Divergence correction techniques for Maxwell solvers based on a hyperbolicmodel

Usually, non-stationary numerical calculations in electromagnetics are base d on the hyperbolic evolution equations for the electric and magnetic field s and leave Gauss' law out of consideration because the latter is a consequ ence of the former and of the charge conservation equation in the continuou s case. However, in the simulation of the self-consistent movement of charg ed particles in electromagnetic fields, it is a well-known fact that the ap proximation of the particle motion introduces numerical errors and that, co nsequently, the charge conservation equation is not satisfied on the dicret e level. Then, in order to avoid the increase of errors in Gauss' law, a di vergence cleaning step which solves a Poisson equation for a correction pot ential is often added. In the present paper, a new method for incorporating Gauss' law into non-stationary electromagnetic simulation codes is develop ed, starting from a constrained formulation of the Maxwell equations. The r esulting system is hyperbolic, and the divergence errors propagate with the speed of light to the boundary of the computational domain. Furthermore, t he basic ideas of the numerical approximation are introduced and the extend ed hyperbolic system is treated numerically within the framework of high-re solution finite-volume schemes. Simulation results obtained with this new t echnique for pure electromagnetic wave propagation and for an electromagnet ic particle-in-cell computation are presented and compared with Other metho ds. (C) 2000 Academic Press.