MFEMScalarFESpace

Overview

This is a convenience class for building finite element spaces to represent scalar variables. The family of shape functions is selected from the fec_type parameter, and the order is controlled using the fec_order parameter.

If you need a finite element space that can't be constructed using the options available in this class, you can use MFEMGenericFESpace instead.

Example Input File Syntax

[FESpaces<<<{"href": "../../../syntax/FESpaces/index.html"}>>>]
  [H1FESpace]
    type = MFEMScalarFESpace<<<{"description": "Convenience class to construct scalar finite element spaces.", "href": "MFEMScalarFESpace.html"}>>>
    fec_type<<<{"description": "Specifies the family of FE shape functions."}>>> = H1
    fec_order<<<{"description": "Order of the FE shape function to use."}>>> = FIRST
  []
[]

[Variables<<<{"href": "../../../syntax/Variables/index.html"}>>>]
  [temperature]
    type = MFEMVariable<<<{"description": "Class for adding MFEM variables to the problem (`mfem::ParGridFunction`s).", "href": "../variables/MFEMVariable.html"}>>>
    fespace<<<{"description": "The finite element space this variable is defined on."}>>> = H1FESpace
  []
[]

Input Parameters

basisGaussLobattoSpecifies the basis used for scalar elements. H1 spaces require a closed basis (GaussLobatto Positive ClosedUniform Serendipity ClosedGL)
Default:GaussLobatto
C++ Type:MooseEnum
Options:GaussLegendre, GaussLobatto, Positive, OpenUniform, ClosedUniform, OpenHalfUniform, Serendipity, ClosedGL, IntegratedGLL
Controllable:No
Description:Specifies the basis used for scalar elements. H1 spaces require a closed basis (GaussLobatto Positive ClosedUniform Serendipity ClosedGL)
fec_orderFIRSTOrder of the FE shape function to use.
Default:FIRST
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH, TENTH, ELEVENTH, TWELFTH, THIRTEENTH, FOURTEENTH, FIFTEENTH, SIXTEENTH, SEVENTEENTH, EIGHTTEENTH, NINETEENTH, TWENTIETH, TWENTYFIRST, TWENTYSECOND, TWENTYTHIRD, TWENTYFOURTH, TWENTYFIFTH, TWENTYSIXTH, TWENTYSEVENTH, TWENTYEIGHTH, TWENTYNINTH, THIRTIETH, THIRTYFIRST, THIRTYSECOND, THIRTYTHIRD, THIRTYFOURTH, THIRTYFIFTH, THIRTYSIXTH, THIRTYSEVENTH, THIRTYEIGHTH, THIRTYNINTH, FORTIETH, FORTYFIRST, FORTYSECOND, FORTYTHIRD
Controllable:No
Description:Order of the FE shape function to use.
fec_typeH1Specifies the family of FE shape functions.
Default:H1
C++ Type:MooseEnum
Options:H1, L2, L2Int
Controllable:No
Description:Specifies the family of FE shape functions.
orderingVDIMOrdering style to use for vector DoFs.
Default:VDIM
C++ Type:MooseEnum
Options:NODES, VDIM
Controllable:No
Description:Ordering style to use for vector DoFs.
submeshSubmesh to define the FESpace on. Leave blank to use base mesh.
C++ Type:std::string
Controllable:No
Description:Submesh to define the FESpace on. Leave blank to use base mesh.
vdim1The number of degrees of freedom per basis function.
Default:1
C++ Type:int
Controllable:No
Description:The number of degrees of freedom per basis function.

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/kernels/diffusion.i)
(test/tests/mfem/complex/complex.i)
(test/tests/mfem/ics/transient_scalar_ic.i)
(test/tests/mfem/kernels/graddiv.i)
(test/tests/mfem/transfers/displaced/mfem_parent.i)
(test/tests/mfem/transfers/mfem_sub_mfem_sub/sub_send.i)
(test/tests/mfem/submeshes/cut_closed_coil.i)
(test/tests/mfem/submeshes/hphi_magnetodynamic.i)
(test/tests/mfem/timesteppers/mfem_multiple_timesequences.i)
(test/tests/mfem/submeshes/nl_hphi_magnetodynamic.i)
(test/tests/mfem/kernels/nldiffusion.i)
(test/tests/mfem/kernels/diffusion_eigenproblem.i)
(test/tests/mfem/transfers/h1_libmesh_parent_mfem_sub/mfem_sub_scalar.i)
(test/tests/mfem/auxkernels/projection.i)
(test/tests/mfem/kernels/diffusion_amr.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/parent.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/sub_complex.i)
(test/tests/mfem/vectorpostprocessors/point_value_sampler/point_value_sampler_diffusion.i)
(test/tests/mfem/timesteppers/mfem_multiple_timesteppers.i)
(test/tests/mfem/transfers/l2_libmesh_parent_mfem_sub/mfem_sub_scalar.i)
(test/tests/mfem/multiapps/sub_cycling_sub.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/mfem_parent_embedded_submesh.i)
(test/tests/mfem/functions/parsed_function_source.i)
(test/tests/mfem/submeshes/domain_submesh_transfer.i)
(test/tests/mfem/ics/scalar_ic.i)
(test/tests/mfem/multiapps/dt_from_parent.i)
(test/tests/mfem/vectorpostprocessors/line_value_sampler/line_value_sampler_diffusion.i)
(test/tests/mfem/kernels/curlcurl.i)
(test/tests/mfem/multiapps/dt_from_parent_sub.i)
(test/tests/mfem/multiapps/full_solve_sub.i)
(test/tests/mfem/submeshes/hphi_magnetostatic.i)
(test/tests/mfem/kernels/heattransfer.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/mfem_sub_embedded_submesh.i)
(test/tests/mfem/transfers/mfem_sub_mfem_sub/sub_recv.i)
(test/tests/mfem/transfers/mfem_sub_mfem_sub/parent.i)
(test/tests/mfem/kernels/nl_heatconduction.i)
(test/tests/mfem/submeshes/domain_submesh.i)
(test/tests/mfem/kernels/nl_heattransfer.i)
(test/tests/mfem/transfers/sibling_transfers/mfem_sub_between_diffusion.i)
(test/tests/mfem/kernels/irrotational.i)
(test/tests/mfem/submeshes/magnetostatic.i)
(test/tests/mfem/auxkernels/2Dmagnetostatic.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/parent_complex.i)
(test/tests/mfem/multiapps/full_solve_parent.i)
(test/tests/mfem/transfers/mfem_parent_mfem_sub/sub.i)
(test/tests/mfem/submeshes/open_coil_source.i)
(test/tests/mfem/multiapps/sub_cycling_parent.i)
(test/tests/mfem/kernels/mixed_heattransfer.i)
(test/tests/mfem/transfers/h1_mfem_parent_libmesh_sub/mfem_parent_scalar.i)
(test/tests/mfem/kernels/darcy.i)
(test/tests/mfem/transfers/displaced/mfem_child.i)
(test/tests/mfem/transfers/l2_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

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

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

[Problem]
  type = MFEMProblem
[]

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

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[BCs]
  active = 'bottom top_convective'
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    coefficient = 1.0
  []
  [top_convective]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = .5
    heat_transfer_coefficient = 5
  []
  [top_dirichlet]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 2.0
  start_time = 0.0
  end_time = 6.0
[]

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

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

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

[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
  []
[]

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

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Outputs]
  active = ParaViewDataCollection
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Diffusion
    vtk_format = ASCII
  []
  [VisItDataCollection]
    type = MFEMVisItDataCollection
    file_base = OutputData/VisItDataCollection
  []
  [ConduitDataCollection]
    type = MFEMConduitDataCollection
    file_base = OutputData/ConduitDataCollection/Run
    protocol = conduit_bin
  []
[]

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

mu = 1.0
epsilon = 1.0
sigma = 20.0
omega = 10.0
kappa_r = 12.7201964951406889525742371916
kappa_i = -7.86151377757423297509831172647

[Mesh]
  type = MFEMMesh
  file = ../mesh/inline-quad.mesh
  dim = 2
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

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

[Variables]
  [u]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [u0_r]
    type = ParsedFunction
    expression = exp(y*${kappa_i})*cos(y*${kappa_r})
  []
  [u0_i]
    type = ParsedFunction
    expression = -exp(y*${kappa_i})*sin(y*${kappa_r})
  []
  [stiffnessCoef]
    type = ParsedFunction
    expression = 1.0/${mu}
  []
  [massCoef]
    type = ParsedFunction
    expression = -${omega}*${omega}*${epsilon}
  []
  [lossCoef]
    type = ParsedFunction
    expression = ${omega}*${sigma}
  []
[]

[BCs]
  [dbc]
    type = MFEMComplexScalarDirichletBC
    variable = u
    coefficient_real = u0_r
    coefficient_imag = u0_i
  []
[]

[Kernels]
  [diffusion_complex]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMDiffusionKernel
      coefficient = stiffnessCoef
    []
    [ImagComponent]
      type = MFEMDiffusionKernel
      coefficient = 0.0
    []
  []
  [mass_complex]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMMassKernel
      coefficient = massCoef
    []
    [ImagComponent]
      type = MFEMMassKernel
      coefficient = lossCoef
    []
  []
[]

[Solver]
  type = MFEMSuperLU
[]

[Executioner]
  type = MFEMSteady
  assembly_level = legacy
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Complex2DQuad
    vtk_format = ASCII
  []
[]

(test/tests/mfem/ics/transient_scalar_ic.i)

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

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [h1_scalar]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [l2_scalar]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [height]
    type = ParsedFunction
    expression = 'z'
  []
[]

[ICs]
  [l2_scalar_ic]
    type = MFEMScalarIC
    variable = l2_scalar
    coefficient = 2.0
  []
  [h1_scalar_ic]
    type = MFEMScalarIC
    variable = h1_scalar
    coefficient = height
  []
[]

[Kernels]
  [h1_laplacian]
    type = MFEMDiffusionKernel
    variable = h1_scalar
    coefficient = 1.0
  []
  [dh1_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = h1_scalar
    coefficient = 1.0
  []
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = h1_scalar
    boundary = '1'
    coefficient = height
  []
  [top_dirichlet]
    type = MFEMScalarDirichletBC
    variable = h1_scalar
    boundary = '2'
    coefficient = height
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  dt = 2.0
  start_time = 0.0
  end_time = 2.0
[]

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

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

# Grad-div problem using method of manufactured solutions,
# based on MFEM Example 4.

[Mesh]
  type = MFEMMesh
  file = ../mesh/beam-tet.mesh
  dim = 3
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
    ordering = "vdim"
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
    basis = GaussLegendre
  []
[]

[Variables]
  [F]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxVariables]
  [divF]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxKernels]
  [div]
    type = MFEMDivAux
    variable = divF
    source = F
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [f]
    type = ParsedVectorFunction
    expression_x = '(1. + 2*kappa * kappa) * cos(kappa * x) * sin(kappa * y)'
    expression_y = '(1. + 2*kappa * kappa) * cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
  [F_exact]
    type = ParsedVectorFunction
    expression_x = 'cos(kappa * x) * sin(kappa * y)'
    expression_y = 'cos(kappa * y) * sin(kappa * x)'
    expression_z = '0'

    symbol_names = kappa
    symbol_values = 3.1415926535
  []
[]

[BCs]
  [dirichlet]
    type = MFEMVectorNormalDirichletBC
    variable = F
    boundary = '1 2 3'
    vector_coefficient = F_exact
  []
[]

[Kernels]
  [divdiv]
    type = MFEMDivDivKernel
    variable = F
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = F
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = F
    vector_coefficient = f
  []
[]

[Preconditioner]
  [ADS]
    type = MFEMHypreADS
    fespace = HDivFESpace
  []
[]

[Solver]
  type = MFEMCGSolver
  preconditioner = ADS
  l_tol = 1e-16
  l_max_its = 1000
  print_level = 2
[]

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

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

(test/tests/mfem/transfers/displaced/mfem_parent.i)

[Problem]
  type = MFEMProblem
  solve = false
[]

[Mesh]
  type = MFEMMesh
  file = base_strip.e
[]

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

[AuxVariables]
  [indicator_nodal]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Executioner]
  type = MFEMTransient
  dt = 0.05
  num_steps = 10
[]

[MultiApps]
  [solid_domain]
    type = TransientMultiApp
    input_files = libmesh_child.i
    execute_on = 'initial timestep_begin'
  []
[]

[Transfers]
  [pull_indicator_nodal]
    type = MultiApplibMeshToMFEMShapeEvaluationTransfer
    from_multi_app = solid_domain
    source_variables = solid_indicator
    variables = indicator_nodal
    displaced_source_mesh = true
    execute_on = 'initial timestep_begin'
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Displaced
    vtk_format = ASCII
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(test/tests/mfem/transfers/mfem_sub_mfem_sub/sub_send.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [back]
    type = MFEMScalarDirichletBC
    variable = send
    boundary = 1
    coefficient = 1.0
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = send
    boundary = 2
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = send
  []
[]

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

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


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

[Executioner]
  type = MFEMSteady
[]

(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/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/timesteppers/mfem_multiple_timesequences.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
    coefficient = 0.1
  []
  [time]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  end_time = 0.8

  # Use as many different time sequence steppers as we could to test the compositionDT
  [TimeSteppers]
    [ConstDT1]
      type = ConstantDT
      dt = 0.2
    []

    [ConstDT2]
      type = ConstantDT
      dt = 0.1
    []

    [LogConstDT]
      type = LogConstantDT
      log_dt = 0.2
      first_dt = 0.1
    []

    [Timesequence1]
      type = TimeSequenceStepper
      time_sequence  = '0  0.25 0.3 0.5 0.8'
    []

    [Timesequence2]
      type = CSVTimeSequenceStepper
      file_name = timesequence.csv
      column_name = time
    []

    [Timesequence3]
      type = ExodusTimeSequenceStepper
      mesh = timesequence.e
    []
  []
[]

[Postprocessors]
  [timestep]
    type = TimePostprocessor
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  csv = true
  file_base='mfem_multiple_timesequences'
[]

(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 = MFEMMesh
    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}
  []
[]

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

[Solver]
  type = MFEMHyprePCG
  preconditioner = ams
  l_tol = 1e-12
  l_max_its = 100
  print_level = 0
[]

[Executioner]
  type = MFEMTransient
  dt = 0.5
  start_time = 0.0
  end_time = 2.0
  nl_max_its = 150
  nl_abs_tol = 1e-5
  print_level = 1
[]

[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
  []
[]

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

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

[Problem]
  type = MFEMProblem
[]

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

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


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

[Functions]
  [initial]
    type = ParsedFunction
    expression = 2*y+1
  []
[]

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'top'
    coefficient = 3.0
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 'bottom'
    coefficient = 1.0
  []

[]

[Kernels]
  active = 'nl'
  [nl]
    type = MFEMNLDiffusionKernel
    variable = concentration
    k_coefficient = concentration
    dk_du_coefficient = 1.0
  []
  [force]
    type = MFEMDomainLFKernel
    variable = concentration
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

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

[Executioner]
  type = MFEMSteady
  device = cpu
  nl_max_its = 100
  nl_abs_tol = 1.0e-10
  nl_rel_tol = 1.0e-9
  print_level = 1
[]

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

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  dim = 2
  serial_refine = 1
[]

[Problem]
  type = MFEMEigenproblem
  num_modes = 5
[]

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

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

[BCs]
  [all]
    type = MFEMScalarDirichletBC
    variable = u
    coefficient = 1.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
    print_level = 0
  []
[]

[Solver]
  type = MFEMHypreLOBPCG
  preconditioner = boomeramg
  print_level = 0
  l_tol = 1e-10
  l_max_its = 300
  random_seed = 75
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

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

(test/tests/mfem/transfers/h1_libmesh_parent_mfem_sub/mfem_sub_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [sides]
    type = MFEMScalarDirichletBC
    variable = mfem_scalar_var
    coefficient = 1.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = mfem_scalar_var
  []
  [source]
    type = MFEMDomainLFKernel
    variable = mfem_scalar_var
    coefficient = 2.0
  []
[]

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

(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/kernels/diffusion_amr.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/square.msh
  nonconforming = true
[]

[Adaptivity]
  [Indicators]
    [l2zz]
      type = MFEML2ZienkiewiczZhuIndicator
      variable = concentration
      kernel = diff
    []
  []
  [Markers]
    [ref]
      type = MFEMRefinementMarker
      threshold = 0.7
      indicator = l2zz
      max_h_level = 1
    []
  []
[]

[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
  []
[]

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 4
    coefficient = 1
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 2
  []
[]

[Functions]
  [D]
    type = ParsedFunction
    expression = 1+1/(1+exp(20*y-10))
  []
  [solution]
    type = ParsedFunction
    expression = (20*y+log(exp(20*y)+2*exp(10))-log(1+2*exp(10)))/(30+log(2+exp(10))-log(1+2*exp(10)))
  []
[]

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

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

(test/tests/mfem/transfers/mfem_parent_mfem_sub/parent.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

[AuxVariables]
  [u]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Executioner]
  type = MFEMSteady
[]

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

[Transfers]
  active = 'copy_from_sub'
  [copy_from_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = u
    variables = u
    from_multi_app = subapp
  []
  [general_transfer_from_sub]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = u
    variables = u
    from_multi_app = subapp
  []
[]

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

(test/tests/mfem/transfers/mfem_parent_mfem_sub/sub_complex.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  numeric_type = complex
[]

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

[Variables]
  [u]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [bottom]
    type = MFEMComplexScalarDirichletBC
    variable = u
    boundary = 2
    coefficient_real = 1
    coefficient_imag = 1
  []
  [top]
    type = MFEMComplexScalarDirichletBC
    variable = u
    boundary = 4
  []
[]

[Kernels]
  [diff]
    type = MFEMComplexKernel
    variable = u
    [RealComponent]
      type = MFEMDiffusionKernel
    []
    [ImagComponent]
      type = MFEMDiffusionKernel
    []
  []
[]

[Solver]
  type = MFEMSuperLU
[]

[Executioner]
  type = MFEMSteady
[]

[MultiApps]
  active = ''
  [subapp]
    type = FullSolveMultiApp
    input_files = parent_complex.i
    execute_on = FINAL
  []
[]

[Transfers]
  active = ''
  [to_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = u
    variables = u
    to_multi_app = subapp
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/DiffusionSubComplex
    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/timesteppers/mfem_multiple_timesteppers.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
    coefficient = 0.1
  []
  [time]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[Functions]
  [dts]
    type = PiecewiseLinear
    x = '0   0.85 2'
    y = '0.2 0.15  0.2'
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  end_time = 0.8
  # Use as many different time steppers as we could to test the compositionDT,
  # SolutionTimeAdaptiveDT give slightly different dt per run, set rel_err = 1e-2
  # to ensure the test won't fail due to the small difference in the high-digit.
  [TimeSteppers]
    [ConstDT1]
      type = ConstantDT
      dt = 0.2
    []

    [FunctionDT]
      type = FunctionDT
      function = dts
    []

    [LogConstDT]
      type = LogConstantDT
      log_dt = 0.2
      first_dt = 0.1
    []

    [IterationAdapDT]
      type = IterationAdaptiveDT
      dt = 0.5
    []

    [Timesequence]
      type = TimeSequenceStepper
      time_sequence  = '0  0.25 0.3 0.5 0.8'
    []
  []
[]

[Postprocessors]
  [timestep]
    type = TimePostprocessor
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  csv = true
  file_base='mfem_multiple_timesteppers'
[]

(test/tests/mfem/transfers/l2_libmesh_parent_mfem_sub/mfem_sub_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

[FESpaces]
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

[Variables]
  [temperature]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [parsed_function]
    type = ParsedFunction
    expression = 'x*x + y*y'
  []
[]

[ICs]
  [libmesh_scalar_var_ic]
    type = MFEMScalarIC
    variable = 'temperature'
    coefficient = parsed_function
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

(test/tests/mfem/multiapps/sub_cycling_sub.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  num_steps = 2
  dt = 0.01
[]

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

(test/tests/mfem/transfers/mfem_parent_mfem_sub/mfem_parent_embedded_submesh.i)

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

[Problem]
  type = MFEMProblem
  solve = false
[]

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

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

[Executioner]
  type = MFEMSteady
[]

[MultiApps]
  [mfem_app]
    type = FullSolveMultiApp
    input_files = mfem_sub_embedded_submesh.i
    execute_on = 'INITIAL'
  []
[]

[Transfers]
  [h1_transfer_from_subapp]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = submesh_potential
    variables = potential
    from_multi_app = mfem_app
  []
[]

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

(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
[]

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

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

[Problem]
  type = MFEMProblem
[]

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

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

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

[AuxVariables]
  [potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = front
    coefficient = 1.0
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = back
  []
[]

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

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

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Transfers]
  [submesh_transfer]
    type = MFEMSubMeshTransfer
    from_variable = submesh_potential
    to_variable = potential
  []
[]

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

(test/tests/mfem/ics/scalar_ic.i)

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

[Problem]
  type = MFEMProblem
  solve = false
[]

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

[Variables]
  [h1_scalar]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [l2_scalar]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [height]
    type = ParsedFunction
    expression = 'z'
  []
[]

[ICs]
  [l2_scalar_ic]
    type = MFEMScalarIC
    variable = l2_scalar
    coefficient = 2.0
  []
  [h1_scalar_ic]
    type = MFEMScalarIC
    variable = h1_scalar
    coefficient = height
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/mfem/multiapps/dt_from_parent.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  num_steps = 10
  dt = 0.2
[]

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

[MultiApps]
  [sub_app]
    type = TransientMultiApp
    app_type = MooseTestApp
    input_files = 'dt_from_parent_sub.i'
  []
[]

(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/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/multiapps/dt_from_parent_sub.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  num_steps = 10
  dt = 1 # This will be constrained by the parent solve
[]

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

(test/tests/mfem/multiapps/full_solve_sub.i)

[Problem]
  type = MFEMProblem
  verbose_multiapps = true
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
      print_level = 0
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 100
  print_level = 0
[]

[Executioner]
  type = MFEMTransient
  num_steps = 2
  dt = 0.01
[]

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

(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/heattransfer.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[BCs]
  active = 'bottom top_convective'
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    coefficient = 1.0
  []
  [top_convective]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = .5
    heat_transfer_coefficient = 5
  []
  [top_dirichlet]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 2.0
  start_time = 0.0
  end_time = 6.0
[]

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

(test/tests/mfem/transfers/mfem_parent_mfem_sub/mfem_sub_embedded_submesh.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

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

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = front
    coefficient = 1.0
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = back
  []
[]

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

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

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
[]

(test/tests/mfem/transfers/mfem_sub_mfem_sub/sub_recv.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

[AuxVariables]
  [recv]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Executioner]
  type = MFEMSteady
[]

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

(test/tests/mfem/transfers/mfem_sub_mfem_sub/parent.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

[MultiApps]
  [recv_app]
    type = FullSolveMultiApp
    input_files = sub_recv.i
    execute_on = FINAL
  []
  [send_app]
    type = FullSolveMultiApp
    input_files = sub_send.i
    execute_on = INITIAL
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Transfers]
  active = 'copy_between_sub'
  [copy_between_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = send
    variables = recv
    from_multi_app = send_app
    to_multi_app = recv_app
  []
  [general_transfer_between_sub]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = send
    variables = recv
    from_multi_app = send_app
    to_multi_app = recv_app
  []
[]

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

# Implementation of MFEM Example 16, for a time dependent nonlinear heat equation problem of the
# form
# dT/dt = \nabla \cdot (\kappa + \alpha T) \nabla T

kappa = 0.5
alpha = 1e-2

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 1
[]

[Problem]
  type = MFEMProblem
[]

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

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

[AuxVariables]
  inactive = average_temperature
  [average_temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxKernels]
  inactive = average_field
  [average_field]
    type = MFEMScalarTimeAverageAux
    variable = average_temperature
    source = temperature
  []
[]

[Functions]
  [initial]
    type = ParsedFunction
    expression = 'if((x*x + y*y > 0.251), 1.0, 2.0)'
  []
  [diffusivity_temperature_dependence]
    type = MFEMParsedFunction
    expression = 'alpha * temperature'
    symbol_names = 'alpha temperature'
    symbol_values = '${alpha} temperature'
  []
[]

[ICs]
  [diffused_ic]
    type = MFEMScalarIC
    coefficient = initial
    variable = temperature
  []
[]

[Kernels]
  [nl_diffusion]
    type = MFEMNLDiffusionKernel
    variable = temperature
    k_coefficient = diffusivity_temperature_dependence
    dk_du_coefficient = ${alpha}
  []
  [linear_diffusion]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = ${kappa}
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
[]

[Solver]
  type = MFEMMUMPS
  print_level = 0
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 1e-2
  start_time = 0.0
  end_time = 0.5

  nl_max_its = 30
  nl_abs_tol = 1.0e-5
  nl_rel_tol = 1.0e-5
  print_level = 1
[]

[VectorPostprocessors]
  [centre_temperature]
    type = MFEMPointValueSampler
    variable = 'temperature'
    points = '0.0 0.0 0.0'
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = OutputData/NLHeatConduction
  csv = true
  time_step_interval = 10

  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/NLHeatConduction
    vtk_format = ASCII
  []
[]

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

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

[Problem]
  type = MFEMProblem
[]

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

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

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

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = front
    coefficient = 1.0
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = submesh_potential
    boundary = back
  []
[]

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

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

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

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

[Problem]
  type = MFEMProblem
[]

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

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

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

[ICs]
  [temperature_ic]
    type = MFEMScalarIC
    coefficient = 200.0
    variable = temperature
  []
[]

[Functions]
  [T_inf]
    type = MFEMParsedFunction
    expression = 'temperature + 1'
    symbol_names = 'temperature'
    symbol_values = 'temperature'
  []
  [htc]
    type = MFEMParsedFunction
    expression = 'temperature/100 + 1'
    symbol_names = 'temperature'
    symbol_values = 'temperature'
  []
  [dhtc_dT]
    type = MFEMParsedFunction
    expression = '1 / 100'
    symbol_names = 'temperature'
    symbol_values = 'temperature'
  []
[]

[Kernels]
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
  [diffusion]
    type = MFEMDiffusionKernel
    variable = temperature
  []
[]

[BCs]
  active = nonlinear
  [nonlinear]
    type = MFEMNLConvectiveHeatFluxBC
    variable = temperature
    boundary = 'right'
    T_infinity = T_inf
    heat_transfer_coefficient = htc
    d_heat_transfer_dT_coefficient = dhtc_dT
  []
  [linearized]
    type = MFEMNLConvectiveHeatFluxBC
    variable = temperature
    boundary = 'right'
    T_infinity = 201.0
    heat_transfer_coefficient = 3.0
    d_heat_transfer_dT_coefficient = 0.0
  []
[]

[VectorPostprocessors]
  [line_sample]
    type = MFEMLineValueSampler
    variable = 'temperature'
    start_point = '0.0 0.5 0.5'
    end_point = '1.0 0.5 0.5'
    num_points = 3
    execute_on = TIMESTEP_END
  []
[]

[Solver]
   type = MFEMMUMPS
   print_level = 0
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 1
  num_steps = 3
  nl_max_its = 150

  nl_abs_tol = 1e-12
  print_level = 1
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/NLHeatTransfer
    vtk_format = ASCII
  []
  [CSV]
    type = CSV
    file_base = OutputData/NLHeatTransfer
    time_step_interval = 3
  []
[]

(test/tests/mfem/transfers/sibling_transfers/mfem_sub_between_diffusion.i)

[Problem]
  type = MFEMProblem
  solve = false
[]

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

[AuxVariables]
  [sent_nodal]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [received_nodal]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [sent_elem]
    type = MFEMVariable
    fespace = L2FESpace
  []
  [received_elem]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [sent_nodal_var_func]
    type = ParsedFunction
    expression = '1 + 2*x*x + 3*y*y*y'
  []
  [sent_elem_var_func]
    type = ParsedFunction
    expression = '2 + 2*x*x + 3*y*y*y'
  []
  [received_nodal_var_func]
    type = ParsedFunction
    expression = '3 + 2*x*x + 3*y*y*y'
  []
  [received_elem_var_func]
    type = ParsedFunction
    expression = '4 + 2*x*x + 3*y*y*y'
  []
[]

[ICs]
  [sent_nodal_var_ic]
    type = MFEMScalarIC
    variable = 'sent_nodal'
    coefficient = sent_nodal_var_func
  []
  [sent_elem_var_ic]
    type = MFEMScalarIC
    variable = 'sent_elem'
    coefficient = sent_elem_var_func
  []
  [received_nodal_var_ic]
    type = MFEMScalarIC
    variable = 'received_nodal'
    coefficient = -1
  []
  [received_elem_var_ic]
    type = MFEMScalarIC
    variable = 'received_elem'
    coefficient = -1
  []

[]

[Executioner]
  type = MFEMTransient
  num_steps = 1
  device = cpu
[]

[VectorPostprocessors]
  [nodal_sample]
    type = MFEMLineValueSampler
    variable = 'received_nodal'
    start_point = '0.0 0.0 0.0'
    end_point = '1.0 1.0 0.0'
    num_points = 14
    execute_on = TIMESTEP_END
  []
  [elem_sample]
    type = MFEMLineValueSampler
    variable = 'received_elem'
    start_point = '0.0 0.0 0.0'
    end_point = '1.0 1.0 0.0'
    num_points = 14
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  csv = true
  inactive = ParaViewDataCollection
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    vtk_format = ASCII
  []
[]

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

# 2D irrotational vortex with Nedelec elements of the first kind.

centre_x = -0.75
centre_y = 0.1

[Mesh]
  type = MFEMMesh
  file = ../mesh/vortex.msh
  dim = 2
[]

[Problem]
  type = MFEMProblem
[]

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

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

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

[Functions]
  [speed]
    type = ParsedFunction
    expression = '1 / sqrt((x-x0)^2 + (y-y0)^2)'
    symbol_names = 'x0 y0'
  symbol_values = '${centre_x} ${centre_y}'
  []
  [theta]
    type = ParsedFunction
    expression = 'atan2(y-y0, x-x0)'
    symbol_names = 'x0 y0'
    symbol_values = '${centre_x} ${centre_y}'
  []
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-v * sin(th)'
    expression_y = 'v * cos(th)'
    symbol_names = 'v th'
    symbol_values = 'speed theta'
  []
[]

[BCs]
  [potential_velocity_boundary]
    type = MFEMScalarDirichletBC
    variable = velocity_potential
    boundary = '1'
    coefficient = theta
  []
[]

[Kernels]
  [laplacian]
    type = MFEMDiffusionKernel
    variable = velocity_potential
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = velocity
    source = velocity_potential
    execute_on = TIMESTEP_END
  []
[]

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [potential_error]
    type = MFEML2Error
    variable = velocity_potential
    function = theta
  []
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Irrotational
    vtk_format = ASCII
  []
  [L2CSV]
    type = CSV
    file_base = OutputData/Irrotational
  []
[]

(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/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/transfers/mfem_parent_mfem_sub/parent_complex.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
  solve = false
  numeric_type = complex
[]

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

[AuxVariables]
  [u]
    type = MFEMComplexVariable
    fespace = H1FESpace
  []
[]

[Executioner]
  type = MFEMSteady
[]

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

[Transfers]
  active = 'copy_from_sub'
  [copy_from_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = u
    variables = u
    from_multi_app = subapp
  []
  [general_transfer_from_sub]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = u
    variables = u
    from_multi_app = subapp
  []
[]

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

(test/tests/mfem/multiapps/full_solve_parent.i)

[Problem]
  type = MFEMProblem
  verbose_multiapps = true
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
      print_level = 0
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-8
  l_max_its = 100
  print_level = 0
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  num_steps = 2
  dt = 0.1
[]

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

[MultiApps]
  [full_solve]
    type = FullSolveMultiApp
    app_type = MooseTestApp
    execute_on = timestep_begin
    input_files = full_solve_sub.i
    keep_full_output_history = true
  []
[]

(test/tests/mfem/transfers/mfem_parent_mfem_sub/sub.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square.msh
[]

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = 2
    coefficient = 1.0
  []
  [top]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = 4
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
[]

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

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

[Executioner]
  type = MFEMSteady
[]

[MultiApps]
  active = ''
  [subapp]
    type = FullSolveMultiApp
    input_files = parent.i
    execute_on = FINAL
  []
[]

[Transfers]
  active = ''
  [to_sub]
    type = MultiAppMFEMCopyTransfer
    source_variables = u
    variables = u
    to_multi_app = subapp
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/DiffusionSub
    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/multiapps/sub_cycling_parent.i)

[Problem]
  type = MFEMProblem
  verbose_multiapps = true
[]

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

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

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

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = u
  []
  [td]
    type = MFEMTimeDerivativeMassKernel
    variable = u
  []
[]

[BCs]
  [left]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = left
    coefficient = 0
  []
  [right]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = right
    coefficient = 1
  []
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  num_steps = 2
  dt = 0.1
[]

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

[MultiApps]
  [sub]
    type = TransientMultiApp
    app_type = MooseTestApp
    execute_on = timestep_end
    positions = '0 0 0'
    input_files = sub_cycling_sub.i
    sub_cycling = true
  []
[]

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

# Mixed heat transfer problem.
# Based on Firedrake Irksome demo_mixed_heat example:
# https://www.firedrakeproject.org/Irksome/demos/demo_mixed_heat.py.html

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

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = FIRST
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = FIRST
  []
[]

[Variables]
  [time_integrated_heat_flux]
    type = MFEMVariable
    fespace = HDivFESpace
    time_derivative = heat_flux
  []
  [temperature]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Kernels]
  [dT_dt,T']
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
  []
  [divh,T']
    type = MFEMVectorFEDivergenceKernel
    trial_variable = heat_flux
    variable = temperature
  []
  [h,h']
    type = MFEMTimeDerivativeVectorFEMassKernel
    variable = time_integrated_heat_flux
  []
  [-T,div.h']
    type = MFEMVectorFEDivergenceKernel
    trial_variable = temperature
    variable = time_integrated_heat_flux
    coefficient = -1.0
    transpose = true
  []
[]

[BCs]
  [gamma_T_right]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = time_integrated_heat_flux
    coefficient = 0.0
    boundary = 2
  []
  [gamma_T_left]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = time_integrated_heat_flux
    coefficient = -1.0
    boundary = 4
  []
  [gamma_h_topbottom]
    type = MFEMVectorNormalDirichletBC
    variable = time_integrated_heat_flux
    vector_coefficient = '0.0 0.0'
    boundary = '1 3'
  []
[]

[Solver]
  type = MFEMSuperLU
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  assembly_level = legacy
  dt = 0.03
  start_time = 0.0
  end_time = 0.09
[]

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

(test/tests/mfem/transfers/h1_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
[]

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

[Variables]
  [mfem_scalar_var]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [libmesh_scalar_var]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [sides]
    type = MFEMScalarDirichletBC
    variable = mfem_scalar_var
    coefficient = 1.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = mfem_scalar_var
  []
  [source]
    type = MFEMDomainLFKernel
    variable = mfem_scalar_var
    coefficient = 2.0
  []
[]

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

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-12
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [libmesh_app]
    type = FullSolveMultiApp
    input_files = libmesh_sub_scalar.i
    execute_on = 'INITIAL'
  []
[]

[Transfers]
  [transfer_from_libmesh]
    type = MultiApplibMeshToMFEMShapeEvaluationTransfer
    source_variables = libmesh_scalar_var
    variables = libmesh_scalar_var
    from_multi_app = libmesh_app
  []
[]

[Postprocessors]
  [Difference]
    type = MFEML2Error
    variable = mfem_scalar_var
    function = libmesh_scalar_var
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = 'mfem_parent_libmesh_sub_scalar_quads'
  csv = true
[]

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

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 2
[]

[Problem]
  type = MFEMProblem
[]

[Functions]
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-exp(x) * sin(y)'
    expression_y = '-exp(x) * cos(y)'
  []
  [exact_pressure]
    type = ParsedFunction
    expression = 'exp(x) * sin(y)'
  []
  [exact_pressure_rhs]
    type = ParsedFunction
    expression = '-exp(x) * sin(y)'
  []
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = SECOND
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = SECOND
    basis = GaussLegendre
  []
[]

[Variables]
  [velocity]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [pressure]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[BCs]
  [flux_boundaries]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = velocity
    coefficient = exact_pressure_rhs
  []
[]

[Kernels]
  [VelocityMass]
    type = MFEMVectorFEMassKernel
    variable = velocity
  []
  [PressureGrad]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = pressure
    variable = velocity
    coefficient = -1
    transpose = true
  []
  [VelocityDiv]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = velocity
    variable = pressure
    coefficient = -1
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
  [pressure_error]
    type = MFEML2Error
    variable = pressure
    function = exact_pressure
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Darcy
    vtk_format = ASCII
  []
  [DarcyErrorCSV]
    type = CSV
    file_base = OutputData/Darcy
  []
[]

(test/tests/mfem/transfers/displaced/mfem_child.i)

[Problem]
  type = MFEMProblem
  solve = false
[]

[Mesh]
  type = MFEMMesh
  file = base_strip.e
[]

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

[AuxVariables]
  [indicator_field]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [background]
    type = ParsedFunction
    expression = '1+x*x'
  []
[]

[ICs]
  [background_ic]
    type = MFEMScalarIC
    coefficient = background
    variable = indicator_field
  []
[]

[Executioner]
  type = MFEMTransient
  dt = 0.05
  num_steps = 10
  device = cpu
[]

(test/tests/mfem/transfers/l2_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

[FESpaces]
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

[Variables]
  [mfem_scalar_var]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxVariables]
  [libmesh_scalar_var]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [parsed_function]
    type = ParsedFunction
    expression = 'x*x + y*y'
  []
[]

[ICs]
  [libmesh_scalar_var_ic]
    type = MFEMScalarIC
    variable = 'mfem_scalar_var'
    coefficient = parsed_function
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [libmesh_app]
    type = FullSolveMultiApp
    input_files = libmesh_sub_scalar.i
    execute_on = 'INITIAL'
  []
[]

[Transfers]
  [transfer_from_libmesh]
    type = MultiApplibMeshToMFEMShapeEvaluationTransfer
    source_variables = libmesh_scalar_var
    variables = libmesh_scalar_var
    from_multi_app = libmesh_app
  []
[]

[Postprocessors]
  [Difference]
    type = MFEML2Error
    variable = mfem_scalar_var
    function = libmesh_scalar_var
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = 'mfem_parent_libmesh_sub_scalar_quads'
  csv = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files