{"title":"Computational aspects of hyperbolic curvature flow","authors":"Monika Suchomelová, Michal Beneš, Miroslav Kolář","doi":"10.1016/j.amc.2025.129301","DOIUrl":null,"url":null,"abstract":"<div><div>The article analyzes behavior of the solution of the hyperbolic curvature flow by means of a class of analytical solutions and by computational studies performed by a semi-discrete finite-volume scheme. A class of analytical solutions is derived and used for the verification of the computational algorithm by numerical convergence to it. An original tangential redistribution is proposed to stabilize the numerical scheme. Its derivation requires a four-dimensional transformation of the evolution law. The role of tangential redistribution is demonstrated on computational examples. Computational studies show evolution of the initially convex and non-convex curves, and include cases when singularities predicted by theory start to develop.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129301"},"PeriodicalIF":3.4000,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325000281","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/23 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The article analyzes behavior of the solution of the hyperbolic curvature flow by means of a class of analytical solutions and by computational studies performed by a semi-discrete finite-volume scheme. A class of analytical solutions is derived and used for the verification of the computational algorithm by numerical convergence to it. An original tangential redistribution is proposed to stabilize the numerical scheme. Its derivation requires a four-dimensional transformation of the evolution law. The role of tangential redistribution is demonstrated on computational examples. Computational studies show evolution of the initially convex and non-convex curves, and include cases when singularities predicted by theory start to develop.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
