Solving Maxwell´s equations by edge element time domain methods

The finite difference time domain (FDTD) algorithm has been used widely in solving the transient responses of electromagnetic problems. However, in its original form, it is difficult to model complex EM problems with curved surfaces using the FDTD method. Many variants have been proposed in the past with the aim to circumvent this difficulty with varying degrees success. Almost all of these approaches are based upon, one form or the other, the use of finite difference approximation in both spatial and temporal domains. This paper shows a finite element time domain formulation, the Whitney (1954) element time domain (WETD) method, which uses Whitney l-forms in the spatial domain and the finite difference in the time domain, respectively, for solving Maxwell´s equations. In this way, the proposed WETD method can be used on a tetrahedral finite element mesh and consequently, it imposes no geometric limitations. We also generalize the formulation by the /spl Theta/ method to three WETD methods depending on the choice of /spl Theta/. In particular, both the WETD1 and WETD3 methods are unconditionally stable. Therefore, the time step used in the computation can always be chosen with compatible resolution with its spatial counterparts.