ON THE CONSTRUCTION OF DISCRETE GAUSS LAWS FOR TIME-DOMAIN METHODS

摘要

The paper presents a method for constructing a suitable discrete Gauss law for a given discretization scheme for the Maxwell equations. Here, suitable means that if the discrete Gauss law is fulfilled initially the discrete time evolution given by the time-domain method ensures that the discrete Gauss law is always fulfilled. Furthermore, conditions for the existence of such a law in the discrete sense are given. The construction of suitable Gauss laws and current interpolations is of importance in the context of Particle-In-Cell methods. In particular, the method is applied to the Longitudinal-Transversal Verlet-Leapfrog scheme.