Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System
An improved Alternating-Direction-Implicit iterative algorithm with Gauss-Seidel ideology for efficient weighted-Laguerre-polynomial finite-difference time-domain method is proposed in 3-D cylindrical coordinate system. By transferring the coefficient matrix of the conventional WLP-FDTD equation to...
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10182262/ |
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| author | Da-Wei Zhu Hai-Lin Chen Jiachen Xu Bo-Ao Xu Li Zhen |
| author_facet | Da-Wei Zhu Hai-Lin Chen Jiachen Xu Bo-Ao Xu Li Zhen |
| author_sort | Da-Wei Zhu |
| collection | DOAJ |
| description | An improved Alternating-Direction-Implicit iterative algorithm with Gauss-Seidel ideology for efficient weighted-Laguerre-polynomial finite-difference time-domain method is proposed in 3-D cylindrical coordinate system. By transferring the coefficient matrix of the conventional WLP-FDTD equation to the right-side of its equal sign, a linear equation system with ADI characteristic is formed, which makes it more flexible. And then, a correction equation is added to the ADI linear equations and the two-steps Gauss-Seidel procedures are applied to instead of the one-step one in the existing scheme, the purpose of these operations is to speed up the convergence and improve the computation in the term of efficiency and accuracy. Meanwhile, a detailed special treatment scheme for on <inline-formula> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula>-axis and <inline-formula> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula>-direction in 3-D cylindrical coordinate system is introduced and discussed, which demonstrates the importance of on <inline-formula> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula>-axis and <inline-formula> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula>-direction treatment in the proposed method. In addition, the choice scheme in the term of the time-scaling factor <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> and the order of the weighted Laguerre polynomials <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> is discussed. Finally, we develop the Perfectly-Matched-Layer implementation to verify the advantage of the proposed method in accuracy. To validate the term of accuracy and efficiency of the proposed method, six numerical examples are provided. At the same time, the discussions of the convergence speed and stability of the proposed method are presented. |
| first_indexed | 2024-03-12T22:28:13Z |
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| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-12T22:28:13Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| spelling | doaj.art-fea3ad1b2b85455a9af6ba1b8e0458af2023-07-21T23:01:09ZengIEEEIEEE Access2169-35362023-01-0111729507297310.1109/ACCESS.2023.329499210182262Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate SystemDa-Wei Zhu0https://orcid.org/0000-0002-4864-0766Hai-Lin Chen1https://orcid.org/0000-0001-9582-7032Jiachen Xu2Bo-Ao Xu3Li Zhen4College of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing, ChinaNational Key Laboratory on Electromagnetic Environmental Effects and Electro-Optical Engineering, PLA Army Engineering University, Nanjing, ChinaCollege of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing, ChinaRocket Force Academy, Beijing, ChinaCollege of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing, ChinaAn improved Alternating-Direction-Implicit iterative algorithm with Gauss-Seidel ideology for efficient weighted-Laguerre-polynomial finite-difference time-domain method is proposed in 3-D cylindrical coordinate system. By transferring the coefficient matrix of the conventional WLP-FDTD equation to the right-side of its equal sign, a linear equation system with ADI characteristic is formed, which makes it more flexible. And then, a correction equation is added to the ADI linear equations and the two-steps Gauss-Seidel procedures are applied to instead of the one-step one in the existing scheme, the purpose of these operations is to speed up the convergence and improve the computation in the term of efficiency and accuracy. Meanwhile, a detailed special treatment scheme for on <inline-formula> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula>-axis and <inline-formula> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula>-direction in 3-D cylindrical coordinate system is introduced and discussed, which demonstrates the importance of on <inline-formula> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula>-axis and <inline-formula> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula>-direction treatment in the proposed method. In addition, the choice scheme in the term of the time-scaling factor <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> and the order of the weighted Laguerre polynomials <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> is discussed. Finally, we develop the Perfectly-Matched-Layer implementation to verify the advantage of the proposed method in accuracy. To validate the term of accuracy and efficiency of the proposed method, six numerical examples are provided. At the same time, the discussions of the convergence speed and stability of the proposed method are presented.https://ieeexplore.ieee.org/document/10182262/Finite-difference time-domain (FDTD) methodweighted Laguerre polynomial (WLP)altering-direction implicit (ADI)Gauss–Seidel ideologycorrection equation |
| spellingShingle | Da-Wei Zhu Hai-Lin Chen Jiachen Xu Bo-Ao Xu Li Zhen Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System IEEE Access Finite-difference time-domain (FDTD) method weighted Laguerre polynomial (WLP) altering-direction implicit (ADI) Gauss–Seidel ideology correction equation |
| title | Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System |
| title_full | Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System |
| title_fullStr | Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System |
| title_full_unstemmed | Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System |
| title_short | Improved ADI Iterative Algorithm With Gauss-Seidel Ideology for Efficient WLP-FDTD Method in 3-D Cylindrical Coordinate System |
| title_sort | improved adi iterative algorithm with gauss seidel ideology for efficient wlp fdtd method in 3 d cylindrical coordinate system |
| topic | Finite-difference time-domain (FDTD) method weighted Laguerre polynomial (WLP) altering-direction implicit (ADI) Gauss–Seidel ideology correction equation |
| url | https://ieeexplore.ieee.org/document/10182262/ |
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