A Cartesian Grid Method for Modeling Charge Distribution on Interfaces via Augmented Technique

In the electrostatic field computations, second-order elliptic interface problems with nonhomogeneous interface jump conditions need to be solved. In realistic applications, often the total electric quantity on the interface is given. However, the charge distribution on the interface corresponding to the nonhomogeneous interface jump condition is unknown. This paper proposes a Cartesian grid method for solving the interface problem with the given total electric quantity on the interface. The proposed method employs both the immersed finite element with the nonhomogeneous interface jump condition and the augmented technique. Numerical experiments are presented to show the accuracy and efficiency of the proposed method.