MFEMGenericFunctorMaterial

Overview

MFEMGenericFunctorMaterial defines one or more scalar material properties with values obtained from a coefficient on one or more subdomains of the mesh, given by the "block" parameter if provided, or applied to the entire mesh if missing. The scalar material properties are named according to members in the "prop_names" parameter, with respective coefficients used to get property values given by the members of "prop_values".

Example Input File Syntax

[FunctorMaterials<<<{"href": "../../../syntax/FunctorMaterials/index.html"}>>>]
  [Rigidium]
    type = MFEMGenericFunctorMaterial<<<{"description": "Declares material scalar properties based on names and coefficients prescribed by input parameters.", "href": "MFEMGenericFunctorMaterial.html"}>>>
    prop_names<<<{"description": "The names of the properties this material will have"}>>> = 'lambda mu'
    prop_values<<<{"description": "The corresponding names of coefficients associated with the named properties. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = '50.0 50.0'
    block<<<{"description": "The list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains."}>>> = 1
  []
  [Bendium]
    type = MFEMGenericFunctorMaterial<<<{"description": "Declares material scalar properties based on names and coefficients prescribed by input parameters.", "href": "MFEMGenericFunctorMaterial.html"}>>>
    prop_names<<<{"description": "The names of the properties this material will have"}>>> = 'lambda mu'
    prop_values<<<{"description": "The corresponding names of coefficients associated with the named properties. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = '1.0 1.0'
    block<<<{"description": "The list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains."}>>> = 2
  []
[]

Input Parameters

prop_namesThe names of the properties this material will have
C++ Type:std::vector<std::string>
Controllable:No
Description:The names of the properties this material will have
prop_valuesThe corresponding names of coefficients associated with the named properties. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
C++ Type:std::vector<MFEMScalarCoefficientName>
Controllable:No
Description:The corresponding names of coefficients associated with the named properties. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.

Required Parameters

blockThe list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains.
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of subdomains (names or ids) that this object will be restricted to. Leave empty to apply to all subdomains.
boundary-1 The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.
Default:-1
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies. Defaults to all boundaries.

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/open_coil_source.i)
(test/tests/mfem/submeshes/hphi_magnetostatic.i)
(test/tests/mfem/kernels/linearelasticity.i)
(test/tests/mfem/submeshes/hphi_magnetodynamic.i)
(test/tests/mfem/submeshes/cut_closed_coil.i)
(test/tests/mfem/auxkernels/projection.i)
(test/tests/mfem/vectorpostprocessors/point_value_sampler/point_value_sampler_diffusion.i)
(test/tests/mfem/auxkernels/2Dmagnetostatic.i)
(test/tests/mfem/kernels/gravity.i)
(test/tests/mfem/submeshes/av_magnetostatic.i)
(test/tests/mfem/vectorpostprocessors/line_value_sampler/line_value_sampler_diffusion.i)
(test/tests/mfem/complex/complex_waveguide.i)
(test/tests/mfem/functions/parsed_function_source.i)

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  dim = 3
  uniform_refine = 2
  displacement = "displacement"
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMVectorFESpace
    fec_type = H1
    fec_order = FIRST
    range_dim = 3
    ordering = "vdim"
  []
[]

[Variables]
  [displacement]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorDirichletBC
    variable = displacement
    boundary = '1'
  []
[]

[FunctorMaterials]
  [Rigidium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '50.0 50.0'
    block = 1
  []
  [Bendium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '1.0 1.0'
    block = 2
  []
  [RigidiumWeightDensity]
    type = MFEMGenericFunctorVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '{0.0 0.0 -1e-2}'
    block = 1
  []
  [BendiumWeightDensity]
    type = MFEMGenericFunctorVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '{0.0 0.0 -5e-3}'
    block = 2
  []
[]

[Kernels]
  [diff]
    type = MFEMLinearElasticityKernel
    variable = displacement
    lambda = lambda
    mu = mu
  []
  [gravity]
    type = MFEMVectorDomainLFKernel
    variable = displacement
    vector_coefficient = gravitational_force_density
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    fespace = H1FESpace
    l_max_its = 20
    l_tol = 1e-5
    print_level = 2
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_max_its = 100
  l_tol = 1e-4
  l_abs_tol = 0.0
  print_level = 2
[]

[Executioner]
  type = MFEMSteady
  device = "cpu"
[]

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

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

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

[Problem]
  type = MFEMProblem
[]

[SubMeshes]
  [wire]
    type = MFEMDomainSubMesh
    block = 1
  []
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [SubMeshH1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
    submesh = wire
  []
[]

[Variables]
  [electric_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [submesh_potential]
    type = MFEMVariable
    fespace = SubMeshH1FESpace
  []
[]

[BCs]
  [high_terminal]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = '1'
    coefficient = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = '2'
    coefficient = 0.0
  []
[]

[FunctorMaterials]
  [Substance]
    type = MFEMGenericFunctorMaterial
    prop_names = conductivity
    prop_values = 1.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = submesh_potential
    coefficient = conductivity
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

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

[Executioner]
  type = MFEMSteady
[]

[Transfers]
  [submesh_potential_transfer]
    type = MFEMSubMeshTransfer
    from_variable = submesh_potential
    to_variable = electric_potential
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/OpenCoilSourceSubMesh
    vtk_format = ASCII
    submesh = wire
  []
[]

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

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

initial_vacuum_domains = 'Exterior'
vacuum_cut_surface = 'Cut'
conductor_current = 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 = permeability
    prop_values = ${vacuum_permeability}
  []
[]

[ICs]
  [vacuum_cut_potential_ic]
    type = MFEMScalarBoundaryIC
    variable = vacuum_cut_potential
    boundary = ${vacuum_cut_surface}
    coefficient = ${conductor_current}
  []
[]

[SubMeshes]
  [cut]
    type = MFEMCutTransitionSubMesh
    cut_boundary = ${vacuum_cut_surface}
    block = ${initial_vacuum_domains}
    transition_subdomain = transition_dom
    transition_subdomain_boundary = transition_bdr
    closed_subdomain = vacuum_dom
  []
  [vacuum]
    type = MFEMDomainSubMesh
    block = vacuum_dom
  []
[]

[FESpaces]
  [VacuumH1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
    submesh = vacuum
  []
  [VacuumHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = vacuum
  []
  [TransitionH1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
    submesh = cut
  []
  [TransitionHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = cut
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
[]

[Variables]
  [vacuum_magnetic_potential]
    type = MFEMVariable
    fespace = VacuumH1FESpace
  []
[]

[AuxVariables]
  [vacuum_cut_potential]
    type = MFEMVariable
    fespace = VacuumH1FESpace
  []
  [transition_cut_potential]
    type = MFEMVariable
    fespace = TransitionH1FESpace
  []
  [transition_cut_function_field]
    type = MFEMVariable
    fespace = TransitionHCurlFESpace
  []
  [background_h_field]
    type = MFEMVariable
    fespace = VacuumHCurlFESpace
  []
  [cut_function_field]
    type = MFEMVariable
    fespace = VacuumHCurlFESpace
  []
  [vacuum_h_field]
    type = MFEMVariable
    fespace = VacuumHCurlFESpace
  []
  [h_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels]
  [update_background_h_field]
    type = MFEMGradAux
    variable = background_h_field
    source = vacuum_magnetic_potential
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [update_transition_cut_function_field]
    type = MFEMGradAux
    variable = transition_cut_function_field
    source = transition_cut_potential
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [update_total_h_field]
    type = MFEMSumAux
    variable = vacuum_h_field
    source_variables = 'background_h_field cut_function_field'
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  # Set zero of magnetic potential on symmetry plane
  [Exterior]
    type = MFEMScalarDirichletBC
    variable = vacuum_magnetic_potential
    boundary = 'Cut'
    coefficient = 0.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = vacuum_magnetic_potential
    coefficient = permeability
  []
  [source]
    type = MFEMMixedGradGradKernel
    trial_variable = vacuum_cut_potential
    variable = vacuum_magnetic_potential
    coefficient = permeability
    block = 'transition_dom'
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 100
[]

[Executioner]
  type = MFEMSteady
[]

[Transfers]
  [submesh_transfer_to_transition]
    type = MFEMSubMeshTransfer
    from_variable = vacuum_cut_potential
    to_variable = transition_cut_potential
    execute_on = TIMESTEP_END
  []
  [submesh_transfer_from_transition]
    type = MFEMSubMeshTransfer
    from_variable = transition_cut_function_field
    to_variable = cut_function_field
    execute_on = TIMESTEP_END
  []
  [submesh_transfer_from_vacuum]
    type = MFEMSubMeshTransfer
    from_variable = vacuum_h_field
    to_variable = h_field
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [MagneticEnergy]
    type = MFEMVectorFEInnerProductIntegralPostprocessor
    coefficient = ${fparse 0.5*vacuum_permeability}
    dual_variable = vacuum_h_field
    primal_variable = vacuum_h_field
    block = 'Exterior'
  []
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/HPhiMagnetostaticClosedCoilCSV
  []
  [VacuumParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HPhiMagnetostaticClosedCoil
    vtk_format = ASCII
    submesh = vacuum
  []
[]

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  dim = 3
  uniform_refine = 2
  displacement = "displacement"
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMVectorFESpace
    fec_type = H1
    fec_order = FIRST
    range_dim = 3
    ordering = "vdim"
  []
[]

[Variables]
  [displacement]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorDirichletBC
    variable = displacement
    boundary = '1'
  []
  [pull_down]
    type = MFEMVectorBoundaryIntegratedBC
    variable = displacement
    boundary = '2'
    vector_coefficient = '0.0 0.0 -0.01'
  []
[]

[FunctorMaterials]
  [Rigidium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '50.0 50.0'
    block = 1
  []
  [Bendium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '1.0 1.0'
    block = 2
  []
[]

[Kernels]
  [diff]
    type = MFEMLinearElasticityKernel
    variable = displacement
    lambda = lambda
    mu = mu
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    l_max_its = 500
    l_tol = 1e-8
    print_level = 2
  []
[]

[Solver]
  type = MFEMHyprePCG
  #preconditioner = boomeramg
  l_max_its = 5000
  l_tol = 1e-8
  l_abs_tol = 0.0
  print_level = 2
[]

[Executioner]
  type = MFEMSteady
  device = "cpu"
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/LinearElasticity
    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/submeshes/cut_closed_coil.i)

# Solve for the electric field on a closed conductor subject to
# global loop voltage constraint.

initial_coil_domains = 'TorusCore TorusSheath'
coil_cut_surface = 'Cut'
coil_loop_voltage = -1.0
coil_conductivity = 1.0

[Problem]
  type = MFEMProblem
[]

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

[FunctorMaterials]
  [Conductor]
    type = MFEMGenericFunctorMaterial
    prop_names = conductivity
    prop_values = ${coil_conductivity}
  []
[]

[ICs]
  [coil_external_potential_ic]
    type = MFEMScalarBoundaryIC
    variable = coil_external_potential
    boundary = ${coil_cut_surface}
    coefficient = ${coil_loop_voltage}
  []
[]

[SubMeshes]
  [cut]
    type = MFEMCutTransitionSubMesh
    cut_boundary = ${coil_cut_surface}
    block = ${initial_coil_domains}
    transition_subdomain = transition_dom
    transition_subdomain_boundary = transition_bdr
    closed_subdomain = coil_dom
  []
  [coil]
    type = MFEMDomainSubMesh
    block = coil_dom
  []
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [CoilH1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
    submesh = coil
  []
  [CoilHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = coil
  []
  [TransitionH1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
    submesh = cut
  []
  [TransitionHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = cut
  []
[]

[Variables]
  [coil_induced_potential]
    type = MFEMVariable
    fespace = CoilH1FESpace
  []
[]

[AuxVariables]
  [coil_external_potential]
    type = MFEMVariable
    fespace = CoilH1FESpace
  []
  [transition_external_potential]
    type = MFEMVariable
    fespace = TransitionH1FESpace
  []
  [transition_external_e_field]
    type = MFEMVariable
    fespace = TransitionHCurlFESpace
  []
  [induced_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [induced_e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [external_e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [e_field]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels]
  [update_induced_e_field]
    type = MFEMGradAux
    variable = induced_e_field
    source = induced_potential
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [update_external_e_field]
    type = MFEMGradAux
    variable = transition_external_e_field
    source = transition_external_potential
    scale_factor = -1.0
    execute_on = TIMESTEP_END
  []
  [update_total_e_field]
    type = MFEMSumAux
    variable = e_field
    source_variables = 'induced_e_field external_e_field'
    execute_on = TIMESTEP_END
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = coil_induced_potential
    coefficient = conductivity
  []
  [source]
    type = MFEMMixedGradGradKernel
    trial_variable = coil_external_potential
    variable = coil_induced_potential
    coefficient = conductivity
    block = 'transition_dom'
  []
[]

[Solver]
  type = MFEMSuperLU
[]

[Executioner]
  type = MFEMSteady
[]

[Transfers]
  [submesh_transfer_from_coil]
    type = MFEMSubMeshTransfer
    from_variable = coil_induced_potential
    to_variable = induced_potential
    execute_on = TIMESTEP_END
  []
  [submesh_transfer_to_transition]
    type = MFEMSubMeshTransfer
    from_variable = coil_external_potential
    to_variable = transition_external_potential
    execute_on = TIMESTEP_END
  []
  [submesh_transfer_from_transition]
    type = MFEMSubMeshTransfer
    from_variable = transition_external_e_field
    to_variable = external_e_field
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  [GlobalParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/WholePotentialCoil
    vtk_format = ASCII
  []
  [TransitionParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/CutPotentialCoil
    vtk_format = ASCII
    submesh = cut
  []
  [CoilParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Coil
    vtk_format = ASCII
    submesh = coil
  []
[]

(test/tests/mfem/auxkernels/projection.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/hinomaru.e
  dim = 2
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [Az]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [J]
    type = MFEMVariable
    fespace = L2FESpace
  []
  [GAz]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [GAz(copy)]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = Az
  []
  [source]
    type = MFEMDomainLFKernel
    variable = Az
    coefficient = J_source
  []
[]

[AuxKernels]
  [J]
    type = MFEMScalarProjectionAux
    variable = J
    coefficient = J_source
  []
  [GAz]
    type = MFEMGradAux
    variable = GAz
    source = Az
  []
  [GAz(copy)]
    type = MFEMVectorProjectionAux
    variable = GAz(copy)
    vector_coefficient = GAz
  []
[]

[BCs]
  [essential]
    type = MFEMScalarDirichletBC
    variable = Az
    boundary = outer
    coefficient = 1
  []
[]

[FunctorMaterials]
  [J_wire]
    type = MFEMGenericFunctorMaterial
    prop_names = J_source
    prop_values = 8.0
    block = wire
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-16
[]

[Executioner]
  type = MFEMSteady
[]

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

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

# MFEM diffusion problem sampled with MFEMPointValueSampler.

[Mesh]
  type = MFEMMesh
  file = ../../mesh/mug.e
[]

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [concentration]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [concentration_gradient]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = concentration_gradient
    source = concentration
    execute_on = TIMESTEP_END
  []
[]

[ICs]
  [diffused_ic]
    type = MFEMScalarIC
    coefficient = one
    variable = concentration
  []
[]

[Functions]
  [one]
    type = ParsedFunction
    expression = 1.0
  []
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom'
    coefficient = 1.0
  []
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'top'
  []
[]

[FunctorMaterials]
  [Substance]
    type = MFEMGenericFunctorMaterial
    prop_names = diffusivity
    prop_values = 1.0
    block = 'the_domain'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
    coefficient = diffusivity
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[VectorPostprocessors]
  [point_sample]
    type = MFEMPointValueSampler
    variable = 'concentration'
    points = '2.125 0 -1.375  2.125 0 1.125'
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/mfem/auxkernels/2Dmagnetostatic.i)

[Mesh]
    type = MFEMMesh
    file = ../mesh/hinomaru.e
[]

[Problem]
    type = MFEMProblem
[]

[FESpaces]
 [H1FESpace]
   type = MFEMScalarFESpace
   fec_type = H1
   fec_order = FIRST
 []
 [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  #For compatible pairing H1 order p -> ND order p -> RT order p-1
  [RTFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
  []
   [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
   [Az]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[FunctorMaterials]
  [J_wire]
    type = MFEMGenericFunctorMaterial
    prop_names = J_source
    prop_values = 8.0
    block = wire
  []
[]

[AuxVariables]
  [J]
    type = MFEMVariable
    fespace = L2FESpace
  []
  [gradAz]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
  [B]
    type = MFEMVariable
    fespace = RTFESpace
  []
[]

[Kernels]
  [diffusion]
    type = MFEMDiffusionKernel
    variable = Az
  []
  [source]
    type = MFEMDomainLFKernel
    variable = Az
    coefficient = J_source
  []
[]

[AuxKernels]
  [J]
    type = MFEMScalarProjectionAux
    variable = J
    coefficient = J_source
  []
  [gradAz]
    type = MFEMGradAux
    variable = gradAz
    source = Az
  []
  [B_from_gradAz]
    type = MFEMNDtoRTAux
    variable = B
    source = gradAz
    scale_factor = 1.0
  []
[]

[BCs]
  [essential]
    type = MFEMScalarDirichletBC
    variable = Az
    boundary = outer
    coefficient = 1
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-8
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMLineValueSampler
    variable = 'B'
    start_point = '0 2 0'
    end_point = '0 -2 0'
    num_points = 10
  []
[]

[Executioner]
  type = MFEMSteady
[]

[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = 2DMagnetostatic
  []
[]

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  dim = 3
  uniform_refine = 2
  displacement = "displacement"
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMVectorFESpace
    fec_type = H1
    fec_order = FIRST
    range_dim = 3
    ordering = "vdim"
  []
[]

[Variables]
  [displacement]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorDirichletBC
    variable = displacement
    boundary = '1'
  []
[]

[FunctorMaterials]
  [Rigidium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '50.0 50.0'
    block = 1
  []
  [Bendium]
    type = MFEMGenericFunctorMaterial
    prop_names = 'lambda mu'
    prop_values = '1.0 1.0'
    block = 2
  []
  [RigidiumWeightDensity]
    type = MFEMGenericFunctorVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '{0.0 0.0 -1e-2}'
    block = 1
  []
  [BendiumWeightDensity]
    type = MFEMGenericFunctorVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '{0.0 0.0 -5e-3}'
    block = 2
  []
[]

[Kernels]
  [diff]
    type = MFEMLinearElasticityKernel
    variable = displacement
    lambda = lambda
    mu = mu
  []
  [gravity]
    type = MFEMVectorDomainLFKernel
    variable = displacement
    vector_coefficient = gravitational_force_density
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    fespace = H1FESpace
    l_max_its = 20
    l_tol = 1e-5
    print_level = 2
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_max_its = 100
  l_tol = 1e-4
  l_abs_tol = 0.0
  print_level = 2
[]

[Executioner]
  type = MFEMSteady
  device = "cpu"
[]

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

(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
  []
[]

(test/tests/mfem/vectorpostprocessors/line_value_sampler/line_value_sampler_diffusion.i)

# MFEM diffusion problem sampled with MFEMLineValueSampler.

[Mesh]
  type = MFEMMesh
  file = ../../mesh/mug.e
[]

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [concentration]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [concentration_gradient]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = concentration_gradient
    source = concentration
    execute_on = TIMESTEP_END
  []
[]

[ICs]
  [diffused_ic]
    type = MFEMScalarIC
    coefficient = one
    variable = concentration
  []
[]

[Functions]
  [one]
    type = ParsedFunction
    expression = 1.0
  []
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom'
    coefficient = 1.0
  []
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'top'
  []
[]

[FunctorMaterials]
  [Substance]
    type = MFEMGenericFunctorMaterial
    prop_names = diffusivity
    prop_values = 1.0
    block = 'the_domain'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
    coefficient = diffusivity
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMLineValueSampler
    variable = 'concentration'
    start_point = '2.125 0 -2.375'
    end_point = '2.125 0 2.625'
    num_points = 11
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/mfem/complex/complex_waveguide.i)

freq = 900e6
angfreq = ${fparse 2*pi*freq}
epsilon0 = 8.8541878176e-12
mu0 = ${fparse 4e-7*pi}
magnetic_reluctivity = ${fparse 1/mu0}
elec_cond_mouse = 0.97
elec_cond_air = 1e-323

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

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

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

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

[Functions]
  [mass_coef_mouse]
    type = ParsedFunction
    expression = -43*${epsilon0}*${angfreq}^2
  []
  [loss_coef_mouse]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_mouse}
  []
  [mass_coef_air]
    type = ParsedFunction
    expression = -${epsilon0}*${angfreq}^2
  []
  [loss_coef_air]
    type = ParsedFunction
    expression = ${angfreq}*${elec_cond_air}
  []
[]

[FunctorMaterials]
  [Mouse]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_mouse loss_coef_mouse ${magnetic_reluctivity}'
    block = 1
  []
  [Air]
    type = MFEMGenericFunctorMaterial
    prop_names = 'massCoef lossCoef MagReluctivity'
    prop_values = 'mass_coef_air loss_coef_air ${magnetic_reluctivity}'
    block = 2
  []
[]

[BCs]
  [tangential_E]
    type = MFEMComplexVectorTangentialDirichletBC
    variable = E
    boundary = '2 3 4'
  []
  [WaveguidePortIn]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '5'
    input_port = true
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
  [WaveguidePortOut]
    type = MFEMRWTE10IntegratedBC
    variable = E
    boundary = '6'
    input_port = false
    port_length_vector = "24.76e-2 0.0 0.0"
    port_width_vector = "0.0 12.38e-2 0.0"
    frequency = ${freq}
    epsilon = ${epsilon0}
    mu = ${mu0}
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMCurlCurlKernel
      coefficient = MagReluctivity
    []
  []
  [mass_loss]
    type = MFEMComplexKernel
    variable = E
    [RealComponent]
      type = MFEMVectorFEMassKernel
      coefficient = massCoef
    []
    [ImagComponent]
      type = MFEMVectorFEMassKernel
      coefficient = lossCoef
    []
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Postprocessors]
  [ObstructionAbsorption]
    type = MFEMComplexVectorPeriodAveragedPostprocessor
    coefficient = ${elec_cond_mouse}
    dual_variable = E
    primal_variable = E
    block = 1
  []
[]


[Outputs]
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/ComplexWaveguide
  []
[]

(test/tests/mfem/functions/parsed_function_source.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/hinomaru.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [variable]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[ICs]
  [ic]
    type = MFEMScalarIC
    variable = variable
    coefficient = material
  []
[]

[BCs]
  [bc]
    type = MFEMScalarDirichletBC
    variable = variable
    boundary = skin
  []
[]

[FunctorMaterials]
  [material]
    type = MFEMGenericFunctorMaterial
    prop_names = material
    prop_values = -100
  []
[]

[Functions]
  [r]
    type = ParsedFunction
    expression = hypot(x,y)
  []
  [p]
    type = ParsedFunction
    expression = atan2(y,x)
  []
  [source]
    type = MFEMParsedFunction
    expression = v*sin(w*p)
    symbol_names = 'p w v'
    symbol_values = 'p 4 variable'
  []
  [solution]
    type = MFEMParsedFunction
    expression = if(r<=1,-c*sin(w*p)*(r^w-r^2)/(w^2-4),0)
    symbol_names = 'r p w c'
    symbol_values = 'r p 4 material'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = variable
  []
  [source]
    type = MFEMDomainLFKernel
    variable = variable
    coefficient = source
    block = wire
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-16
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [error]
    type = MFEML2Error
    variable = variable
    function = solution
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/ParsedFunctionSource
[]

Overview
Example Input File Syntax
Input Parameters
Input Files