Number of steps for given dt - rounding error?

[danielru]

In runconvergence.py in acoustic_1d_imex:

• run simulation until Tend=1.0 with Nsteps = 64, i.e. dt = 0.015625. In this case, the output from the last step reads 2015-12-02 13:42:04,252 - Process 0 on time 0.984375 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 1 -- Residual: 1.87173732e-03 2015-12-02 13:42:04,260 - Process 0 on time 0.984375 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 2 -- Residual: 3.94070291e-05 2015-12-02 13:42:04,270 - Process 0 on time 0.984375 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 3 -- Residual: 8.01802483e-07 2015-12-02 13:42:04,279 - Process 0 on time 0.984375 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 4 -- Residual: 1.57838695e-08. The time matches Tend-dt = 1.0 - 0.015625 = 0.984375
• when chaning to Nsteps=65, the output from the last step becomes: 2015-12-02 13:47:50,509 - Process 0 on time 1.000000 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 1 -- Residual: 1.80955876e-03 2015-12-02 13:47:50,518 - Process 0 on time 1.000000 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 2 -- Residual: 3.72419523e-05 2015-12-02 13:47:50,527 - Process 0 on time 1.000000 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 3 -- Residual: 7.40115315e-07 2015-12-02 13:47:50,536 - Process 0 on time 1.000000 at stage IT_FINE_SWEEP: Level: L0 -- Iteration: 4 -- Residual: 1.42181506e-08 and the plotted solution suddenly deviates significantly (i.e. visibly in the generated plot) from the exact solution. For some reason, the final time is now exactly Tend instead of Tend-dt as in the case above!

The only difference in parameters in both simulations is the increase in time steps from 64 to 65.

[danielru]

See this commit: 87a4ccf

[pancetta]

OK, I don't know what happens here, but to avoid misunderstandings, the
statement "Process p on time t" means that process p takes care of the
step [t,t+dt]. So in the last step, p should deal with [Tend-dt,Tend]
and the results should correspond to the state at Tend.

It seems that in the second case, the controller does one additional
step.. looks like somewhere the condition "t < Tend" does not give the
expected result. I'll have to look into this. For now, stop using weird
Nsteps... just kidding, I put that on the todo list.

On 02.12.15 14:57, Daniel Ruprecht wrote:

See this commit: 87a4ccf
87a4ccf

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#47 (comment).

[danielru]

Yes, I recalled that what is reported in the log is the beginning of the last step, not the end. Nevertheless, the fact that it suddenly adds another step is ... weird. Screws up the dots-on-line when too many steps are used ;)

[pancetta]

Can reproduce that with the heat_1d example using dt = 1.0/14 and Tend = 1.0.

On 02.12.15 14:51, Daniel Ruprecht wrote:

In |runconvergence.py| in acoustic_1d_imex:

run simulation until Tend=1.0 with Nsteps = 64, i.e. dt = 0.015625.
In this case, the output from the last step reads |2015-12-02
13:42:04,252 - Process 0 on time 0.984375 at stage IT_FINE_SWEEP:
Level: L0 -- Iteration: 1 -- Residual: 1.87173732e-03
2015-12-02 13:42:04,260 - Process 0 on time 0.984375 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 2 -- Residual: 3.94070291e-05
2015-12-02 13:42:04,270 - Process 0 on time 0.984375 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 3 -- Residual: 8.01802483e-07
2015-12-02 13:42:04,279 - Process 0 on time 0.984375 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 4 -- Residual:
1.57838695e-08|. The time matches Tend-dt = 1.0 - 0.015625 = 0.984375

when chaning to Nsteps=65, the output from the last step becomes:
|2015-12-02 13:47:50,509 - Process 0 on time 1.000000 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 1 -- Residual: 1.80955876e-03
2015-12-02 13:47:50,518 - Process 0 on time 1.000000 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 2 -- Residual: 3.72419523e-05
2015-12-02 13:47:50,527 - Process 0 on time 1.000000 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 3 -- Residual: 7.40115315e-07
2015-12-02 13:47:50,536 - Process 0 on time 1.000000 at stage
IT_FINE_SWEEP: Level: L0 -- Iteration: 4 -- Residual:
1.42181506e-08| and the plotted solution suddenly deviates
significantly (i.e. visibly in the generated plot) from the exact
solution. /For some reason, the final time is now exactly Tend
instead of Tend-dt as in the case above!/

The only difference in parameters in both simulations is the increase in
time steps from 64 to 65.

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