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 one of the following option:

For a single pole Debye dispersion model, you can enter the Relaxation time and Relative permittivity contribution. These parameters can be either scalar, or diagonal matrices to account for possible anisotropy in the material.

For the Multipole Debye model, you can enter any number of Relaxation time and the corresponding Relative permittivity contribution values using an input table with dynamically changed size. However, only scalar values can be entered.

Both models are directly suitable for Eigenfrequency, Frequency Domain and Time Dependent study types. And for these study types, 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 Low frequency limit).

In the Thermal Effects section, you can select the Shift function type, which will be used to compute the effective relaxation time accounting for the temperature effects.

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 use an equivalent Multipole Debye model and automatically deduce the necessary number of 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 the Cole-Cole model, you enter a fractional order parameter, the Complementary broadening parameter αCC that controls a symmetric (in log-space) broadening of the spectrum. Note that its acceptable value is limited to the range from 0 to 1.

For the Havriliak-Negami model, you can enter two fractional order parameters, the Symmetric broadening parameter βHN with the value limited to the range from 0 to 1, and the Asymmetric broadening parameter γHN with the value limited to the range from 0 to 1/βHN.

At the Time Domain and Eigenfrequency section, you can compute an approximation for the complex valued relative permittivity contribution.

By default, the approximation is not computed. Without it, the Cole-Cole and Havriliak-Negami models are limited to Frequency Domain study type only.

The approximation computation needs to be done as a preprocessing step. Use the Compute approximation () action button that is available at the Time Domain and Eigenfrequency section. Once the computation has been performed, you can preview it using the Preview plot () action button that will become active at the section. The approximation corresponds to the Multipole Debye model. You can check the Show approximation data checkbox to inspect the computed parameter values.

For all study types, 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 Low frequency limit).

Enter expressions for the real and imaginary parts of the relative permittivity contribution, Δε’ and Δε''. Also enter the value of the real part of the contribution in the low frequency limit Δε'(0). Note that the imaginary part of the contribution is always assumed to be zero in the low frequency limit.

At the Time Domain and Eigenfrequency section, you can compute an approximation for the complex valued relative permittivity contribution.

By default, the approximation is not computed. Without it, the User defined model is limited to Frequency Domain study type only.

The approximation computation needs to be done as a preprocessing step. Use the Compute approximation () action button that is available at the Time Domain and Eigenfrequency section. Once the computation has been performed, you can preview it using the Preview plot () action button that will become active at the section. The approximation corresponds to the Multipole Debye model. You can check the Show approximation data checkbox to inspect the computed parameter values.

Note that for the User defined dispersion model, the relative permittivity input, εrS, on the parent node will be interpreted should be interpreted as the low frequency limit.

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. 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 checkbox 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 either Charge Conservation or Charge Conservation, Piezoelectric node selected in the model tree: