{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T11:41:45Z","timestamp":1770464505455,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T00:00:00Z","timestamp":1660867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62105367"],"award-info":[{"award-number":["62105367"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42175154"],"award-info":[{"award-number":["42175154"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020JJ4662"],"award-info":[{"award-number":["2020JJ4662"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["62105367"],"award-info":[{"award-number":["62105367"]}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["42175154"],"award-info":[{"award-number":["42175154"]}]},{"name":"Hunan Provincial Natural Science Foundation of China","award":["2020JJ4662"],"award-info":[{"award-number":["2020JJ4662"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The invariant imbedding T-matrix (IIM T-matrix) model is regarded as one of the most promising models for calculating the scattering parameters of non-spherical particles. However, the IIM T-matrix model needs to be iterated along the radial direction when calculating the T-matrix, which involves complex calculations such as matrix inversion and multiplication. Therefore, how to improve its computational efficiency is an important problem to be solved. Focused on particles with N-fold symmetric geometry, this paper deduced the symmetry in the calculation process of the IIM T-matrix model, derived the block iteration scheme of the T-matrix, and contracted the IIM T-matrix program for particles with N-fold symmetric geometry. Discrete Dipole Approximation (DDA) and Geometrical Optics Approximation (IGOA) were employed to verify the accuracy of the improved IIM T-matrix model. The results show that the six phase matrix elements (P11, P12\/P11, P22\/P11, P33\/P11, P34\/P11 and P44\/P11) calculated by our model are in good agreement with other models. The computational efficiency of the improved IIM T-matrix model was further investigated. As demonstrated by the results, the computational efficiency for the particles with N-fold symmetry improved by nearly 70% with the improvement of the symmetry of U matrix and T matrix. In conclusion, the improved model can remarkably reduce the calculation time while maintaining high accuracy.<\/jats:p>","DOI":"10.3390\/rs14164061","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T01:56:40Z","timestamp":1661133400000},"page":"4061","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Computational Optimization of the Invariant Imbedding T Matrix Method for the Particles with N-Fold Symmetry"],"prefix":"10.3390","volume":"14","author":[{"given":"Jiaqi","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Shuai","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3393-3988","authenticated-orcid":false,"given":"Xichuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Shulei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"D10S02","DOI":"10.1029\/2004JD004798","article-title":"Aerosol remote sensing from POLDER\/ADEOS over the ocean: Improved retrieval using a nonspherical particle model","volume":"110","author":"Herman","year":"2005","journal-title":"J. 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