Formulations in Transient electric
Transient electric is the most generic formulation of electric field analysis in the absence of magnetic field. In this formulation, the field sources (voltage or current) can be arbitrary functions of time, and electric properties of materials can vary with electric field.
The problem formulation is similar to AC conduction: \[ -∇ \left [ σ(E) · ∇ U \right ] - \frac{\partial}{\partial t} ∇ · \left[ ε(E) · ∇ U \right] = 0, \]
where electric conductivity σ and electric permittivity ε can be nonlinear or anisotropic.