Fix intern time integration method with fixed time step

[bennibolm]

Save the manually set time step to allow simulations without a stepsize callback. Before it was overwritten within modify_dt_for_tstops!.

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.10%. Comparing base (cd097fc) to head (9f0d930).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1919      +/-   ##
==========================================
+ Coverage   91.96%   96.10%   +4.13%     
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  Files         451      451              
  Lines       36218    36241      +23     
==========================================
+ Hits        33307    34826    +1519     
+ Misses       2911     1415    -1496     

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[DanielDoehring]

You confirmed that one can now set the time step manually, right?

[bennibolm]

You confirmed that one can now set the time step manually, right?

Basically yes. The time step set was just ignored after #1677.
I just tested all setups again and found a new bug I created when actually using the SaveSolutionCallback with a fixed dt interval. I'll take a look at it and hopefully fix it.

[DanielDoehring]

Okay, feel free to notify me when you think this is ready!

[bennibolm]

I'm a little bit lost right now. The first problem was that if we want to use a fixed time step (so with disabled stepsize callback), the time step is set to tspan[1]-t (or tstop-t when the savesolution callback saves every fixed time interval).
The overwriting process is done in modify_dt_for_tstops!.
So, I added the current dt to each minimum calculation in there (which is by the way not done in OrdinaryDiffEq's modify_dt_for_tstops!).

But now, if we are close to one of these tstops the time step is set to the needed minimum. So, it works to get the correct time step. But after this timestep, dt stays at this small values. This is of course expected since I added the minimum of dt and something bigger the calculation.
For instance: using a fixes dt of dt = 1.0e-3, tspan = (0.0, 1.0) and

save_solution = SaveSolutionCallback(dt = 0.1+1.0e-6,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     solution_variables = cons2prim)

The timesteps are

#timesteps:      1 │ Δt: 1.0000e-03 │ sim. time: 1.0000e-03 (0.100%)   │ run time: 8.6168e-03 s
#timesteps:      2 │ Δt: 1.0000e-03 │ sim. time: 2.0000e-03 (0.200%)   │ run time: 1.5407e-02 s
#timesteps:      3 │ Δt: 1.0000e-03 │ sim. time: 3.0000e-03 (0.300%)   │ run time: 2.2556e-02 s
...
#timesteps:     99 │ Δt: 1.0000e-03 │ sim. time: 9.9000e-02 (9.900%)   │ run time: 7.0780e-01 s
#timesteps:    100 │ Δt: 1.0000e-03 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.1488e-01 s
#timesteps:    101 │ Δt: 1.0000e-06 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.2227e-01 s
#timesteps:    102 │ Δt: 1.0000e-06 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.3212e-01 s
#timesteps:    103 │ Δt: 1.0000e-06 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.3887e-01 s
#timesteps:    104 │ Δt: 1.0000e-06 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.5214e-01 s
#timesteps:    105 │ Δt: 1.0000e-06 │ sim. time: 1.0000e-01 (10.000%)  │ run time: 7.7050e-01 s
#timesteps:    106 │ Δt: 1.0000e-06 │ sim. time: 1.0001e-01 (10.001%)  │ run time: 7.9454e-01 s
....

@ranocha Do you have an idea how to fix this or how it is done in OrdinaryDiffEq (as I said, OrdinaryDiffEq uses the same version of modify_dt_for_tstops! as in our main right now, see here).

EDIT: An idea would be to add a variable to the integrator which saves the set time step for the whole simulation and reset dt with it for instance after every time step. But this seems to be a bit ugly. Maybe OrdinaryDiffEq has a better solution for this. Unfortunately, I can't find anything right now.

[ranocha]

OrdinaryDiffEq.jl has a working implementation:

julia> using OrdinaryDiffEq

julia> ode = ODEProblem((du, u, p, t) -> du .= u, [1.0], (0.0, 1.0))
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
timespan: (0.0, 1.0)
u0: 1-element Vector{Float64}:
 1.0

julia> sol = solve(ode, Euler(); adaptive = false, dt = 0.11, tstops = (0.5))
retcode: Success
Interpolation: 3rd order Hermite
t: 11-element Vector{Float64}:
 0.0
 0.11
 0.22
 0.33
 0.44
 0.5
 0.61
 0.72
 0.83
 0.94
 1.0
u: 11-element Vector{Vector{Float64}}:
 [1.0]
 [1.11]
 [1.2321000000000002]
 [1.3676310000000003]
 [1.5180704100000002]
 [1.6091546346000003]
 [1.7861616444060002]
 [1.9826394252906603]
 [2.200729762072633]
 [2.4428100359006226]
 [2.58937863805466]

[ranocha]

Note the dtcache in the code you linked above

[bennibolm]

Note the dtcache in the code you linked above

Oh yes. Thanks a lot

[ranocha]

Could you please add a test for this fix?