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An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity

Abstract

In plasma simulation, we often only know the total electric quantity on the surface of the object, not the charge density distribution on the surface which appears as the non-homogeneous flux jump condition in the usual interface problems. Based on structured meshes independent of the interface, this article proposes an iterative method, which employs both the immersed finite element (IFE) method with non-homogeneous flux jump conditions and the regular finite element method with ghost nodes introduced in the object, to solve the 2D interface problem for the potential field according to the given total electric quantity on the surface of the object. Numerical experiments are provided to illustrate the accuracy and efficiency of the proposed method.