MFEMMesh

Summary

Class to read in and store an mfem::ParMesh from file.

Overview

MFEMMesh is responsible for building an mfem::ParMesh object from the provided mesh input file for use in an MFEMProblem. Exodus files are supported, along with other mesh formats listed here.

As MOOSE checks for the existence of a libMesh MOOSE mesh at various points during setup, MFEMMesh currently builds an dummy MOOSE mesh of a single quad alongside the MFEM mesh. This dummy mesh should not be used in an MFEMProblem; all MFEM objects should access the mfem::ParMesh via the getMFEMParMesh() accessor as needed.

Example Input File Syntax

[Problem]
  type = MFEMProblem
[]
[Mesh]
  type = MFEMMesh
  file = gold/mug.e
  dim = 3
[]

Input Parameters

fileThe name of the mesh file to read
C++ Type:MeshFileName
Unit:(no unit assumed)
Controllable:No
Description:The name of the mesh file to read

Required Parameters

add_sideset_idsThe listed sideset ids will be assumed valid for the mesh. This permits setting up boundary restrictions for sidesets initially containing no sides. Names for this sidesets may be provided using add_sideset_names. In this case this list and add_sideset_names must contain the same number of items.
C++ Type:std::vector<short>
Unit:(no unit assumed)
Controllable:No
Description:The listed sideset ids will be assumed valid for the mesh. This permits setting up boundary restrictions for sidesets initially containing no sides. Names for this sidesets may be provided using add_sideset_names. In this case this list and add_sideset_names must contain the same number of items.
add_sideset_namesThe listed sideset names will be assumed valid for the mesh. This permits setting up boundary restrictions for sidesets initially containing no sides. Ids for this sidesets may be provided using add_sideset_ids. In this case this list and add_sideset_ids must contain the same number of items.
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The listed sideset names will be assumed valid for the mesh. This permits setting up boundary restrictions for sidesets initially containing no sides. Ids for this sidesets may be provided using add_sideset_ids. In this case this list and add_sideset_ids must contain the same number of items.
add_subdomain_idsThe listed subdomain ids will be assumed valid for the mesh. This permits setting up subdomain restrictions for subdomains initially containing no elements, which can occur, for example, in additive manufacturing simulations which dynamically add and remove elements. Names for this subdomains may be provided using add_subdomain_names. In this case this list and add_subdomain_names must contain the same number of items.
C++ Type:std::vector<unsigned short>
Unit:(no unit assumed)
Controllable:No
Description:The listed subdomain ids will be assumed valid for the mesh. This permits setting up subdomain restrictions for subdomains initially containing no elements, which can occur, for example, in additive manufacturing simulations which dynamically add and remove elements. Names for this subdomains may be provided using add_subdomain_names. In this case this list and add_subdomain_names must contain the same number of items.
add_subdomain_namesThe listed subdomain names will be assumed valid for the mesh. This permits setting up subdomain restrictions for subdomains initially containing no elements, which can occur, for example, in additive manufacturing simulations which dynamically add and remove elements. IDs for this subdomains may be provided using add_subdomain_ids. Otherwise IDs are automatically assigned. In case add_subdomain_ids is set too, both lists must contain the same number of items.
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The listed subdomain names will be assumed valid for the mesh. This permits setting up subdomain restrictions for subdomains initially containing no elements, which can occur, for example, in additive manufacturing simulations which dynamically add and remove elements. IDs for this subdomains may be provided using add_subdomain_ids. Otherwise IDs are automatically assigned. In case add_subdomain_ids is set too, both lists must contain the same number of items.
allow_renumberingTrueIf allow_renumbering=false, node and element numbers are kept fixed until deletion
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If allow_renumbering=false, node and element numbers are kept fixed until deletion
build_all_side_lowerd_meshFalseTrue to build the lower-dimensional mesh for all sides.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to build the lower-dimensional mesh for all sides.
clear_spline_nodesFalseIf clear_spline_nodes=true, IsoGeometric Analyis spline nodes and constraints are removed from an IGA mesh, after which only C^0 Rational-Bernstein-Bezier elements will remain.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If clear_spline_nodes=true, IsoGeometric Analyis spline nodes and constraints are removed from an IGA mesh, after which only C^0 Rational-Bernstein-Bezier elements will remain.
coord_blockBlock IDs for the coordinate systems. If this parameter is specified, then it must encompass all the subdomains on the mesh.
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:Block IDs for the coordinate systems. If this parameter is specified, then it must encompass all the subdomains on the mesh.
displacementOptional variable to use for mesh displacement.
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Optional variable to use for mesh displacement.
ghosting_patch_sizeThe number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.
max_leaf_size10The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.
Default:10
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.
parallel_refine0Number of parallel refinements to perform on the mesh.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Number of parallel refinements to perform on the mesh.
parallel_typeDEFAULTDEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh
Default:DEFAULT
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:DEFAULT, REPLICATED, DISTRIBUTED
Controllable:No
Description:DEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh
serial_refine0Number of serial refinements to perform on the mesh. Equivalent to uniform_refine.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Number of serial refinements to perform on the mesh. Equivalent to uniform_refine.
skip_refine_when_use_splitTrueTrue to skip uniform refinements when using a pre-split mesh.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to skip uniform refinements when using a pre-split mesh.
uniform_refine0Number of serial refinements to perform on the mesh. Equivalent to serial_refine
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Number of serial refinements to perform on the mesh. Equivalent to serial_refine

Optional Parameters

alpha_rotationThe number of degrees that the domain should be alpha-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The number of degrees that the domain should be alpha-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
beta_rotationThe number of degrees that the domain should be beta-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The number of degrees that the domain should be beta-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
gamma_rotationThe number of degrees that the domain should be gamma-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The number of degrees that the domain should be gamma-rotated using the Euler angle ZXZ convention from https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix in order to align with a canonical physical space of your choosing.
length_unitHow much distance one mesh length unit represents, e.g. 1 cm, 1 nm, 1 ft, 5inches
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:How much distance one mesh length unit represents, e.g. 1 cm, 1 nm, 1 ft, 5inches
up_directionSpecify what axis corresponds to the up direction in physical space (the opposite of the gravity vector if you will). If this parameter is provided, we will perform a single 90 degree rotation of the domain--if the provided axis is 'x' or 'z', we will not rotate if the axis is 'y'--such that a point which was on the provided axis will now lie on the y-axis, e.g. the y-axis is our canonical up direction. If you want finer grained control than this, please use the 'alpha_rotation', 'beta_rotation', and 'gamma_rotation' parameters.
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:X, Y, Z
Controllable:No
Description:Specify what axis corresponds to the up direction in physical space (the opposite of the gravity vector if you will). If this parameter is provided, we will perform a single 90 degree rotation of the domain--if the provided axis is 'x' or 'z', we will not rotate if the axis is 'y'--such that a point which was on the provided axis will now lie on the y-axis, e.g. the y-axis is our canonical up direction. If you want finer grained control than this, please use the 'alpha_rotation', 'beta_rotation', and 'gamma_rotation' parameters.

Transformations Relative To Parent Application Frame Of Reference Parameters

coord_typeXYZType of the coordinate system per block param
Default:XYZ
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:XYZ, RZ, RSPHERICAL
Controllable:No
Description:Type of the coordinate system per block param
rz_coord_axisYThe rotation axis (X | Y) for axisymmetric coordinates
Default:Y
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:X, Y
Controllable:No
Description:The rotation axis (X | Y) for axisymmetric coordinates
rz_coord_blocksBlocks using general axisymmetric coordinate systems
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:Blocks using general axisymmetric coordinate systems
rz_coord_directionsAxis directions for each block in 'rz_coord_blocks'
C++ Type:std::vector<libMesh::VectorValue<double>>
Unit:(no unit assumed)
Controllable:No
Description:Axis directions for each block in 'rz_coord_blocks'
rz_coord_originsAxis origin points for each block in 'rz_coord_blocks'
C++ Type:std::vector<libMesh::Point>
Unit:(no unit assumed)
Controllable:No
Description:Axis origin points for each block in 'rz_coord_blocks'

Coordinate System Parameters

centroid_partitioner_directionSpecifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:x, y, z, radial
Controllable:No
Description:Specifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial
partitionerdefaultSpecifies a mesh partitioner to use when splitting the mesh for a parallel computation.
Default:default
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:default, metis, parmetis, linear, centroid, hilbert_sfc, morton_sfc
Controllable:No
Description:Specifies a mesh partitioner to use when splitting the mesh for a parallel computation.

Partitioning Parameters

construct_node_list_from_side_listTrueWhether or not to generate nodesets from the sidesets (usually a good idea).
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to generate nodesets from the sidesets (usually a good idea).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
dim1This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!
Default:1
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:1, 2, 3
Controllable:No
Description:This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.
nemesisFalseIf nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.
patch_size40The number of nodes to consider in the NearestNode neighborhood.
Default:40
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of nodes to consider in the NearestNode neighborhood.
patch_update_strategyneverHow often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all secondary nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all secondary nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of secondary nodes for which penetration is not detected. If there can be substantial relative motion between the primary and secondary surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.
Default:never
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:never, always, auto, iteration
Controllable:No
Description:How often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all secondary nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all secondary nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of secondary nodes for which penetration is not detected. If there can be substantial relative motion between the primary and secondary surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.

Advanced Parameters

Input Files

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_from_sub/sub.i)
(test/tests/kernels/diffusion_partial.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/parent.i)
(test/tests/variables/mfem_variables_from_moose.i)
(test/tests/outputs/datacollections.i)
(test/tests/kernels/curlcurl.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_to_sub/parent.i)
(test/tests/kernels/heatconduction_element.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_to_sub/sub.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/sub_recv.i)
(test/tests/kernels/gravity.i)
(test/tests/kernels/irrotational.i)
(test/tests/kernels/heattransfer.i)
(test/tests/kernels/linearelasticity.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_from_sub/parent.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/sub_send.i)
(test/tests/kernels/diffusion.i)
(test/tests/kernels/graddiv.i)
(test/tests/kernels/heatconduction.i)

(test/tests/kernels/diffusion.i)

[Mesh]
  type = MFEMMesh
  file = gold/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 = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_from_sub/sub.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[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
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = 4
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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


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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

(test/tests/kernels/diffusion_partial.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = diffused
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = diffused
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

[Preconditioner]
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

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

[Executioner]
  type = MFEMSteady
  assembly_level = partial
[]

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/parent.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

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

[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]
    [./to_sub]
        type = MultiAppMFEMCopyTransfer
        source_variable = send
        variable = recv
        from_multi_app = send_app
        to_multi_app = recv_app 
    [../]
[]

(test/tests/variables/mfem_variables_from_moose.i)

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

[Problem]
  type = MFEMProblem
[]

[Variables]
  [scalar_var]
    family = LAGRANGE
    order = FIRST
  []
  [vector_var]
    family = LAGRANGE_VEC
    order = FIRST
  []  
[]

[AuxVariables]
  [scalar_auxvar]
    family = MONOMIAL
    order = CONSTANT
  []
  [vector_auxvar]
    family = MONOMIAL_VEC
    order = CONSTANT
  []  
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = scalar_var
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = scalar_var
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  dt = 1.0
  start_time = 0.0
  end_time = 1.0
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/VariableSetupTest
  []
[]

(test/tests/outputs/datacollections.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = diffused
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = diffused
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/kernels/curlcurl.i)

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

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

[Problem]
  type = MFEMProblem
[]

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

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

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

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

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

    symbol_names = kappa
    symbol_values = 3.1415926535
  []

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

    symbol_names = kappa
    symbol_values = 3.1415926535
  []  
[]

[BCs]
  [tangential_E_bdr]
    type = MFEMVectorFunctionTangentialDirichletBC
    variable = e_field
    function = exact_e_field
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = one
    prop_values = 1.0
  []
[]

[Kernels]
  [curlcurl]
    type = MFEMCurlCurlKernel
    variable = e_field
    coefficient = one
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = e_field
    coefficient = one
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = e_field
    function = forcing_field
  []    
[]

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_to_sub/parent.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[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
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = u
    boundary = 4
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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


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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

[Transfers]
    [./to_sub]
        type = MultiAppMFEMCopyTransfer
        source_variable = u
        variable = u
        to_multi_app = subapp
    [../]
[]

(test/tests/kernels/heatconduction_element.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = 'thermal_conductivity volumetric_heat_capacity'
    prop_values = '1.0 1.0'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = thermal_conductivity
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
    coefficient = volumetric_heat_capacity
  []  
[]

[Preconditioner]
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMCGSolver
  preconditioner = jacobi
  l_tol = 1e-16
  l_max_its = 1000
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  dt = 0.25
  start_time = 0.0
  end_time = 1.0
  assembly_level = element
[]

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_to_sub/sub.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]


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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/sub_recv.i)

[Mesh]
  type = MFEMMesh
  file = square.msh 
  dim = 3
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/kernels/gravity.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [dirichlet]
    type = MFEMVectorDirichletBC
    variable = displacement
    boundary = '1'
    values = '0.0 0.0 0.0'
  []
[]

[Materials]
  [Rigidium]
    type = MFEMGenericConstantMaterial
    prop_names = 'lambda mu'
    prop_values = '50.0 50.0'
    block = 1
  []
  [Bendium]
    type = MFEMGenericConstantMaterial
    prop_names = 'lambda mu'
    prop_values = '1.0 1.0'
    block = 2
  []
  [RigidiumWeightDensity]
    type = MFEMGenericConstantVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '0.0 0.0 -1e-2'
    block = 1
  []
  [BendiumWeightDensity]
    type = MFEMGenericConstantVectorMaterial
    prop_names = 'gravitational_force_density'
    prop_values = '0.0 0.0 -5e-3'
    block = 2
  []  
[]

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

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

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

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

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

(test/tests/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 = gold/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 = MFEMScalarFunctionDirichletBC
    variable = velocity_potential
    boundary = '1'
    function = theta
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = one
    prop_values = 1.0
  []
[]

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

[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
    execution_order_group = 1
  []
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
    execution_order_group = 1
  []
[]

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

(test/tests/kernels/heattransfer.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[Functions]
  [reservoir_far_temperature]
    type = ParsedFunction
    expression = 0.5
  []
  [heat_transfer_coefficient]
    type = ParsedFunction
    expression = 5.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = thermal_conductivity
  []  
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
    coefficient = volumetric_heat_capacity
  []    
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    value = 1.0
  []
  [top]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = reservoir_far_temperature
    heat_transfer_coefficient = heat_transfer_coefficient
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = 'thermal_conductivity volumetric_heat_capacity'
    prop_values = '1.0 1.0'
  []
[]

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

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

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

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

(test/tests/kernels/linearelasticity.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

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

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

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

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

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

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

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_from_sub/parent.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Transfers]
    [./to_sub]
        type = MultiAppMFEMCopyTransfer
        source_variable = u
        variable = u
        from_multi_app = subapp
    [../]
[]

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

(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/sub_send.i)

[Mesh]
  type = MFEMMesh
  file = square.msh
  dim = 3
[]

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = send
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = send
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

[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
  device = cpu
[]

(test/tests/kernels/diffusion.i)

[Mesh]
  type = MFEMMesh
  file = gold/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 = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = diffusivity
    prop_values = 1.0
  []
[]

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

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

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

[Executioner]
  type = MFEMSteady
  device = cpu
[]

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

(test/tests/kernels/graddiv.i)

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

[Mesh]
  type = MFEMMesh
  file = gold/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
  []  
[]

[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 = MFEMVectorFunctionNormalDirichletBC
    variable = F
    boundary = '1 2 3'
    function = F_exact
  []
[]

[Materials]
  [Beamium]
    type = MFEMGenericConstantMaterial
    prop_names = 'alpha beta'
    prop_values = '1.0 1.0'
    block = '1 2'
  []
[]

[Kernels]
  [divdiv]
    type = MFEMDivDivKernel
    variable = F
    coefficient = alpha
  []
  [mass]
    type = MFEMVectorFEMassKernel
    variable = F
    coefficient = beta
  []
  [source]
    type = MFEMVectorFEDomainLFKernel
    variable = F
    function = 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/kernels/heatconduction.i)

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

[Problem]
  type = MFEMProblem
[]

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

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

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    value = 1.0
  []
  [low_terminal]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '2'
    value = 0.0
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = 'thermal_conductivity volumetric_heat_capacity'
    prop_values = '1.0 1.0'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = thermal_conductivity
  []
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
    coefficient = volumetric_heat_capacity
  []  
[]

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

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

[Executioner]
  type = MFEMTransient
  device = cpu
  dt = 0.25
  start_time = 0.0
  end_time = 1.0
[]

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

Summary
Overview
Example Input File Syntax
Input Parameters
Input Files