Abstract-In this paper, we describe two parallel MRTD algorithms. Both algorithms are proved to be feasible by comparing the result of the serial MRTD method, the efficiency of them are also compared in order to evaluate a better strategy. Moreover, a novel implementation of "complex frequency-shifted" perfect matched layer (CFS-PML) with auxiliary differential equation (ADE) is presented for the MRTD method. The implementation is easier to obtain and more memory saving when treating more generalized media, and numerical results demonstrate that the CFS-PML with ADE is more absorptive than the popularly used APML. Furthermore, using one of the parallel algorithms and the CFS-PML, the characteristic of the field crosssection distribution of the electromagnetic pulse (EMP) propagation in vaulted tunnel is studied.