Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions
Abstract To obtain high accuracy and efficiency in the simulations, an optimum time step should be taken in finite‐difference time‐domain (FDTD) methods. The authors investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-06-01
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| Series: | IET Microwaves, Antennas & Propagation |
| Online Access: | https://doi.org/10.1049/mia2.12068 |
| _version_ | 1811188148376436736 |
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| author | Yu Cheng Guangzhi Chen Xiang‐Hua Wang Shunchuan Yang |
| author_facet | Yu Cheng Guangzhi Chen Xiang‐Hua Wang Shunchuan Yang |
| author_sort | Yu Cheng |
| collection | DOAJ |
| description | Abstract To obtain high accuracy and efficiency in the simulations, an optimum time step should be taken in finite‐difference time‐domain (FDTD) methods. The authors investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously analytical and numerical analysis, it is found that small time steps of the FDTD methods do not always have small numerical errors. Our findings reveal that these two FDTD methods present different behaviours with respect to time steps: (1) for the FDTD(2,2) method, smaller time steps limited by the Courant‐Friedrichs‐Lewy condition increase numerical dispersion and lead to larger simulation errors and (2) for the FDTD(2,4) method, as the time step increases, numerical dispersion errors first decrease and then increase. Our findings are also comprehensively validated from one‐ to three‐dimensional cases through several numerical examples including wave propagation, resonant frequencies of cavities and a practical engineering problem. |
| first_indexed | 2024-04-11T14:14:36Z |
| format | Article |
| id | doaj.art-692aaaf2711244349910469b3372dfc7 |
| institution | Directory Open Access Journal |
| issn | 1751-8725 1751-8733 |
| language | English |
| last_indexed | 2024-04-11T14:14:36Z |
| publishDate | 2021-06-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Microwaves, Antennas & Propagation |
| spelling | doaj.art-692aaaf2711244349910469b3372dfc72022-12-22T04:19:33ZengWileyIET Microwaves, Antennas & Propagation1751-87251751-87332021-06-0115769170310.1049/mia2.12068Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusionsYu Cheng0Guangzhi Chen1Xiang‐Hua Wang2Shunchuan Yang3School of Electronic and Information Engineering Beihang University Haidian District Beijing ChinaSchool of Electronic and Information Engineering Beihang University Haidian District Beijing ChinaSchool of Science Tianjin University of Technology and Education Hexi District Tianjin ChinaResearch Institute for Frontier Science and the School of Electronic and Information Engineering Beihang University Haidian District Beijing ChinaAbstract To obtain high accuracy and efficiency in the simulations, an optimum time step should be taken in finite‐difference time‐domain (FDTD) methods. The authors investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously analytical and numerical analysis, it is found that small time steps of the FDTD methods do not always have small numerical errors. Our findings reveal that these two FDTD methods present different behaviours with respect to time steps: (1) for the FDTD(2,2) method, smaller time steps limited by the Courant‐Friedrichs‐Lewy condition increase numerical dispersion and lead to larger simulation errors and (2) for the FDTD(2,4) method, as the time step increases, numerical dispersion errors first decrease and then increase. Our findings are also comprehensively validated from one‐ to three‐dimensional cases through several numerical examples including wave propagation, resonant frequencies of cavities and a practical engineering problem.https://doi.org/10.1049/mia2.12068 |
| spellingShingle | Yu Cheng Guangzhi Chen Xiang‐Hua Wang Shunchuan Yang Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions IET Microwaves, Antennas & Propagation |
| title | Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions |
| title_full | Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions |
| title_fullStr | Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions |
| title_full_unstemmed | Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions |
| title_short | Investigation of numerical dispersion with time step of the FDTD methods: avoiding erroneous conclusions |
| title_sort | investigation of numerical dispersion with time step of the fdtd methods avoiding erroneous conclusions |
| url | https://doi.org/10.1049/mia2.12068 |
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