MFEMSteady

Executioner for steady state MFEM problems.

Overview

MFEMSteady is the MFEMExecutioner type used to solve time independent MFEM finite element problems.

As in all MFEMExecutioner derived classes, the desired device and assembly level to use during problem set-up and solution can be selected.

Example Input File Syntax

[Executioner]
  type = MFEMSteady
  device = cpu
[]

Input Parameters

assembly_levellegacyMatrix assembly level. Options: legacy, full, element, partial, none.
Default:legacy
C++ Type:MooseEnum
Options:legacy, full, element, partial, none
Controllable:No
Description:Matrix assembly level. Options: legacy, full, element, partial, none.
devicecpuRun app on the chosen device.
Default:cpu
C++ Type:std::string
Controllable:No
Description:Run app on the chosen device.
time0System time
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:System time
verboseFalseSet to true to print additional information
Default:False
C++ Type:bool
Controllable:No
Description:Set to true to print additional information

Optional Parameters

accept_on_max_fixed_point_iterationFalseTrue to treat reaching the maximum number of fixed point iterations as converged.
Default:False
C++ Type:bool
Controllable:No
Description:True to treat reaching the maximum number of fixed point iterations as converged.
auto_advanceFalseWhether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
custom_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
custom_ppPostprocessor for custom fixed point convergence check.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor for custom fixed point convergence check.
custom_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
direct_pp_valueFalseTrue to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
Default:False
C++ Type:bool
Controllable:No
Description:True to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
disable_fixed_point_residual_norm_checkFalseDisable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
Default:False
C++ Type:bool
Controllable:No
Description:Disable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
fixed_point_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
fixed_point_algorithmpicardThe fixed point algorithm to converge the sequence of problems.
Default:picard
C++ Type:MooseEnum
Options:picard, secant, steffensen
Controllable:No
Description:The fixed point algorithm to converge the sequence of problems.
fixed_point_force_normsFalseForce the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
Default:False
C++ Type:bool
Controllable:No
Description:Force the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
fixed_point_max_its1Specifies the maximum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Specifies the maximum number of fixed point iterations.
fixed_point_min_its1Specifies the minimum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Specifies the minimum number of fixed point iterations.
fixed_point_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
relaxation_factor1Fraction of newly computed value to keep.Set between 0 and 2.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of newly computed value to keep.Set between 0 and 2.
transformed_postprocessorsList of main app postprocessors to transform during fixed point iterations
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:List of main app postprocessors to transform during fixed point iterations
transformed_variablesList of main app variables to transform during fixed point iterations
C++ Type:std::vector<std::string>
Controllable:No
Description:List of main app variables to transform during fixed point iterations

Fixed Point Iterations 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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Advanced Parameters

max_xfem_update4294967295Maximum number of times to update XFEM crack topology in a step due to evolving cracks
Default:4294967295
C++ Type:unsigned int
Controllable:No
Description:Maximum number of times to update XFEM crack topology in a step due to evolving cracks
update_xfem_at_timestep_beginFalseShould XFEM update the mesh at the beginning of the timestep
Default:False
C++ Type:bool
Controllable:No
Description:Should XFEM update the mesh at the beginning of the timestep

Xfem Fixed Point Iterations Parameters

Restart Parameters

Input Files

(test/tests/outputs/datacollections.i)
(test/tests/kernels/diffusion.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_from_sub/sub.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_to_sub/parent.i)
(test/tests/kernels/graddiv.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_recv.i)
(test/tests/kernels/diffusion_partial.i)
(test/tests/kernels/irrotational.i)
(test/tests/kernels/gravity.i)
(test/tests/transfers/multiapp_copy_transfers/mfem_linear_lagrange_between_subapps/sub_send.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/parent.i)
(test/tests/kernels/linearelasticity.i)
(test/tests/kernels/curlcurl.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/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/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/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/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 = MFEMVectorFunctorNormalDirichletBC
    variable = F
    boundary = '1 2 3'
    vector_coefficient = 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
    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/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_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/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/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 = MFEMScalarFunctorDirichletBC
    variable = velocity_potential
    boundary = '1'
    coefficient = 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/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/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/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/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/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/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 = MFEMVectorFunctorTangentialDirichletBC
    variable = e_field
    vector_coefficient = 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
    vector_coefficient = 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
  []
[]

Overview
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