MFEMProblem

Summary

Problem type for building and solving finite element problem using the MFEM finite element library.

Overview

MFEMProblem is derived from MOOSE's ExternalProblem Problem type, customised to set up the finite element problem using the MFEM FE library instead of MOOSE's default libMesh. Use of MFEM allows problem assembly and solution on GPU architectures as well as on CPU; desired device can be controlled by the MFEMExecutioner used to solve the problem.

MFEMProblem methods are called by Actions during parsing of the user's input file, which add and/or initialize members of the owned MFEMProblemData struct. The order in which these actions are executed respects the dependencies declared in PlatypusApp.

Example Input File Syntax

In order to build the FE problem using the MFEM library on the backend, the MFEMProblem type must be used in Problem block in the user input.

[Problem]
  type = MFEMProblem
[]

Input Parameters

linear_sys_namesThe linear system names
C++ Type:std::vector<LinearSystemName>
Unit:(no unit assumed)
Controllable:No
Description:The linear system names
not_zeroed_tag_vectorsExtra vector tags which the sytem will not zero when other vector tags are zeroed. The outer index is for which nonlinear system the extra tag vectors should be added for
C++ Type:std::vector<std::vector<TagName>>
Unit:(no unit assumed)
Controllable:No
Description:Extra vector tags which the sytem will not zero when other vector tags are zeroed. The outer index is for which nonlinear system the extra tag vectors should be added for
regard_general_exceptions_as_errorsFalseIf we catch an exception during residual/Jacobian evaluaton for which we don't have specific handling, immediately error instead of allowing the time step to be cut
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If we catch an exception during residual/Jacobian evaluaton for which we don't have specific handling, immediately error instead of allowing the time step to be cut
solveTrueWhether or not to actually solve the Nonlinear system. This is handy in the case that all you want to do is execute AuxKernels, Transfers, etc. without actually solving anything
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:Yes
Description:Whether or not to actually solve the Nonlinear system. This is handy in the case that all you want to do is execute AuxKernels, Transfers, etc. without actually solving anything

Optional Parameters

allow_initial_conditions_with_restartFalseTrue to allow the user to specify initial conditions when restarting. Initial conditions can override any restarted field
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to allow the user to specify initial conditions when restarting. Initial conditions can override any restarted field
force_restartFalseEXPERIMENTAL: If true, a sub_app may use a restart file instead of using of using the master backup file
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:EXPERIMENTAL: If true, a sub_app may use a restart file instead of using of using the master backup file
restart_file_baseFile base name used for restart (e.g. / or /LATEST to grab the latest file available)
C++ Type:FileNameNoExtension
Unit:(no unit assumed)
Controllable:No
Description:File base name used for restart (e.g. / or /LATEST to grab the latest file available)

Restart Parameters

allow_invalid_solutionFalseSet to true to allow convergence even though the solution has been marked as 'invalid'
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to true to allow convergence even though the solution has been marked as 'invalid'
immediately_print_invalid_solutionFalseWhether or not to report invalid solution warnings at the time the warning is produced instead of after the calculation
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to report invalid solution warnings at the time the warning is produced instead of after the calculation
show_invalid_solution_consoleTrueSet to true to show the invalid solution occurance summary in console
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to true to show the invalid solution occurance summary in console

Solution Validity Control Parameters

boundary_restricted_elem_integrity_checkTrueSet to false to disable checking of boundary restricted elemental object variable dependencies, e.g. are the variable dependencies defined on the selected boundaries?
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to false to disable checking of boundary restricted elemental object variable dependencies, e.g. are the variable dependencies defined on the selected boundaries?
boundary_restricted_node_integrity_checkTrueSet to false to disable checking of boundary restricted nodal object variable dependencies, e.g. are the variable dependencies defined on the selected boundaries?
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to false to disable checking of boundary restricted nodal object variable dependencies, e.g. are the variable dependencies defined on the selected boundaries?
check_uo_aux_stateFalseTrue to turn on a check that no state presents during the evaluation of user objects and aux kernels
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to turn on a check that no state presents during the evaluation of user objects and aux kernels
error_on_jacobian_nonzero_reallocationFalseThis causes PETSc to error if it had to reallocate memory in the Jacobian matrix due to not having enough nonzeros
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:This causes PETSc to error if it had to reallocate memory in the Jacobian matrix due to not having enough nonzeros
fv_bcs_integrity_checkTrueSet to false to disable checking of overlapping Dirichlet and Flux BCs and/or multiple DirichletBCs per sideset
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to false to disable checking of overlapping Dirichlet and Flux BCs and/or multiple DirichletBCs per sideset
kernel_coverage_block_listList of subdomains for kernel coverage check. The meaning of this list is controlled by the parameter 'kernel_coverage_check' (whether this is the list of subdomains to be checked, not to be checked or not taken into account).
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:List of subdomains for kernel coverage check. The meaning of this list is controlled by the parameter 'kernel_coverage_check' (whether this is the list of subdomains to be checked, not to be checked or not taken into account).
material_coverage_block_listList of subdomains for material coverage check. The meaning of this list is controlled by the parameter 'material_coverage_check' (whether this is the list of subdomains to be checked, not to be checked or not taken into account).
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:List of subdomains for material coverage check. The meaning of this list is controlled by the parameter 'material_coverage_check' (whether this is the list of subdomains to be checked, not to be checked or not taken into account).
material_coverage_checkTRUEControls, if and how a material subdomain coverage check is performed. With 'TRUE' or 'ON' all subdomains are checked (the default). Setting 'FALSE' or 'OFF' will disable the check for all subdomains. To exclude a predefined set of subdomains 'SKIP_LIST' is to be used, while the subdomains to skip are to be defined in the parameter 'material_coverage_block_list'. To limit the check to a list of subdomains, 'ONLY_LIST' is to be used (again, using the parameter 'material_coverage_block_list').
Default:TRUE
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:FALSE, TRUE, OFF, ON, SKIP_LIST, ONLY_LIST
Controllable:No
Description:Controls, if and how a material subdomain coverage check is performed. With 'TRUE' or 'ON' all subdomains are checked (the default). Setting 'FALSE' or 'OFF' will disable the check for all subdomains. To exclude a predefined set of subdomains 'SKIP_LIST' is to be used, while the subdomains to skip are to be defined in the parameter 'material_coverage_block_list'. To limit the check to a list of subdomains, 'ONLY_LIST' is to be used (again, using the parameter 'material_coverage_block_list').
material_dependency_checkTrueSet to false to disable material dependency check
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to false to disable material dependency check

Simulation Checks Parameters

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.
default_ghostingFalseWhether or not to use libMesh's default amount of algebraic and geometric ghosting
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to use libMesh's default amount of algebraic and geometric ghosting
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.

Advanced Parameters

extra_tag_matricesExtra matrices to add to the system that can be filled by objects which compute residuals and Jacobians (Kernels, BCs, etc.) by setting tags on them. The outer index is for which nonlinear system the extra tag vectors should be added for
C++ Type:std::vector<std::vector<TagName>>
Unit:(no unit assumed)
Controllable:No
Description:Extra matrices to add to the system that can be filled by objects which compute residuals and Jacobians (Kernels, BCs, etc.) by setting tags on them. The outer index is for which nonlinear system the extra tag vectors should be added for
extra_tag_solutionsExtra solution vectors to add to the system that can be used by objects for coupling variable values stored in them.
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:Extra solution vectors to add to the system that can be used by objects for coupling variable values stored in them.
extra_tag_vectorsExtra vectors to add to the system that can be filled by objects which compute residuals and Jacobians (Kernels, BCs, etc.) by setting tags on them. The outer index is for which nonlinear system the extra tag vectors should be added for
C++ Type:std::vector<std::vector<TagName>>
Unit:(no unit assumed)
Controllable:No
Description:Extra vectors to add to the system that can be filled by objects which compute residuals and Jacobians (Kernels, BCs, etc.) by setting tags on them. The outer index is for which nonlinear system the extra tag vectors should be added for

Tagging Parameters

identify_variable_groups_in_nlTrueWhether to identify variable groups in nonlinear systems. This affects dof ordering
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to identify variable groups in nonlinear systems. This affects dof ordering

Nonlinear System(S) Parameters

near_null_space_dimension0The dimension of the near nullspace
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The dimension of the near nullspace
null_space_dimension0The dimension of the nullspace
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The dimension of the nullspace
transpose_null_space_dimension0The dimension of the transpose nullspace
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The dimension of the transpose nullspace

Null Space Removal Parameters

parallel_barrier_messagingFalseDisplays messaging from parallel barrier notifications when executing or transferring to/from Multiapps (default: false)
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Displays messaging from parallel barrier notifications when executing or transferring to/from Multiapps (default: false)
verbose_multiappsFalseSet to True to enable verbose screen printing related to MultiApps
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to True to enable verbose screen printing related to MultiApps
verbose_setupfalseSet to 'true' to have the problem report on any object created. Set to 'extra' to also display all parameters.
Default:false
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:false, true, extra
Controllable:No
Description:Set to 'true' to have the problem report on any object created. Set to 'extra' to also display all parameters.

Verbosity 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