AB2PredictorCorrector

Implements second order Adams-Bashforth method for timestep calculation.

This time stepper first adds an AdamsPredictor to the problem. The predictor uses previous solutions to compute a predicted solution vector. This prediction is then compared using a $var element = document.getElementById("moose-equation-101ab5ee-a4a6-420e-aa1c-3efe9e2a2162");katex.render("L\\_infty", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ norm to the solution. If the error is lower than "e_max", then the time step is accepted. If not, then it is reduced.

The time step is regularly increased based on the "steps_between_increase" parameter. The magnitude of the increase is based on the magnitude of the prediction error.

The AB2PredictorCorrector may be used with the following three time integration schemes: implicit Euler (default in MOOSE), Crank Nicholson and 2nd order backward differences (BDF2).

Example input syntax

In this example, we solve a simple heating problem with backwards differences and a predictor corrector scheme. The prediction and correction steps can be observed during the solve.

[Executioner]
  type = Transient
  scheme = 'BDF2'
  #scheme = 'crank-nicolson'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
  [./TimeStepper]
    type = AB2PredictorCorrector
    dt = .01
    e_max = 10
    e_tol = 1
  [../]
[]

Input Parameters

dtInitial time step size
C++ Type:double
Controllable:No
Description:Initial time step size
e_maxMaximum acceptable error.
C++ Type:double
Controllable:No
Description:Maximum acceptable error.
e_tolTarget error tolerance.
C++ Type:double
Controllable:No
Description:Target error tolerance.

Required Parameters

cutback_factor_at_failure0.5Factor to apply to timestep if a time step fails to converge.
Default:0.5
C++ Type:double
Controllable:No
Description:Factor to apply to timestep if a time step fails to converge.
max_increase1e+09Maximum ratio that the time step can increase.
Default:1e+09
C++ Type:double
Controllable:No
Description:Maximum ratio that the time step can increase.
reset_dtFalseUse when restarting a calculation to force a change in dt.
Default:False
C++ Type:bool
Controllable:No
Description:Use when restarting a calculation to force a change in dt.
scaling_parameter0.8scaling parameter for dt selection
Default:0.8
C++ Type:double
Controllable:No
Description:scaling parameter for dt selection
start_adapting2when to start taking adaptive time steps
Default:2
C++ Type:int
Controllable:No
Description:when to start taking adaptive time steps
steps_between_increase1the number of time steps before recalculating dt
Default:1
C++ Type:int
Controllable:No
Description:the number of time steps before recalculating dt

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.
enableTruewhether or not to enable the time stepper
Default:True
C++ Type:bool
Controllable:Yes
Description:whether or not to enable the time stepper

Advanced Parameters

Input Files

(test/tests/time_steppers/time_stepper_system/AB2PredictorCorrector.i)
(test/tests/time_integrators/aee/aee.i)

(test/tests/time_integrators/aee/aee.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  nx = 10

  xmin = 0.0
  xmax = 1.0

[]

#still need BC for Energy, IC's for both.
[Variables]
  active = 'Time'

  [./Time]
    order =  FIRST
    family = LAGRANGE
    initial_condition = 0.0
  [../]
[]

[Functions]
  active = 'func'

  [./func]
    type = ParsedFunction
    expression = 2.0*t
  [../]
[]

[Kernels]
  active = 't_time func_time'

  [./t_time]
    type = TimeDerivative
    variable = Time
  [../]

  [./func_time]
    type = BodyForce
    variable = Time
    function = func
  [../]
[]

[BCs]
  active = 'Top_Temperature'

  [./Top_Temperature]
    type = NeumannBC
    variable = Time
    boundary = 'left right'
  [../]

[]

[Executioner]
  type = Transient
  scheme = 'BDF2'
  #scheme = 'crank-nicolson'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
 [./TimeStepper]
    type = AB2PredictorCorrector
    dt = .01
    e_max = 10
    e_tol = 1
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/time_steppers/time_stepper_system/AB2PredictorCorrector.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  nx = 10

  xmin = 0.0
  xmax = 1.0

[]

#still need BC for Energy, IC's for both.
[Variables]
  active = 'Time'

  [./Time]
    order =  FIRST
    family = LAGRANGE
    initial_condition = 0.0
  [../]
[]

[Functions]
  active = 'func'

  [./func]
    type = ParsedFunction
    expression = 2.0*t
  [../]
[]

[Kernels]
  active = 't_time func_time'

  [./t_time]
    type = TimeDerivative
    variable = Time
  [../]

  [./func_time]
    type = BodyForce
    variable = Time
    function = func
  [../]
[]

[BCs]
  active = 'Top_Temperature'

  [./Top_Temperature]
    type = NeumannBC
    variable = Time
    boundary = 'left right'
  [../]

[]

[Executioner]
  type = Transient
  scheme = 'BDF2'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
  # Use the same test case as AB2PredictorCorrector test, add one more time stepper
  # to test if AB2PredictorCorrector works correctly with time stepper composition
 [TimeSteppers]
    [AB2]
      type = AB2PredictorCorrector
      dt = .01
      e_max = 10
      e_tol = 1
    []
    [IterationAdapDT]
      type = IterationAdaptiveDT
      dt = 100
    []
  []
[]

[Outputs]
  exodus = true
  file_base='aee_out'
[]

(test/tests/time_integrators/aee/aee.i)

[Mesh]
  type = GeneratedMesh
  dim = 1

  nx = 10

  xmin = 0.0
  xmax = 1.0

[]

#still need BC for Energy, IC's for both.
[Variables]
  active = 'Time'

  [./Time]
    order =  FIRST
    family = LAGRANGE
    initial_condition = 0.0
  [../]
[]

[Functions]
  active = 'func'

  [./func]
    type = ParsedFunction
    expression = 2.0*t
  [../]
[]

[Kernels]
  active = 't_time func_time'

  [./t_time]
    type = TimeDerivative
    variable = Time
  [../]

  [./func_time]
    type = BodyForce
    variable = Time
    function = func
  [../]
[]

[BCs]
  active = 'Top_Temperature'

  [./Top_Temperature]
    type = NeumannBC
    variable = Time
    boundary = 'left right'
  [../]

[]

[Executioner]
  type = Transient
  scheme = 'BDF2'
  #scheme = 'crank-nicolson'
  start_time = 0
  num_steps = 4
  nl_abs_tol = 1e-15
  petsc_options = '-snes_converged_reason'
  abort_on_solve_fail = true
 [./TimeStepper]
    type = AB2PredictorCorrector
    dt = .01
    e_max = 10
    e_tol = 1
  [../]
[]

[Outputs]
  exodus = true
[]

Example input syntax
Input Parameters
Input Files