Efficient algorithms for crank-nicolson-based finite-difference time-domain methods
This paper presents new efficient algorithms for implementing 3-D Crank-Nicolson-based finite-difference time-domain (FDTD) methods. Two recent methods are considered, namely, the Crank-Nicolson direct-splitting (CNDS) and Crank-Nicolson cycle-sweep-uniform (CNCSU) FDTD methods. The algorithms invol...
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/138297 |
| _version_ | 1811682087847067648 |
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| author | Tan, Eng Leong |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Tan, Eng Leong |
| author_sort | Tan, Eng Leong |
| collection | NTU |
| description | This paper presents new efficient algorithms for implementing 3-D Crank-Nicolson-based finite-difference time-domain (FDTD) methods. Two recent methods are considered, namely, the Crank-Nicolson direct-splitting (CNDS) and Crank-Nicolson cycle-sweep-uniform (CNCSU) FDTD methods. The algorithms involve update equations whose right-hand sides are much simpler and more concise than the original ones. Analytical proof is provided to show the equivalence of original and present methods. Comparison of their implementations signifies substantial reductions of the floating-point operations count in the new algorithms. Other computational aspects are also optimized, particularly in regard to the for-looping overhead and the memory space requirement. Through numerical simulation and Fourier stability analysis, it is found that while the CNDS FDTD is unconditionally stable, the CNCSU FDTD may actually become unstable. |
| first_indexed | 2024-10-01T03:51:16Z |
| format | Journal Article |
| id | ntu-10356/138297 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:51:16Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1382972020-04-30T05:12:43Z Efficient algorithms for crank-nicolson-based finite-difference time-domain methods Tan, Eng Leong School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Computational Electromagnetics Finite-difference Time-domain Methods This paper presents new efficient algorithms for implementing 3-D Crank-Nicolson-based finite-difference time-domain (FDTD) methods. Two recent methods are considered, namely, the Crank-Nicolson direct-splitting (CNDS) and Crank-Nicolson cycle-sweep-uniform (CNCSU) FDTD methods. The algorithms involve update equations whose right-hand sides are much simpler and more concise than the original ones. Analytical proof is provided to show the equivalence of original and present methods. Comparison of their implementations signifies substantial reductions of the floating-point operations count in the new algorithms. Other computational aspects are also optimized, particularly in regard to the for-looping overhead and the memory space requirement. Through numerical simulation and Fourier stability analysis, it is found that while the CNDS FDTD is unconditionally stable, the CNCSU FDTD may actually become unstable. Accepted version 2020-04-30T05:12:42Z 2020-04-30T05:12:42Z 2008 Journal Article Tan, E. L. (2008). Efficient algorithms for crank-nicolson-based finite-difference time-domain methods. IEEE Transactions on Microwave Theory and Techniques, 56(2), 408-413. doi:10.1109/TMTT.2007.914641 0018-9480 https://hdl.handle.net/10356/138297 10.1109/TMTT.2007.914641 2-s2.0-38849184093 2 56 408 413 en IEEE Transactions on Microwave Theory and Techniques © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TMTT.2007.914641 application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Computational Electromagnetics Finite-difference Time-domain Methods Tan, Eng Leong Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title | Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title_full | Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title_fullStr | Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title_full_unstemmed | Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title_short | Efficient algorithms for crank-nicolson-based finite-difference time-domain methods |
| title_sort | efficient algorithms for crank nicolson based finite difference time domain methods |
| topic | Engineering::Electrical and electronic engineering Computational Electromagnetics Finite-difference Time-domain Methods |
| url | https://hdl.handle.net/10356/138297 |
| work_keys_str_mv | AT tanengleong efficientalgorithmsforcranknicolsonbasedfinitedifferencetimedomainmethods |