]
  inactive = 'submesh_transfer_to_fluxsurface'
  [from_coil]
    type = MultiAppMFEMCopyTransfer
    source_variables = e_field
    variables = e_field
    from_multi_app = coil
  []
  [submesh_transfer_to_fluxsurface]
    type = MFEMSubMeshTransfer
    from_variable = e_field
    to_variable = flux_e_field
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  inactive = 'CoilCurrent'
  [CoilPower]
    type = MFEMVectorFEInnerProductIntegralPostprocessor
    coefficient = conductivity
    dual_variable = e_field
    primal_variable = e_field
    block = 'TorusCore TorusSheath'
  []
  [CoilCurrent]
    type = MFEMVectorBoundaryFluxIntegralPostprocessor
    coefficient = conductivity_boundary
    variable = flux_e_field
    boundary = 'MeasurementPlane'
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/MagnetostaticClosedCoil
    vtk_format = ASCII
  []
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/AVMagnetostaticClosedCoilCSV
  []
[]

(test/tests/mfem/submeshes/nl_hphi_magnetodynamic.i)

# Solve for the magnetic field around a closed superconductor subject to
# global current constraint.

conductor_domains = 'TorusCore TorusSheath'
vacuum_permeability = 1.0
n_value = 20.0
j_c = 1.0
e_c = 1.0

[Problem]
  type = MFEMProblem
[]

[Mesh]
  type = MFEMFileMesh
  file = ../mesh/split_embedded_concentric_torus.e
[]

[SubMeshes]
  [conductor]
    type = MFEMDomainSubMesh
    block = ${conductor_domains}
    submesh_boundary = conductor_surface
  []
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
    submesh = conductor
  []
  [CoilHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = conductor
  []
[]

[Variables]
  [coil_induced_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
[]

[AuxVariables]
  [coil_external_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
  [j_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [update_j_field]
    type = MFEMCurlAux
    variable = j_field
    source = coil_induced_h_field
    scale_factor = 1.0
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [resistivity]
    type = MFEMParsedFunction
    expression = '(e_c/j_c) * (j/j_c)^(n_val-1)'
    symbol_names = 'j e_c j_c n_val'
    symbol_values = 'coil_induced_h_field_curl_mag ${e_c} ${j_c} ${n_value}'
  []
  [j_dresistivity_dj]
    type = MFEMParsedFunction
    expression = '(n_val-1) * resistivity'
    symbol_names = 'n_val resistivity'
    symbol_values = '${n_value} resistivity'
  []
[]

[FunctorMaterials]
  [Vacuum]
    type = MFEMGenericFunctorMaterial
    prop_names = 'permeability'
    prop_values = '${vacuum_permeability}'
  []
[]


[BCs]
  [conductor_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = coil_induced_h_field
    vector_coefficient = coil_external_h_field
    boundary = conductor_surface
  []
[]

[Kernels]
  [dBdt]
    type = MFEMTimeDerivativeVectorFEMassKernel
    variable = coil_induced_h_field
    coefficient = permeability
  []
  [curlE]
    type = MFEMNLCurlCurlKernel
    variable = coil_induced_h_field
    k_coefficient = resistivity
    curlu_dk_dcurlu_coefficient = j_dresistivity_dj
    block = ${conductor_domains}
  []
[]

[Solvers]
  [ams]
    type = MFEMHypreAMS
    fespace = CoilHCurlFESpace
  []
  [pcg]
    type = MFEMHyprePCG
    preconditioner = ams
    l_tol = 1e-12
    l_max_its = 100
    print_level = 0
  []
  [newton]
    type = MFEMNewtonNonlinearSolver
    max_its = 150
    abs_tol = 1e-5
    print_level = 1
  []
[]

[Executioner]
  type = MFEMTransient
  dt = 0.5
  start_time = 0.0
  end_time = 2.0
[]

[MultiApps]
  [hphi_magnetostatic]
    type = FullSolveMultiApp
    input_files = hphi_magnetostatic.i
    execute_on = INITIAL
  []
[]

[Transfers]
  [from_external_field]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = h_field
    variables = coil_external_h_field
    from_multi_app = hphi_magnetostatic
  []
[]

[Postprocessors]
  [CoilPower]
    type = MFEMVectorFEInnerProductIntegralPostprocessor
    coefficient = resistivity
    dual_variable = j_field
    primal_variable = j_field
    block = 'TorusCore TorusSheath'
  []
[]

[Outputs]
  inactive = ConductorParaViewDataCollection
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/HPhiMagnetodynamicNLClosedCoilCSV
  []
  [ConductorParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HPhiMagnetodynamicNLClosedCoil
    vtk_format = ASCII
    submesh = conductor
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files