Unconditionally Stable Leapfrog Complying Divergence Implicit FDTD Method with Lumped Elements

This article presents a rapid calculation approach of the leapfrog complying divergence implicit (LCDI) finite-difference time-domain (FDTD) method incorporating lumped elements for highly efficient electromagnetic (EM) simulations. First, the current densities corresponding to lumped resistor, capacitor, and inductor are integrated into the fundamental equations of the LCDI-FDTD method. Then, a stability analysis based on von Neumann method and Jury criterion demonstrates that the proposed method achieves unconditional stability under different lumped elements. The program of this proposed method is constructed upon the basic LCDI-FDTD framework, rendering it highly feasible and straightforward to implement. The detailed implementation process numerical boundaries in the proposed method is analyzed, as is the introduction of lumped elements to the LCDI-FDTD program. Finally, the numerical verification of three absorbers shows that the computational speedup ratio (SR) of the proposed method is more than 20 times that of the traditional FDTD method. Furthermore, the proposed method is more efficient and has a smaller numerical error than leapfrog alternating direction implicit (LADI) FDTD method. The proposed method facilitates the design and analysis of EM devices with lumped elements.