MFEMHypreAMS

Overview

Defines and builds an mfem::HypreAMS solver to use as a preconditioner or solver to solve the MFEM equation system. Most effective for preconditioning and solving a curl-curl problem when using Nédélec elements, in which case the $var element = document.getElementById("moose-equation-4a01d441-26e9-4f9b-9511-f496b879ef98");katex.render("H(\\mathrm{curl})", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ FE space should be passed to the mfem::HypreAMS solver during construction.

If the system of equations is singular - commonly arising, for example, when solving for the magnetic vector potential in magnetostatic systems in the steady state - users should set the singular parameter to true to add a small mass term to ensure solvability.

A Low-Order-Refined (LOR) version of this solver may be used instead by setting the parameter "low_order_refined" to true. Using an LOR solver improves performance for high polynomial order systems.

Example Input File Syntax

[FESpaces<<<{"href": "../../../syntax/FESpaces/index.html"}>>>]
  [HCurlFESpace]
    type = MFEMVectorFESpace<<<{"description": "Convenience class to construct vector finite element spaces, abstracting away some of the mathematical complexity of specifying the dimensions.", "href": "../fespaces/MFEMVectorFESpace.html"}>>>
    fec_type<<<{"description": "Specifies the family of FE shape functions."}>>> = ND
    fec_order<<<{"description": "Order of the FE shape function to use."}>>> = FIRST
  []
[]

[Preconditioner<<<{"href": "../../../syntax/Preconditioner/index.html"}>>>]
  [ams]
    type = MFEMHypreAMS<<<{"description": "Hypre auxiliary-space Maxwell solver and preconditioner for the iterative solution of MFEM equation systems.", "href": "MFEMHypreAMS.html"}>>>
    fespace<<<{"description": "H(curl) FESpace to use in HypreAMS setup."}>>> = HCurlFESpace
  []
[]

[Solver<<<{"href": "../../../syntax/Solver/index.html"}>>>]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-12
[]

Input Parameters

fespaceH(curl) FESpace to use in HypreAMS setup.
C++ Type:MFEMFESpaceName
Controllable:No
Description:H(curl) FESpace to use in HypreAMS setup.
low_order_refinedFalseSet usage of Low-Order Refined solver.
Default:False
C++ Type:bool
Controllable:No
Description:Set usage of Low-Order Refined solver.
print_level2Set the solver verbosity.
Default:2
C++ Type:int
Controllable:No
Description:Set the solver verbosity.
singularFalseDeclare that the system is singular; use when solving curl-curl problem if mass term is zero
Default:False
C++ Type:bool
Controllable:No
Description:Declare that the system is singular; use when solving curl-curl problem if mass term is zero

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/magnetostatic.i)
(test/tests/mfem/submeshes/hphi_magnetodynamic.i)
(test/tests/mfem/vectorpostprocessors/line_value_sampler/line_value_sampler_curlcurl.i)
(test/tests/mfem/kernels/maxwell_eigenproblem.i)
(test/tests/mfem/kernels/curlcurl.i)
(test/tests/mfem/vectorpostprocessors/point_value_sampler/point_value_sampler_curlcurl.i)
(test/tests/mfem/submeshes/av_magnetostatic.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 = MFEMMesh
  file = ../mesh/small_fichera.mesh
  dim = 3
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  inactive = "L2FESpace"
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

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

[AuxVariables]
  inactive = "joule_heating"
  [db_dt_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [joule_heating]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxKernels]
  inactive = "joule_Q_aux"
  [curl]
    type = MFEMCurlAux
    variable = db_dt_field
    source = e_field
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [joule_Q_aux]
    type = MFEMInnerProductAux
    variable = joule_heating
    first_source_vec = e_field
    second_source_vec = e_field
    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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-12
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/CurlCurl
    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 = MFEMMesh
  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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
    singular = true
  []
[]

[Solver]
  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
  []
[]

(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 = MFEMMesh
    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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = CoilHCurlFESpace
  []
[]

[Solver]
  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/vectorpostprocessors/line_value_sampler/line_value_sampler_curlcurl.i)

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

[Mesh]
  type = MFEMMesh
  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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-6
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMLineValueSampler
    variable = 'e_field'
    start_point = '1 1 -1'
    end_point = '1 1 1'
    num_points = 11
  []
[]


[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  dim = 3
[]

[Problem]
  type = MFEMEigenproblem
  num_modes = 5
[]

[FESpaces]
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
[]

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

[BCs]
  [all]
    type = MFEMVectorTangentialDirichletBC
    variable = E
    vector_coefficient = '0 0 0'
  []
[]

[Kernels]
  [diff]
    type = MFEMCurlCurlKernel
    variable = E
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
    print_level = 0
    singular = true
  []
[]

[Solver]
  type = MFEMHypreAME
  preconditioner = ams
  print_level = 0
  l_tol = 1e-8
  l_max_its = 100
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[VectorPostprocessors]
  [eigenvalues]
    type = MFEMEigenvaluesPostprocessor
  []
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
  file_base = OutputData/MaxwellEigenproblem
[]

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

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

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

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  inactive = "L2FESpace"
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

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

[AuxVariables]
  inactive = "joule_heating"
  [db_dt_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [joule_heating]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxKernels]
  inactive = "joule_Q_aux"
  [curl]
    type = MFEMCurlAux
    variable = db_dt_field
    source = e_field
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [joule_Q_aux]
    type = MFEMInnerProductAux
    variable = joule_heating
    first_source_vec = e_field
    second_source_vec = e_field
    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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-12
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/mfem/vectorpostprocessors/point_value_sampler/point_value_sampler_curlcurl.i)

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

[Mesh]
  type = MFEMMesh
  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
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = ams
  l_tol = 1e-6
[]

[VectorPostprocessors]
  [point_sample]
    type = MFEMPointValueSampler
    variable = 'e_field'
    points = '1 1 -0.5  1 1 0.5'
  []
[]


[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Outputs]
  execute_on = 'timestep_end'
  csv = true
[]

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

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

[Mesh]
  type = MFEMMesh
  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
  []
[]

[Functions]
  [exact_a_field]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '0'
    expression_z = '0'
  []
[]

[BCs]
  [tangential_a_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = a_field
    vector_coefficient = exact_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'
  []
[]

[Preconditioner]
  [ams]
    type = MFEMHypreAMS
    fespace = HCurlFESpace
  []
[]

[Solver]
  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
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files