Implementation of convolutional perfectly matched layer for three-dimensional hybrid implicit-explicit finite-difference time-domain method

The hybrid implicit-explicit (HIE) finite-difference time-domain (FDTD) method with the convolutional perfectly matched layer (CPML) is extended to a full three-dimensional scheme in this article. To demonstrate the application of the CPML better, the entire derivation process is presented, in which the fine scale structure is changed from y-direction to z-direction of the propagation innovatively. The numerical examples are adopted to verify the efficiency and accuracy of the proposed method. Numerical results show that the HIE-FDTD with CPML truncation has the similar relative reflection error with the FDTD with CPML method, but it is much better than the methods with Mur absorbing boundary. Although Courant-Friedrich-Levy number climbs to 8, the maximum relative error of the proposed HIE-CPML remains more below than -71 dB, and CPU time is nearly 72.1% less than the FDTD-CPML. As an example, a low-pass filter is simulated by using the FDTD-CPML and HIE-CPML methods. The curves obtained are highly fitted between two methods; the maximum errors are lower than -79 dB. Furthermore, the CPU time saved much more, accounting for only 26.8% of the FDTD-CPML method while the same example simulated.