Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations
In this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD m...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023012?viewType=HTML |
| _version_ | 1811252068423303168 |
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| author | Li Zhang Maohua Ran Hanyue Zhang |
| author_facet | Li Zhang Maohua Ran Hanyue Zhang |
| author_sort | Li Zhang |
| collection | DOAJ |
| description | In this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD method and show that the ADI-FDTD method is approximately energy-preserving. In comparison with the energy in theory, the numerical one has two perturbation terms and can be used in computation in order to keep it approximately energy-preserving. Numerical experiments are given to show the performance of the proposed ADI-FDTD method which confirm the theoretical results. |
| first_indexed | 2024-04-12T16:29:20Z |
| format | Article |
| id | doaj.art-78411bc919f9479f88b1a3b563be6be4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T16:29:20Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-78411bc919f9479f88b1a3b563be6be42022-12-22T03:25:13ZengAIMS PressAIMS Mathematics2473-69882023-01-018126428410.3934/math.2023012Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equationsLi Zhang0Maohua Ran1Hanyue Zhang21. V. C. & V. R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610068, China 2. School of Mathematical Science, Sichuan Normal University, Chengdu 610068, China2. School of Mathematical Science, Sichuan Normal University, Chengdu 610068, China 3. School of Mathematics, Aba Teachers University, Aba 623002, China2. School of Mathematical Science, Sichuan Normal University, Chengdu 610068, ChinaIn this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD method and show that the ADI-FDTD method is approximately energy-preserving. In comparison with the energy in theory, the numerical one has two perturbation terms and can be used in computation in order to keep it approximately energy-preserving. Numerical experiments are given to show the performance of the proposed ADI-FDTD method which confirm the theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2023012?viewType=HTMLmaxwell's equationsadi-fdtdenergy methodapproximately energy-preserving |
| spellingShingle | Li Zhang Maohua Ran Hanyue Zhang Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations AIMS Mathematics maxwell's equations adi-fdtd energy method approximately energy-preserving |
| title | Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations |
| title_full | Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations |
| title_fullStr | Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations |
| title_full_unstemmed | Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations |
| title_short | Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations |
| title_sort | energy analysis of the adi fdtd method with fourth order accuracy in time for maxwell s equations |
| topic | maxwell's equations adi-fdtd energy method approximately energy-preserving |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023012?viewType=HTML |
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