Nonlinear Solution - 3D AC Conduction Solver

Unlike linear problems in which the field solution is assumed to be based on the sinusoidal complex peak field values in a steady state, nonlinear problems are usually based on all harmonic components of the fields.

The 3D AC Conduction solver supports the J-E and D-E nonlinear properties, as stated in the constitutive relations:

Thus for nonlinear problems, though the electric field is sinusoidal due to sinusoidal excitations, the resulting D and/or J fields can be “harmonically rich” due to the material nonlinearity.

Although the D and J fields are not sinusoidal at output, the Maxwell 3D AC Conduction solver uses an effective property based on the sinusoidal E to approximate nonlinear field behavior associated with the assigned nonlinear JE and DE characteristic. Using the JE curve as an example, the effective conductivity is expressed by

The above equation is used to obtain the effective material property for each electric field value in the original curve, allowing to generate a new curve based on the effective properties. During the simulation process, the effective curve is used to calculate the conductivity and permittivity.