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One‐Step Leapfrog Locally 1D Theory with Higher‐Order Enhanced Absorption for Fine‐Details Simulation

One‐Step Leapfrog Locally 1D Theory with Higher‐Order Enhanced Absorption for Fine‐Details... Based on a higher‐order concept and one‐step leapfrog formulation, an unconditionally stable leapfrog locally 1D (LOD) perfectly matched layer (PML) is proposed to not only enhance the absorbing performance in terminating an unbounded finite‐difference time‐domain (FDTD) algorithm but also improve the computational efficiency compared with the LOD‐FDTD algorithm. Most precisely, the PML is implemented by the auxiliary differential equations method. By applying the proposed scheme to a 3D electromagnetics simulation, the proposal can utilize the unconditionally stable algorithm, one‐step leapfrog formulation, and higher‐order concept in terms of attenuating low‐frequency propagation waves, enhancing the performance, and improving the computational efficiency. Numerical examples including the magic‐T waveguide model, very large‐scale integration circuits, and the structure of metamaterials are investigated to further demonstrate the efficiency, performance, and unconditional stability. The results help conclude that the proposed scheme can attain better performance and efficiency when the time step far surpasses the Courant–Friedrichs–Lewy limit. Most importantly, by employing the one‐step leapfrog formulation in the LOD algorithm, the memory requirements and simulation duration can be reduced significantly, indicating the improvement of the algorithm compared with the published LOD schemes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Theory and Simulations Wiley

One‐Step Leapfrog Locally 1D Theory with Higher‐Order Enhanced Absorption for Fine‐Details Simulation

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References (17)

Publisher
Wiley
Copyright
© 2022 Wiley‐VCH GmbH
eISSN
2513-0390
DOI
10.1002/adts.202200073
Publisher site
See Article on Publisher Site

Abstract

Based on a higher‐order concept and one‐step leapfrog formulation, an unconditionally stable leapfrog locally 1D (LOD) perfectly matched layer (PML) is proposed to not only enhance the absorbing performance in terminating an unbounded finite‐difference time‐domain (FDTD) algorithm but also improve the computational efficiency compared with the LOD‐FDTD algorithm. Most precisely, the PML is implemented by the auxiliary differential equations method. By applying the proposed scheme to a 3D electromagnetics simulation, the proposal can utilize the unconditionally stable algorithm, one‐step leapfrog formulation, and higher‐order concept in terms of attenuating low‐frequency propagation waves, enhancing the performance, and improving the computational efficiency. Numerical examples including the magic‐T waveguide model, very large‐scale integration circuits, and the structure of metamaterials are investigated to further demonstrate the efficiency, performance, and unconditional stability. The results help conclude that the proposed scheme can attain better performance and efficiency when the time step far surpasses the Courant–Friedrichs–Lewy limit. Most importantly, by employing the one‐step leapfrog formulation in the LOD algorithm, the memory requirements and simulation duration can be reduced significantly, indicating the improvement of the algorithm compared with the published LOD schemes.

Journal

Advanced Theory and Simulations – Wiley

Published: Nov 1, 2022

Keywords: auxiliary differential equations (ADE); finite‐difference time‐domain (FDTD); locally 1D (LOD); one‐step leapfrog formulation; perfectly matched layer (PML)

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