The Dispersion subnode to Charge Conservation and Charge Conservation, Piezoelectric allows you to model possible dielectric losses in the material. The effect can be accounted for in Eigenfrequency, Frequency Domain and Time Dependent study.

Under the Material model, you can select either Debye (default) or Multipole Debye dispersion option.

For a single pole Debye dispersion choice, you can enter the Relaxation time and Relative permittivity contribution. In the Thermal Effects tab, you can select the Shift function type, which will be used to compute the effective relaxation time accounting for the temperature effects.

For the Multipole Debye dispersion, you can select two options to enter the Relaxation Data.

Constant Loss Tangent option. In this case, you enter the Loss Tangent η(fc) together with the Center frequency fc. You also specify the model Bandwidth (decades) that defines a frequency interval centered at fc, in which the loss tangent will be approximately constant and equal to η(fc). You can also select the Accuracy for the approximation to be either Normal (default) or High. The software will automatically deduce the necessary number of Debye poles together with the values of the corresponding relaxation times and relative permittivity contributions, which will be used in computations to maintain the requested bandwidth and accuracy.

For all cases, you can specify how the relative permittivity input, εrS, on the parent node should be interpreted by selecting the Static response (the default value is High frequency limit). This setting will have effect in Eigenfrequency, Frequency Domain, and Time Dependent study types.

Dispersion properties depend on the temperature. For many materials, a change in the temperature can be transformed directly into a change in the time scale. Thus, the relaxation time is modified to aT(T)τm, where aT(T) is a shift function.

Select a Shift function — None, Vogel-Fulcher, Arrhenius, Williams-Landel-Ferry, Tool-Narayanaswamy-Moynihan, or User defined.

To display this section, click the Show More Options button () and select Discretization from the Show More Options dialog box. Select the element order from the list box for the auxiliary electric field vector variables en.

You can change the solution algorithm by using the check box Use local time integration (checked by default). When unchecked, the solution of the equations for the auxiliary dependent variables in Time Dependent study will be governed by the time stepper algorithm used in the solver.

Physics tab with Charge Conservation, Piezoelectric node selected in the model tree: