A new finite-difference time-domain algorithm for solving Maxwell´s equations

An algorithm is presented for deriving finite-difference-time-domain (FD-TD) solutions of Maxwell´s equations. When compared with Yee´s method (1966), it is found that the stability conditions for this method exceed those of Yee´s method by the factors 1.41 and 1.73, respectively, for the two-dimensional and three-dimensional cases. The algorithm is compatible with both Yee´s method and the finite-element-time domain method, thereby allowing for unification of the two. The algorithm will also provide greater flexibility in formulating and studying the multigrid method, the variable mesh method, and the method of finite difference approximations of the boundary conditions.<>