Numerical studies of the phase field model describing electric breakdown in a heterogeneous medium

This paper presents the results of numerical studies of the phase field model for the development of an electrical breakdown path. The model consists of Maxwell's equations in the quasi(electro)stationary approximation, the electric charge balance equation, and the Allen—Cahn equation describing the phase field evolution. Several problem settings concerning the development of a breakdown path in homogeneous as well as macro- and microheterogeneous media are considered.