Simcenter Amesim Tolerance Methods

Automatic tolerancesThe Simcenter Amesim solver for explicit models is a variable-step solver with local error control at each step (LSODA). At each step, the solver carries out an error estimate on each state, and validates the step if, and only if this error estimate is less than a user-defined tolerance. You can define the tolerance in several ways as described below.

Fixed tolerances

The classical approach consists in comparing the error estimate to the following EWT vector:

Where and are the relative and absolute user-defined tolerance values for the state i. This approach is used in Simcenter Amesim up to release 2504, with a unique tolerance value set by default to 10-7, which is modifiable in the Run Parameters window.

Automatic tolerances

With the fixed tolerance method, the absolute tolerance term becomes dominant when the state absolute value is close to zero. When this occurs, the solver compares its error estimate to a fixed value

, which may not be always relevant according to the scale of the associated state. Therefore, another approach to define the tolerance consists in considering a scaling of each state and defining the absolute tolerance term accordingly. Basically, the objective is to have:

where is based on the maximal value of since the beginning of the simulation. In addition, in order to avoid too small or too high values of the absolute term of the tolerance, we also impose that this term is greater or equal to an absolute user-defined tolerance value , and less than min . We therefore use the following definition of the EWT vector:

The same tolerance values are considered for all states, so the method depends on two user-defined parameters

Rtol

and

Atol

.

This approach is used in Simcenter Amesim from release 2511 onward, with an absolute tolerance default value of 10-8, and a relative tolerance default value of 0-6, which is modifiable in the Run parameters window.

Choice of the method in SIMP00

The SIMP00 component allows the user to choose either the fixed or automatic tolerance method. In addition, it also allows the user to use one of these methods with user-defined tolerance values. For the fixed tolerance method, the user can set different values for both Atol and Rtol (instead of a unique one).

Messages at run-time

A message is given at run-time in the Run Details window to indicate which method is used and that it can be tuned with the SIMP00 component as described in the previous section.

General remarks

• The automatic tolerance method is used for explicit models that are integrated with the Simcenter Amesim standard integrator based on the LSODA solver. For implicit models integrated using DASSL, only the fixed tolerance method can be used.

• Attention should be paid to the fact that the scaling evolves during the simulation insofar as it is the maximum absolute value of the states since the beginning of the simulation. Consequently, different initial conditions may have an effect on the results if their amplitudes are very different.