WETD - a finite element time-domain approach for solving Maxwell´s equations

A family of finite element time-domain methods, WETD(Θ), is derived to solve the time-varying Maxwell´s equations. The proposed methodology is based upon the application of the Faedo-Galerkin procedure and the use of the Whitney 1-forms as bases to result in an ordinary differential equation in time for the electric field. Moreover, the resultant ordinary differential equation is solved by employing central and/or backward difference approximations. Since the WETD methods presented here are used in conjunction with tetrahedral finite element meshes, it imposes no limitations on the problem geometry. Also, in this contribution, a general stability condition has been derived for the WETD(Θ) method of which the central and backward differences are special cases corresponding to Θ=1 and Θ=0, respectively