Preconditioners and linear solvers

MOOSE allows users to utilise the full power of the PETSc preconditioners and linear solvers. The following choices have been found to be effective for various types of PorousFlow simulations.

pc_type = lu, pc_factor_mat_solver_package = mumps (the most robust choice)
pc_type = bjacobi, ksp_type = bcgs
pc_type = bjacobi, ksp_type = gmres
pc_type = asm, pc_asm_overlap = 2, sub_pc_type = lu, sub_pc_factor_shift_type = NONZERO, ksp_type = gmres
pc_type = asm, pc_asm_overlap = 2, sub_pc_type = lu, sub_pc_factor_shift_type = NONZERO, ksp_type = gmres along with the following options -ksp_diagonal_scale -ksp_diagonal_scale_fix -ksp_gmres_modifiedgramschmidt

These options can be set in the Preconditioning block in the input file

Example of using solver options

[Preconditioning<<<{"href": "../../syntax/Preconditioning/index.html"}>>>]
  [andy]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
    petsc_options<<<{"description": "Singleton PETSc options"}>>> = '-snes_converged_reason'
    petsc_options_iname<<<{"description": "Names of PETSc name/value pairs"}>>> = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol '
    petsc_options_value<<<{"description": "Values of PETSc name/value pairs (must correspond with \"petsc_options_iname\""}>>> = 'gmres asm lu 100 NONZERO 2 1E-14 1E-12'
  []
[]

The "mumps" method is usually superior to the "asm + LU" method, but isn't always installed on all computer systems. Increasing the pc_asm_overlap improves the strength of the preconditioner, but uses a huge amount of memory. The NONZERO shifting helps reduce problems when the diagonal of the Jacobian contains zeroes.

(modules/porous_flow/test/tests/newton_cooling/nc04.i)

# Newton cooling from a bar.  Heat conduction
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  ny = 1
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 1
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temp'
    number_fluid_phases = 0
    number_fluid_components = 0
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp]
    type = FunctionIC
    variable = temp
    function = '2-x/100'
  []
[]

[Kernels]
  [conduction]
    type = PorousFlowHeatConduction
    variable = temp
  []
[]

[Materials]
  [temperature]
    type = PorousFlowTemperature
    temperature = temp
  []
  [thermal_conductivity_irrelevant]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '1E2 0 0 0 1E2 0 0 0 1E2'
  []
[]

[BCs]
  [left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 2
  []
  [newton]
    type = PorousFlowPiecewiseLinearSink
    variable = temp
    boundary = right
    pt_vals = '0 1 2'
    multipliers = '-1 0 1'
    flux_function = 1
  []
[]

[VectorPostprocessors]
  [temp]
    type = LineValueSampler
    variable = temp
    start_point = '0 0.5 0'
    end_point = '100 0.5 0'
    sort_by = x
    num_points = 11
    execute_on = timestep_end
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options = '-snes_converged_reason'
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_max_it -sub_pc_factor_shift_type -pc_asm_overlap -snes_atol -snes_rtol '
    petsc_options_value = 'gmres asm lu 100 NONZERO 2 1E-14 1E-12'
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  file_base = nc04
  execute_on = timestep_end
  exodus = false
  [along_line]
    type = CSV
    execute_vector_postprocessors_on = timestep_end
  []
[]