Reference documentation for deal.II version 9.5.0

#include <deal.II/base/discrete_time.h>
Public Member Functions  
DiscreteTime (const double start_time, const double end_time, const double desired_start_step_size=0.)  
double  get_current_time () const 
double  get_next_time () const 
double  get_previous_time () const 
double  get_start_time () const 
double  get_end_time () const 
bool  is_at_start () const 
bool  is_at_end () const 
double  get_next_step_size () const 
double  get_previous_step_size () const 
unsigned int  get_step_number () const 
void  set_desired_next_step_size (const double time_step_size) 
void  set_next_step_size (const double time_step_size) 
void  advance_time () 
void  restart () 
Private Attributes  
double  start_time 
double  end_time 
double  current_time 
double  next_time 
double  previous_time 
double  start_step_size 
unsigned int  step_number 
This class provides a means to keep track of the simulation time in a timedependent simulation. It manages stepping forward from a start time \(T_{\text{start}}\) to an end time \(T_{\text{end}}\). It also allows adjusting the time step size during the simulation. This class provides the necessary interface to be incorporated in any timedependent simulation. The usage of this class is demonstrated in step19 and step21.
This class provides a number of invariants that are guaranteed to be true at all times.
The model this class follows is that one sets a desired time step length either through the constructor or using set_desired_next_step_size() function. This step size will then be used in all following calls to the advance_time() function, but may be adjusted slightly towards the end of the simulation to ensure that the simulation time hits the end time exactly. The adjustment is useful for the following reasons:
Let's say that you loop over all of the time steps by using a for
loop
or, if you like this better, the equivalent while
loop:
In the above example the time starts at \(T_{\text{start}} = 0\) until \(T_{\text{end}}=1\). Assuming the time step \(dt = 0.3\) is not modified inside the loop, the time is advanced from \(t = 0\) to \(t = 0.3\), \(t = 0.6\), \(t = 0.9\) and finally it reaches the end time at \(t = 1.0\). Here, the final step size needs to be reduced from its desired value of 0.3 to \(dt = 0.1\) in order to ensure that we finish the simulation exactly at the specified end time. In fact, you should assume that not only the last time step length may be adjusted, but also previously ones – for example, this class may take the liberty to spread the decrease in time step size out over several time steps and increment time from \(t=0\), to \(0.3\), \(0.6\), \(0.8\), and finally \(t=T_{\text{end}}=1\) to avoid too large a change in time step size from one step to another.
The other situation in which the time step needs to be adjusted (this time to slightly larger values) is if a time increment falls just short of the final time. Imagine, for example, a similar situation as above, but with different end time:
Here, the time step from \(t=0.9\) to \(t=1.2\) falls just short of the final time \(T_{\text{end}}=1.21\). Instead of following up with a very small step of length \(dt=0.01\), the class stretches the last time step (or last time steps) slightly to reach the desired end time.
The examples above make clear that the time step size given to this class is only a desired step size. You can query the actual time step size using the get_next_step_size() function.
Since time is marched forward in a discrete manner in our simulations, we need to discuss how we increment time. During time stepping we enter two separate alternating regimes in every step.
Tecplot
, Paraview
, and VisIt
. Additionally, during the snapshot stage, the code can assess the quality of the previous step and decide whether it wants to increase or decrease the time step size. The step size for the next time step can be modified here, by calling set_desired_next_step_size().The update stage (the transition stage, the inconsistent stage): In this section of the program, the internal state of the simulation is getting updated from \(t_n\) to \(t_{n+1}\). All of the variables need to be updated one by one, the step number is incremented, the time is incremented by \(dt = t_{n+1}  t_n\), and timeintegration algorithms are used to update the other simulation quantities. In the middle of this stage, some variables have been updated to \(t_{n+1}\) but other variables still represent their value at \(t_n\). Thus, we call this the inconsistent stage, requiring that no postprocessing output related to the state variables take place within it. The state variables, namely those related to time, the solution field and any internal variables, are not synchronized and then get updated one by one. In general, the order of updating variables is arbitrary, but some care should be taken if there are interdependencies between them. For example, if some variable such as \(x\) depends on the calculation of another variable such as \(y\), then \(y\) must be updated before \(x\) can be updated.
The question arises whether time should be incremented before updating state quantities. Multiple possibilities exist, depending on program and formulation requirements, and possibly the programmer's preferences:
advance_time()
command that was performed previously. In the following example code, we are assuming that a
and b
are two state variables that need to be updated in this time step. a
, and b
are no longer consistent with each other until after the last statement. At that point, the variables are all consistent again.advance_time()
command that will happen subsequently. advance_time()
. One thing to note is that, during the update phase, \(dt\) is referred to either next or previous time step size, depending on whether advance_time() has been called yet. The notion of current time step size is illdefined. In fact, in the update stage the definition of every variable depends on whether it has been updated yet or not, hence the name the inconsistent stage.
The following code snippet shows the code sections for the snapshot stage and the update stage in the context of a complete timedependent simulation. This code follows the coding conventions incorporated in the tutorial examples. Note that even though this example is written in the format of a for
loop, it can equivalently be written as a while
or do while
loop (as shown in step21).
The run()
function in step19 shows a very similar example where the call to advance_time() ends the update stage and is followed by generating graphical output with the thencurrent time.
Definition at line 232 of file discrete_time.h.
DiscreteTime::DiscreteTime  (  const double  start_time, 
const double  end_time,  
const double  desired_start_step_size = 0. 

) 
Constructor.
[in]  start_time  The time at the start of the simulation. 
[in]  end_time  The time at the end of the simulation. 
[in]  desired_start_step_size  A desired step size for incrementing time for the first step. It is not guaranteed that this value will be actually used as the size of the first step, as discussed in the introduction. 
desired_start_step_size
must be nonnegative.desired_start_step_size
is an optional parameter. If it is not provided or it is specified as zero, it indicates that the desired size for the time step will be calculated at a different location in the code. In this case, the created object cannot increment time until the step size is changed by calling set_desired_next_step_size(). Definition at line 45 of file discrete_time.cc.

inline 
Return the current time.
Definition at line 497 of file discrete_time.h.

inline 
Return the next time that we would reach if we were to advance the time by one step.
Definition at line 505 of file discrete_time.h.

inline 
Return the time we were at before advance_time()
was called last time.
Definition at line 513 of file discrete_time.h.

inline 
Return the start time.
Definition at line 449 of file discrete_time.h.

inline 
Return the end of the time interval. The final time step ends exactly at this point. This exact floatingpoint equality is very important because it allows us to equalitycompare current time with end time and decide whether we have reached the end of the simulation.
Definition at line 457 of file discrete_time.h.

inline 
Return whether no step has taken place yet.
Definition at line 465 of file discrete_time.h.

inline 
Return whether time has reached the end time.
Definition at line 473 of file discrete_time.h.

inline 
Return the size of the step from current time step to the next. As discussed in the introduction to the class, this is the actual time step, and may differ from the desired time step set in the constructor or through the set_desired_next_step_size() function.
Definition at line 481 of file discrete_time.h.

inline 
Return the step size of the previous step.
Definition at line 489 of file discrete_time.h.

inline 
Return the number of times the simulation time has been incremented. Return zero when the simulation is at the start time.
Definition at line 521 of file discrete_time.h.
void DiscreteTime::set_desired_next_step_size  (  const double  time_step_size  ) 
Set the desired value of the next time step size. By calling this method, we are indicating the next time advance_time() is called, we would like time_step_size
to be used to advance the simulation time. However, if the step is too large such that the next simulation time exceeds the end time, the step size is truncated. Additionally, if the step size is such that the next simulation time approximates the end time (but falls just slightly short of it), the step size is adjusted such that the next simulation time exactly matches the end time.
Definition at line 62 of file discrete_time.cc.
void DiscreteTime::set_next_step_size  (  const double  time_step_size  ) 
Set the actual value of the next time step size. By calling this method, we are indicating the next time advance_time() is called, time_step_size
is to be used to advance the simulation time.
Definition at line 70 of file discrete_time.cc.
void DiscreteTime::advance_time  (  ) 
Advance the current time based on the value of the current step. If you want to adjust the next time step size, call the method set_desired_next_step_size() before calling this method. If you call this function repeatedly, the time is increased with the same step size until it reaches the end time. See the documentation of set_desired_next_step_size() for explanation of the rules for automatic adjustment of the step size.
Definition at line 84 of file discrete_time.cc.
void DiscreteTime::restart  (  ) 
Set the current time equal to start time and set the step size to the initial step size.
Definition at line 100 of file discrete_time.cc.

private 
The beginning of the time interval.
Definition at line 401 of file discrete_time.h.

private 
The end of the time interval.
Definition at line 406 of file discrete_time.h.

private 
The current time.
Definition at line 411 of file discrete_time.h.

private 
The time at the next step.
Definition at line 425 of file discrete_time.h.

private 
The previous time.
Definition at line 430 of file discrete_time.h.

private 
The size of the first step.
Definition at line 435 of file discrete_time.h.

private 
The step number i.e. the number of times the simulation time ha been incremented.
Definition at line 441 of file discrete_time.h.