From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods
The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes...
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| フォーマット: | Journal Article |
| 言語: | English |
| 出版事項: |
2022
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| オンライン･アクセス: | https://hdl.handle.net/10356/160623 |
| _version_ | 1826128227122282496 |
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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 | The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date. |
| first_indexed | 2024-10-01T07:21:29Z |
| format | Journal Article |
| id | ntu-10356/160623 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:21:29Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1606232022-07-28T08:06:54Z From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods Tan, Eng Leong School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Alternating Direction Implicit Computational Electromagnetics The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date. Published version 2022-07-28T08:06:54Z 2022-07-28T08:06:54Z 2022 Journal Article Tan, E. L. (2022). From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods. Axioms, 11(1), 23-. https://dx.doi.org/10.3390/axioms11010023 2075-1680 https://hdl.handle.net/10356/160623 10.3390/axioms11010023 2-s2.0-85123451510 1 11 23 en Axioms © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Alternating Direction Implicit Computational Electromagnetics Tan, Eng Leong From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title | From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title_full | From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title_fullStr | From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title_full_unstemmed | From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title_short | From time-collocated to leapfrog fundamental schemes for ADI and CDI FDTD Methods |
| title_sort | from time collocated to leapfrog fundamental schemes for adi and cdi fdtd methods |
| topic | Engineering::Electrical and electronic engineering Alternating Direction Implicit Computational Electromagnetics |
| url | https://hdl.handle.net/10356/160623 |
| work_keys_str_mv | AT tanengleong fromtimecollocatedtoleapfrogfundamentalschemesforadiandcdifdtdmethods |