Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations

Three-dimensional (3-D) orthogonal vector basis functions are developed for the time-domain finite element solution of vector wave equations. These basis functions enforce both the tangential continuity of the electric field and the normal continuity of the electric flux. The stability of the resulting time-domain finite element schemes is investigated and demonstrated to be guaranteed. The use of the proposed basis functions completely eliminates the matrix solution at each time step required by the time-domain finite element solution of vector wave equations. The computational cost thereby scales as O(N_tN) with N_t and N denoting the number of time steps and the number of unknowns, respectively. Defined over tetrahedral elements, the proposed basis functions increase the solution efficiency without compromising the geometry modeling flexibility. Both numerical results and comparison with traditional vector basis functions demonstrate the accuracy as well as the efficiency of the proposed three-dimensional orthogonal vector bases.