{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:38Z","timestamp":1760241158188,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T00:00:00Z","timestamp":1574899200000},"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":["11802194, 11602157"],"award-info":[{"award-number":["11802194, 11602157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004480","name":"Natural Science Foundation of Shanxi Province","doi-asserted-by":"publisher","award":["201801D221118"],"award-info":[{"award-number":["201801D221118"]}],"id":[{"id":"10.13039\/501100004480","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Taiyuan University of Science and Technology Scientific Research Initial Funding","award":["TYUST SRIF. 20152027, 2016203"],"award-info":[{"award-number":["TYUST SRIF. 20152027, 2016203"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used. The ILU preconditioners of linear systems are performed on the different computation nodes of multi-central processing unit (CPU) cores. Firstly, the preconditioner of general tridiagonal matrix equations is tested on supercomputers. Then, the effects of partial-differential equation systems on the speedup of parallel multiprocessors are examined. The numerical results estimate that the parallel efficiency is higher than in other algorithms.<\/jats:p>","DOI":"10.3390\/sym11121461","type":"journal-article","created":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T10:54:10Z","timestamp":1574938450000},"page":"1461","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Investigation of High-Efficiency Iterative ILU Preconditioner Algorithm for Partial-Differential Equation Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1544-3026","authenticated-orcid":false,"given":"Yan-Hong","family":"Fan","sequence":"first","affiliation":[{"name":"Department of Mechanics, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling-Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"You","family":"Jia","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing-Guo","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-Xia","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5129-8041","authenticated-orcid":false,"given":"Chih-Cheng","family":"Chen","sequence":"additional","affiliation":[{"name":"Information and Engineering College, Jimei University, Xiamen 361021, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.parco.2005.07.005","article-title":"A parallel hybrid banded system solver: The spike algorithm","volume":"32","author":"Polizzi","year":"2006","journal-title":"Parallel Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cam.2004.10.015","article-title":"Convergence of nonstationary multi-splitting methods using ILU factorizations","volume":"180","author":"Yun","year":"2005","journal-title":"J. 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