Uniform Treatment of Numerical Time-Integrations of the Maxwell Equations

摘要

In this paper we show how the existing numerical time-integration methods of the Maxwell equations can be handled in the framework of the theory of operator splitting methods. We consider the classical Yee-method, the Namiki-Zheng-Chen-Zhang alternating direction implicit method (NZCZ) and the Kole-Figge-De Raedt method (KFR). The unconditional stability of the NZCZ-method has been proven only by means of extensive use of computer algebraic tools. We give a pure mathematical proof. We compare the methods from the point of view of accuracy and computational speed.