Stepsize#

For transient problems, a festim.Stepsize is required. It represents the time discretisation of the problem. Here is an example creating a stepsize of 1.2 seconds:

import festim as F
my_stepsize = F.Stepsize(initial_value=1.2)

To use the adaptive time stepping implemented in FESTIM, the arguments stepsize_change_ratio needs to be set to a value above 1.

my_stepsize = F.Stepsize(initial_value=1.2, stepsize_change_ratio=1.5)

When doing so, the stepsize will grow according to this ratio when the numerical solver converges in 4 iterations or less. It will shrink by the same ratio when the solver needs more than 4 iterations to converge. This is extremely useful when solving transient problems with a large time range, as the time step will be large when the solution is smooth and small when the solution is changing rapidly. Moreover, if the solver doesn’t converge, the stepsize will be reduced and the solver will be called again. Setting the dt_min argument will prevent the stepsize from becoming too small and will stop the simulation when this happens. To cap the stepsize after some time, the parameters t_stop and stepsize_stop_max can be used.

my_stepsize = F.Stepsize(
    initial_value=1.2,
    stepsize_change_ratio=1.5,
    dt_min=1e-6,
    t_stop=10,
    stepsize_stop_max=1.5)

Warning

Please note that parameters t_stop and stepsize_stop_max will be deprecated in a future release.

Another option for controlling the stepsize is to use the max_stepsize parameter. This parameter defines the maximal value of the stepsize during simulations, and it can be set as a constant or a callable function of time:

def max_stepsize(t):
    if t <= 5:
        return 1.5
    elif t > 5 and t < 10:
        return 2.5
    else:
        return None

my_stepsize = F.Stepsize(
    initial_value=1.2,
    stepsize_change_ratio=1.5,
    dt_min=1e-6,
    max_stepsize=max_stepsize)

The milestones argument can be used to make sure the simulation passes through specific times. This will modify the stepsize as needed.

my_stepsize = F.Stepsize(
    initial_value=1.2,
    stepsize_change_ratio=1.5,
    dt_min=1e-6,
    max_stepsize=5,
    milestones=[1, 5, 6, 10]
    )

Note

If your stepsize is constant, you can define it simply as a float or int:

my_model = F.Simulation()

my_model.dt = 2.0

Stepsize#

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