Fast alternating direction iterative method for poisson equation of potential
A fast alternating direction iterative (ADI) method is presented for solving Poisson equation of potential. The method has all right-hand sides (RHS) free of differential operator with the forcing function to be included in one step only. The derivation of Poisson equation is carried out based on Ga...
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| Format: | Conference Paper |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/10356/178498 |
| _version_ | 1811693338784432128 |
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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 | A fast alternating direction iterative (ADI) method is presented for solving Poisson equation of potential. The method has all right-hand sides (RHS) free of differential operator with the forcing function to be included in one step only. The derivation of Poisson equation is carried out based on Gauss’s law and Coulomb gauge for inhomogeneous media. The formulation of classical ADI method is also considered whereby the RHS still contain differential operators. Introducing the temporary auxiliary variable and manipulating the RHS terms lead to formulation of the fast ADI method. The computational efficiency is discussed in terms of flops count and memory requirement. Compared to the classical method, the fast ADI method has led to substantial flops count reduction and both methods require the same amount of memory space. Numerical results are illustrated with considerable simplification of each iteration using the fast ADI method having operator-free RHS. |
| first_indexed | 2024-10-01T06:50:06Z |
| format | Conference Paper |
| id | ntu-10356/178498 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:50:06Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1784982024-06-28T15:38:55Z Fast alternating direction iterative method for poisson equation of potential Tan, Eng Leong School of Electrical and Electronic Engineering 2022 International Conference on Electromagnetics in Advanced Applications (ICEAA) Engineering Finite-difference method Alternating direction iterative Poisson equation Potential Gauge condition A fast alternating direction iterative (ADI) method is presented for solving Poisson equation of potential. The method has all right-hand sides (RHS) free of differential operator with the forcing function to be included in one step only. The derivation of Poisson equation is carried out based on Gauss’s law and Coulomb gauge for inhomogeneous media. The formulation of classical ADI method is also considered whereby the RHS still contain differential operators. Introducing the temporary auxiliary variable and manipulating the RHS terms lead to formulation of the fast ADI method. The computational efficiency is discussed in terms of flops count and memory requirement. Compared to the classical method, the fast ADI method has led to substantial flops count reduction and both methods require the same amount of memory space. Numerical results are illustrated with considerable simplification of each iteration using the fast ADI method having operator-free RHS. Ministry of Education (MOE) Submitted/Accepted version The author would like to acknowledge the support from Singapore Ministry of Education through research grant RG49/21. 2024-06-24T08:29:16Z 2024-06-24T08:29:16Z 2022 Conference Paper Tan, E. L. (2022). Fast alternating direction iterative method for poisson equation of potential. 2022 International Conference on Electromagnetics in Advanced Applications (ICEAA), 133-136. https://dx.doi.org/10.1109/ICEAA49419.2022.9899999 978-1-6654-8112-0 https://hdl.handle.net/10356/178498 10.1109/ICEAA49419.2022.9899999 133 136 en RG49/21 © 2022 IEEE. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1109/ICEAA49419.2022.9899999. application/pdf |
| spellingShingle | Engineering Finite-difference method Alternating direction iterative Poisson equation Potential Gauge condition Tan, Eng Leong Fast alternating direction iterative method for poisson equation of potential |
| title | Fast alternating direction iterative method for poisson equation of potential |
| title_full | Fast alternating direction iterative method for poisson equation of potential |
| title_fullStr | Fast alternating direction iterative method for poisson equation of potential |
| title_full_unstemmed | Fast alternating direction iterative method for poisson equation of potential |
| title_short | Fast alternating direction iterative method for poisson equation of potential |
| title_sort | fast alternating direction iterative method for poisson equation of potential |
| topic | Engineering Finite-difference method Alternating direction iterative Poisson equation Potential Gauge condition |
| url | https://hdl.handle.net/10356/178498 |
| work_keys_str_mv | AT tanengleong fastalternatingdirectioniterativemethodforpoissonequationofpotential |