研究目的
To develop a one-step leapfrog hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method for Drude dispersive media and verify its stability and efficiency, particularly for simulating surface plasmon polaritons on graphene sheets.
研究成果
The proposed one-step leapfrog HIE-FDTD method for Drude media maintains the same stability condition as conventional HIE-FDTD and is efficient for simulating fine-grid structures like graphene sheets, with acceptable errors and reduced computational time compared to other methods.
研究不足
The method's stability is conditional on the grid cell size along one direction, and errors increase with higher CFLN. It is specifically tailored for Drude media and may not generalize to other dispersive models without modification.
1：Experimental Design and Method Selection:
The study employs a one-step leapfrog HIE-FDTD method for Drude media, using a semi-implicit auxiliary differential equation to model the current source. Stability is analyzed using the von Neumann method, and numerical experiments are conducted to validate the method.
2：Sample Selection and Data Sources:
A plasma-filled perfect electric conductor (PEC) cavity and a one-atom-thick graphene sheet are used as test cases. Parameters include grid cell sizes, frequencies, and material properties.
3：List of Experimental Equipment and Materials:
Computational simulations are performed using a ThinkPad PC with Intel i7 7820 processor and 16 GB RAM. No physical equipment is mentioned.
4：Experimental Procedures and Operational Workflow:
The method involves discretizing Maxwell's equations, applying the Crank–Nicolson method, and implementing update equations for electric and magnetic fields. Simulations are run with varying Courant–Friedrich–Levy numbers (CFLN) to test stability and accuracy.
5：Data Analysis Methods:
Relative errors are calculated by comparing results with conventional FDTD. Stability is assessed through numerical analysis of growing factors.
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