Incident plane-wave source formulations for leapfrog complying-divergence implicit FDTD method

• Main Authors: Liu, Shuo, Tan, Eng Leong, Zou, Bin
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2024
• Subjects: Engineering; Finite-difference time-domain method; Unconditionally stable method; Complying-divergence implicit; Scattered field techniques; Total-field/scattered field techniques
• Online Access: https://hdl.handle.net/10356/178488
• Institution: Nanyang Technological University

The commonly used unconditionally stable finite-difference time-domain (FDTD) methods such as alternating direction implicit (ADI)-FDTD, and its one-step formulation, leapfrog ADI-FDTD, have been found to violate the divergence condition of Gauss's law. The recently proposed leapfrog complying-divergence implicit (CDI)-FDTD not only addresses this problem, but also features many advantages, including unconditional stability, minimal floating-point operations and one-step leapfrog update. To further expand its application, this paper presents the incident plane-wave source formulations for leapfrog CDI-FDTD. Two stable and efficient formulations with different advantages are presented for introducing the far-zone plane-wave source into the FDTD problem space, namely, the scattered-field (SF) formulation and total-field / scattered field (TF/SF) formulation. To deal with the discontinuity and inconsistency across TF/SF boundaries, the fields on the boundaries need special treatments with careful modifications to ensure stability and proper plane-wave injection. Numerical results show that the incident fields can be effectively injected into the problem space with the stability of leapfrog CDI-FDTD maintained in both formulations. In addition, comparisons of radar cross sections computed using leapfrog CDI-FDTD, leapfrog ADI-FDTD and explicit FDTD with both SF and TF/SF formulations are presented. These demonstrate the advantages of leapfrog CDI-FDTD method in solving far-zone plane-wave source problems, including high efficiency, unconditional stability and complying divergence.