6.1.2 Calculations

As already outlined above, some calculations can be performed decoupledly from the system of differential equations.

A typical example for this type of calculations is the transformation of input data from SI units to internal units. The internal units are necessary in order to guarantee good numerical properties [Sch97].

Another task which can be fulfilled in the preprocessing unit concerns the hysteresis parameters: To allow an easy switch between the different types of shape function, a mapping function was implemented. Thus both functions are controlled with the same keyword ShapeFerro. If the $\textsf {tanh}$ shape function is used, the parameter remains unchanged,

$$w=\texttt{ShapeFerro},$$ (6.1)

whereas for the $\textsf {arctan}$ function the parameter $w$ is calculated in such a way that the remanent polarization $P_\mathrm{rem}$ is identical. This transformation reads

$$w = \tan \Bigr(\pi \cdot \textsf{tanh}( \texttt{ShapeFerro}\cdot E_\mathrm{c})\cdot 2 \Bigl).$$ (6.2)

Another typical task of preprocessing is the inclusion of models which take long term effects and temperature dependence into consideration. These topics are being heavily investigated today [GLB+98], and the extraction of useful models is expected in the near future.

Finally, an on-grid representation of the macroscopic device description of physical input quantities has to be calculated. The resulting data flow is outlined in Fig. 6.3.

Figure 6.3: Data flow of preprocessing