A Numerical Method Without Coordinate Transformations to the Electromagnetic Problem Involving Objects in Arbitrary Translational Motion

A novel numerical time-domain method, referred to as Maxwell-Minkowski precise integration time-domain (MM-PITD) method which combines MM equations and the precise integration (PI) technique, is developed in this paper to solve the problems involving moving objects. In the proposed method, the computation cells in different regions bear different governing equations for electromagnetic fields. With the suggested criterion to distinguish the governing equations in these cells, the discretized formulations for the whole computation domain are obtainable. Since the coefficient matrix used in the PI technique is required to be constant or piecewise constant, an approximation approach to locally linearizing the time-variant equation system is provided. Two appealing superiorities of the proposed method to other methods are: 1) the speed of the object can be either constant or time variant and 2) multiple objects can be taken into account conveniently. In addition, the proposed method is more efficient compared with the other methods wherein two or more coordinate frames are used. Several numerical experiments are carried out to test the MM-PITD method. Its effectiveness, efficiency, and generality are thereby confirmed.