WHITNEY ELEMENTS TIME-DOMAIN (WETD) METHODS

In this paper, we propose two time domain formulations, based upon the use of Whitney elements, on tetrahedral meshes for solving transient responses of electromagnetic problems. Among the two formulations, one is an implicit unconditionally stable scheme, whereas the other is an explicit scheme which does not involve matrix inversions. Although the implicit scheme results in worse computational complexity, it is extremely appealing for modeling EM problems with fine features. This is because the time step used in the algorithm is determined by accuracy not by stability. Furthermore, we also present in this paper stability analysis using the Z-transform, computational complexity, and several numerical results for the implicit algorithm.