Mapping NabLab --> Arcane

Time and time step

Arcane manages the simulation time automatically:

• time is incremented automatically at each time loop like this: tn+1 = tn + deltatn+1.
• time and time step are reserved variables called m_global_time and m_global_time_step. Setting those variables will change time/time step of the next loop, i.e. tn+1, deltatn+1.
• tn-1 and deltatn-1 are stored in the m_old_time and m_old_time_step variables.

In some numerical schemes, the current time step is set while the iteration has started, like in the following pseudo code example:

y = 0.0;
tn = 0.0;

do
{
   y = f(x, tn);
   deltat = g(y);
   z = h(y);
   tn+1 = tn + deltat
} while (true); // time loop stop condition

In NabLab, the example will be implemented like this:

module Example1;

with CartesianMesh2D.*;

def real f(real a, real b) {
    return 0.0;
}

def real g(real a) {
    return 0.0;
}

def real h(real a) {
    return 0.0;
}

real[2] X{nodes};
real t, delta_t;
real x, y, z;

iterate n while (true);

IniX: x = 0.0;
IniT: t^{n=0} = 0.0;

ComputeY: y = f(x, t^{n});
ComputeDeltaT: delta_t = g(y);
ComputeZ: z = h(y);
ComputeT: t^{n+1} = t^{n} + delta_t;

The above example will give the following job graph for the initialzation:

The above example will give the following job graph for the time loop:

This graph shows that the ComputeDeltaT job is executed at each time loop iteration.

In Arcane, setting the m_global_time_step variable changes the value of the deltatn+1 numerical value. Consequently, the pseudo code algorithm presented above must be refactored as follows:

x = 0.0;
tn = 0.0;
yn = f(x, tn);
deltatn = g(y);

do
{
   z = h(yn);
   yn+1 = f(x, tn);
   deltatn+1 = g(y+1);
   tn+1 = tn + deltatn+1
} while (true); // time loop stop condition

How such configuration can be detected