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-70a86a0f-257e-498f-8973-45842901ff57");katex.render("L\\_infty", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ 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
Unit:(no unit assumed)
Controllable:No
Description:Initial time step size
e_maxMaximum acceptable error.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum acceptable error.
e_tolTarget error tolerance.
C++ Type:double
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:scaling parameter for dt selection
start_adapting2when to start taking adaptive time steps
Default:2
C++ Type:int
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:Yes
Description:whether or not to enable the time stepper

Advanced Parameters

(moose/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
[]