An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation
The alternating direction implicit parabolic equation (ADI-PE) method and the Crank–Nicolson parabolic equation (CN-PE) method have been widely used for solving the 3D parabolic equation (3D-PE) in radio wave propagation. The ADI-PE method is more computationally efficient than the CN-PE method. The...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2023/9955888 |
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| _version_ | 1849699783609942016 |
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| author | Xiaoping Wu Zihao Li Zhixi Liang Yunliang Long |
| author_facet | Xiaoping Wu Zihao Li Zhixi Liang Yunliang Long |
| author_sort | Xiaoping Wu |
| collection | DOAJ |
| description | The alternating direction implicit parabolic equation (ADI-PE) method and the Crank–Nicolson parabolic equation (CN-PE) method have been widely used for solving the 3D parabolic equation (3D-PE) in radio wave propagation. The ADI-PE method is more computationally efficient than the CN-PE method. The accuracy of the ADI-PE method is improved by the higher-order Mitchell–Fairweather (MF)-ADI method. This paper presents an iterative high-accuracy (IHA)-ADI method for the 3D parabolic equation. A derivation of the proposed method is presented. The convergence and stability of the proposed method are estimated. Several numerical examples are considered to illustrate the advantages of the proposed method. The results of error analysis and a comparative study show that the proposed method is unconditionally stable and computationally efficient. The proposed method is more numerically accurate than the MF-ADI method. |
| format | Article |
| id | doaj-art-326e2394327e4762ad0409fce04dabe2 |
| institution | DOAJ |
| issn | 1687-5877 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-326e2394327e4762ad0409fce04dabe22025-08-20T03:18:30ZengWileyInternational Journal of Antennas and Propagation1687-58772023-01-01202310.1155/2023/9955888An Iterative High-Accuracy ADI Method for the 3D Parabolic EquationXiaoping Wu0Zihao Li1Zhixi Liang2Yunliang Long3School of Electronics and Information TechnologySchool of Electronics and Information TechnologySchool of Electronics and Information TechnologySchool of Electronics and Information TechnologyThe alternating direction implicit parabolic equation (ADI-PE) method and the Crank–Nicolson parabolic equation (CN-PE) method have been widely used for solving the 3D parabolic equation (3D-PE) in radio wave propagation. The ADI-PE method is more computationally efficient than the CN-PE method. The accuracy of the ADI-PE method is improved by the higher-order Mitchell–Fairweather (MF)-ADI method. This paper presents an iterative high-accuracy (IHA)-ADI method for the 3D parabolic equation. A derivation of the proposed method is presented. The convergence and stability of the proposed method are estimated. Several numerical examples are considered to illustrate the advantages of the proposed method. The results of error analysis and a comparative study show that the proposed method is unconditionally stable and computationally efficient. The proposed method is more numerically accurate than the MF-ADI method.http://dx.doi.org/10.1155/2023/9955888 |
| spellingShingle | Xiaoping Wu Zihao Li Zhixi Liang Yunliang Long An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation International Journal of Antennas and Propagation |
| title | An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation |
| title_full | An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation |
| title_fullStr | An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation |
| title_full_unstemmed | An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation |
| title_short | An Iterative High-Accuracy ADI Method for the 3D Parabolic Equation |
| title_sort | iterative high accuracy adi method for the 3d parabolic equation |
| url | http://dx.doi.org/10.1155/2023/9955888 |
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