TimeStepper

The time stepper module is responsible for advancing the system in time. Two different time steppers are available, namely a fixed length stepper and a simple adaptive stepper.

Constant step length

The constant time stepper advances the system in time at a fixed rate \(\Delta t\) set by the user. The user always needs to specify the maximum simulation time, \(t_{\rm max}\), but can choose to either specify the step length \(\Delta t\) or the number of steps to take, \(N_t\). The options are set using the following code in the Python interface:

ds = DREAMSettings()
...
ds.timestep.setTmax(1e-2)
ds.timestep.setDt(5e-4)

# or, alternatively...
ds.timestep.setTmax(1e-2)
ds.timestep.setNt(20)

Reducing number of saved steps

By default, every time step taken is saved to the output file. For long simulations with fine time resolution this may however require a significant amount of memory and disk space. To reduce the amount of space needed, the constant time stepper can instructed to only store a certain number of time steps in the final output file. This is achieved using the setNumberOfSaveSteps() method as follows:

ds = DREAMSettings()
...
ds.timestep.setNt(6000)
ds.timestep.setNumberOfSaveSteps(1000)

This will cause the DREAM output file to only contain every 6th time step taken by the solver. Note that the solutions are unaffected by this downsampling—the finer time resolution is still used for evolving the system in time—and the only effect is that the output file contains fewer of the time steps actually taken.

Adaptive step length

A simple adaptive time stepper has been implemented for DREAM. Since DREAM uses an Euler backward method for time stepping, the adaptive scheme uses basic two-point time step refinement to estimate the current error in the solution. The scheme consists of the following steps:

  1. Evaluate the solution \(\boldsymbol{x}(t+\Delta t)\) from \(\boldsymbol{x}(t)\)

  2. Evaluate the solution \(\boldsymbol{x}(t+\Delta t/2)\) from \(\boldsymbol{x}(t)\), and then the solution \(\boldsymbol{x}(t+\Delta t)\) from \(\boldsymbol{x}(t+\Delta t/2)\).

  3. Estimate the error in each unknown quantity from the difference between the two solutions for \(t+\Delta t\) obtained in steps 1 and 2.

  4. If the errors in all monitored unknown quantities are acceptably low, the solution is accepted and the optimal time step length for the next step is estimated. If the error in one or more of the monitored quantities is too large, however, a new optimal time step is estimated based on the error and the scheme is repeated for the same time \(t\) from step 1 above.

Warning

The adaptive time stepper is currently considered too unstable to be used in simulations.

Todo

Provide more details about the adaptive time stepper scheme.

Class documentation

class DREAM.Settings.TimeStepper.TimeStepper(ttype=1, checkevery=0, tmax=None, dt=None, nt=None, nSaveSteps=0, reltol=0.01, verbose=False, constantstep=False)

Bases: object

__init__(ttype=1, checkevery=0, tmax=None, dt=None, nt=None, nSaveSteps=0, reltol=0.01, verbose=False, constantstep=False)

Constructor.

fromdict(data)

Load settings from the given dictionary.

set(ttype=1, checkevery=0, tmax=None, dt=None, nt=None, nSaveSteps=0, reltol=0.01, verbose=False, constantstep=False)

Set properties of the time stepper.

setCheckInterval(checkevery)
setConstantStep(constantstep)
setDt(dt)
setNt(nt)
setNumberOfSaveSteps(nSaveSteps)

Sets the number of time steps to save to the output file. This number must be <= Nt. If 0, all time steps are saved.

setRelTol(reltol)
setRelativeTolerance(reltol)
setTmax(tmax)
setType(ttype)
setVerbose(verbose=True)
todict(verify=True)

Returns a Python dictionary containing all settings of this TimeStepper object.

verifySettings()

Verify that the TimeStepper settings are consistent.