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The finite difference time domain method (FDTD) is a popular and effective numerical approach for electromagnetic analysis. However, the original explicit FDTD suffers from two primary limitations: the time step is constrained by the Courant-Friedrich-Levy (CFL) condition, and it requires significant amounts of computer memory, particularly when analyzing large objects with fine structures. In this paper, we present a new FDTD algorithm called Reduced-Leapfrog Alternating-Direction-Implicit FDTD (R-Leapfrog ADI-FDTD), which is unconditionally stable and reduces computer memory usage by approximately 23%. The algorithm is based on a conservation formula derived from the conventional electromagnetic divergence. This formula describes the spatial dependence of the field components obtained by the one-step leapfrog ADI-FDTD. By leveraging this spatial dependence, we are able to locally calculate and temporarily store two of the six field components during each iteration, while the remaining four components are stored over the entire 3D spatial grid as usual. Our simulations show that the results are in excellent agreement with those obtained from the original explicit FDTD and one-step leapfrog ADI-FDTD, demonstrating the algorithm’s unconditional stability and accuracy. R-Leapfrog ADI-FDTD is a valuable tool for electromagnetic analysis when computer memory is a critical factor.
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