{"title":"模拟兰道-利夫希茨-吉尔伯特方程有限时间炸毁解的自适应移动网格法","authors":"Zheyue Fang, Xiaoping Wang","doi":"10.4208/eajam.2023-322.250224","DOIUrl":null,"url":null,"abstract":"We present a moving mesh finite element method to study the finite-time\nblowup solution of the Landau-Lifshitz-Gilbert (LLG) equation, considering both the\nheat flow of harmonic map and the full LLG equation. Our approach combines projection methods for solving the LLG equation with an iterative grid redistribution method\nto generate adaptive meshes. Through iterative remeshing, we successfully simulate\nblowup solutions with maximum gradient magnitudes up to $10^4$ and minimum mesh\nsizes of $10^{−5}.$ We investigate the self-similar patterns and blowup rates of these solutions, and validate our numerical findings by comparing them to established analytical\nresults from a recent study","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Adaptive Moving Mesh Method for Simulating Finite-time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation\",\"authors\":\"Zheyue Fang, Xiaoping Wang\",\"doi\":\"10.4208/eajam.2023-322.250224\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a moving mesh finite element method to study the finite-time\\nblowup solution of the Landau-Lifshitz-Gilbert (LLG) equation, considering both the\\nheat flow of harmonic map and the full LLG equation. Our approach combines projection methods for solving the LLG equation with an iterative grid redistribution method\\nto generate adaptive meshes. Through iterative remeshing, we successfully simulate\\nblowup solutions with maximum gradient magnitudes up to $10^4$ and minimum mesh\\nsizes of $10^{−5}.$ We investigate the self-similar patterns and blowup rates of these solutions, and validate our numerical findings by comparing them to established analytical\\nresults from a recent study\",\"PeriodicalId\":48932,\"journal\":{\"name\":\"East Asian Journal on Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"East Asian Journal on Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/eajam.2023-322.250224\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.2023-322.250224","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
An Adaptive Moving Mesh Method for Simulating Finite-time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation
We present a moving mesh finite element method to study the finite-time
blowup solution of the Landau-Lifshitz-Gilbert (LLG) equation, considering both the
heat flow of harmonic map and the full LLG equation. Our approach combines projection methods for solving the LLG equation with an iterative grid redistribution method
to generate adaptive meshes. Through iterative remeshing, we successfully simulate
blowup solutions with maximum gradient magnitudes up to $10^4$ and minimum mesh
sizes of $10^{−5}.$ We investigate the self-similar patterns and blowup rates of these solutions, and validate our numerical findings by comparing them to established analytical
results from a recent study
期刊介绍：
The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.
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