A problem about TF/SF technique in the FDTD simulations of cylindrical waves and spherical waves

The finite difference time domain methods(FDTD methods) are the most popular simulation methods of the electromagnetic waves, and the total field/scattered field technique(TF/SF technique) is the main source technique of the FDTD methods. The amplitude of the electric fields and the amplitude of the magnetic fields are considered as invariant in the connection interface between the total field regions and the scattered field regions, when cylindrical waves and spherical waves are simulated by the FDTD methods and the TF/SF technique is applied. But this consideration is wrong because that the amplitude of cylindrical waves and the amplitude of spherical waves are both not constants on the direction of propagation, and thus the computational results are effected. A new method for applying TF/SF technique in the FDTD simulations of cylindrical waves and spherical waves is brought forward. The method considers the variations of the amplitude of cylindrical waves and the amplitude of spherical waves on the direction of propagation, and thus the problem is solved. Numerical experiments were done, and the experiments indicate that the new method can effectively improve the simulation results.