MFEMNewtonNonlinearSolver

Overview

Defines and builds an mfem::NewtonSolver to solve nonlinear MFEM equation systems.

This solver requires Jacobian information from the MFEM operator and uses the externally configured MFEM linear solver for the inner linear solves.

Define this object in the Solvers block.

Input Parameters

abs_tol1e-50Absolute nonlinear tolerance.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute nonlinear tolerance.
max_its1Maximum nonlinear iterations.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Maximum nonlinear iterations.
print_level1Solver verbosity.
Default:1
C++ Type:unsigned int
Controllable:No
Description:Solver verbosity.
rel_tol1e-08Relative nonlinear tolerance.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative nonlinear tolerance.
use_initial_guessTrueWhether to preserve the current MFEM solution vector as the initial guess for an iterative solver.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to preserve the current MFEM solution vector as the initial guess for an iterative solver.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/mfem/nonlinear/nlheatconduction.i)
(test/tests/mfem/nonlinear/nlheattransfer.i)
(test/tests/mfem/nonlinear/nldiffusion_newton.i)
(test/tests/mfem/submeshes/nl_hphi_magnetodynamic.i)

(test/tests/mfem/nonlinear/nlheatconduction.i)

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

kappa = 0.5
alpha = 1e-2

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

[Problem]
  type = MFEMProblem
[]

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

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

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

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

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

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

[Solvers]
  [nl]
    type = MFEMNewtonNonlinearSolver
    max_its = 30
    abs_tol = 1.0e-5
    rel_tol = 1.0e-5
    print_level = 1
  []
  [main]
    type = MFEMMUMPS
    print_level = 0
  []
[]

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

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

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

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

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

(test/tests/mfem/nonlinear/nlheattransfer.i)

[Problem]
  type = MFEMProblem
[]

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

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

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

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

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

[Solvers]
  [nl]
    type = MFEMNewtonNonlinearSolver
    max_its = 150
    abs_tol = 1e-12
    rel_tol = 1.0e-8
    print_level = 1
  []
  [linear]
    type = MFEMMUMPS
    print_level = 0
  []
[]

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

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

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

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

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

(test/tests/mfem/nonlinear/nldiffusion_newton.i)

!include nldiffusion_common.i

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

[Solvers]
  [lin]
    type = MFEMHyprePCG
    preconditioner = boomeramg
    print_level = 1
    l_tol = 1e-12
    l_max_its = 1000
  []
  [native_mfem_nl]
    type = MFEMNewtonNonlinearSolver
    max_its = 100
    abs_tol = 1.0e-10
    rel_tol = 1.0e-9
    print_level = 1
  []
[]

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

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

conductor_domains = 'TorusCore TorusSheath'
vacuum_permeability = 1.0
n_value = 20.0
j_c = 1.0
e_c = 1.0

[Problem]
  type = MFEMProblem
[]

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

[SubMeshes]
  [conductor]
    type = MFEMDomainSubMesh
    block = ${conductor_domains}
    submesh_boundary = conductor_surface
  []
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = CONSTANT
    submesh = conductor
  []
  [CoilHCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
    submesh = conductor
  []
[]

[Variables]
  [coil_induced_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
[]

[AuxVariables]
  [coil_external_h_field]
    type = MFEMVariable
    fespace = CoilHCurlFESpace
  []
  [j_field]
    type = MFEMVariable
    fespace = HDivFESpace
  []
[]

[AuxKernels]
  [update_j_field]
    type = MFEMCurlAux
    variable = j_field
    source = coil_induced_h_field
    scale_factor = 1.0
    execute_on = TIMESTEP_END
  []
[]

[Functions]
  [resistivity]
    type = MFEMParsedFunction
    expression = '(e_c/j_c) * (j/j_c)^(n_val-1)'
    symbol_names = 'j e_c j_c n_val'
    symbol_values = 'coil_induced_h_field_curl_mag ${e_c} ${j_c} ${n_value}'
  []
  [j_dresistivity_dj]
    type = MFEMParsedFunction
    expression = '(n_val-1) * resistivity'
    symbol_names = 'n_val resistivity'
    symbol_values = '${n_value} resistivity'
  []
[]

[FunctorMaterials]
  [Vacuum]
    type = MFEMGenericFunctorMaterial
    prop_names = 'permeability'
    prop_values = '${vacuum_permeability}'
  []
[]


[BCs]
  [conductor_bdr]
    type = MFEMVectorTangentialDirichletBC
    variable = coil_induced_h_field
    vector_coefficient = coil_external_h_field
    boundary = conductor_surface
  []
[]

[Kernels]
  [dBdt]
    type = MFEMTimeDerivativeVectorFEMassKernel
    variable = coil_induced_h_field
    coefficient = permeability
  []
  [curlE]
    type = MFEMNLCurlCurlKernel
    variable = coil_induced_h_field
    k_coefficient = resistivity
    curlu_dk_dcurlu_coefficient = j_dresistivity_dj
    block = ${conductor_domains}
  []
[]

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

[Solvers]
  [pcg]
    type = MFEMHyprePCG
    preconditioner = ams
    l_tol = 1e-12
    l_max_its = 100
    print_level = 0
  []
  [newton]
    type = MFEMNewtonNonlinearSolver
    max_its = 150
    abs_tol = 1e-5
    print_level = 1
  []
[]

[Executioner]
  type = MFEMTransient
  dt = 0.5
  start_time = 0.0
  end_time = 2.0
[]

[MultiApps]
  [hphi_magnetostatic]
    type = FullSolveMultiApp
    input_files = hphi_magnetostatic.i
    execute_on = INITIAL
  []
[]

[Transfers]
  [from_external_field]
    type = MultiAppMFEMShapeEvaluationTransfer
    source_variables = h_field
    variables = coil_external_h_field
    from_multi_app = hphi_magnetostatic
  []
[]

[Postprocessors]
  [CoilPower]
    type = MFEMVectorFEInnerProductIntegralPostprocessor
    coefficient = resistivity
    dual_variable = j_field
    primal_variable = j_field
    block = 'TorusCore TorusSheath'
  []
[]

[Outputs]
  inactive = ConductorParaViewDataCollection
  [ReportedPostprocessors]
    type = CSV
    file_base = OutputData/HPhiMagnetodynamicNLClosedCoilCSV
  []
  [ConductorParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HPhiMagnetodynamicNLClosedCoil
    vtk_format = ASCII
    submesh = conductor
  []
[]

Overview
Input Parameters
Input Files