{"title":"Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations","authors":"Qinjiao Gao, Zhengjie Sun, Zongmin Wu","doi":"10.1016/j.aml.2025.109460","DOIUrl":null,"url":null,"abstract":"This paper presents an innovative energy-equidistributed moving mesh strategy for simulating Hamiltonian partial differential equations (PDEs) characterized by solitons and rapid temporal variations. A novel framework, named the Energy Equidistribution Principles (EEPs), is introduced, highlighting the critical role of energy conservation in achieving accurate simulations. Building on EEPs, three kinds of energy-equidistributed moving mesh PDEs (EMMPDEs) are proposed, each grounded in different methodologies. These strategies are rigorously examined in terms of their convergence conditions and rates. Both theoretical analysis and numerical experiments demonstrate that the proposed EMMPDEs offer superior robustness and effectiveness in long-term simulations, compared to traditional arc-length-equidistributed MMPDEs.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"66 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.aml.2025.109460","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents an innovative energy-equidistributed moving mesh strategy for simulating Hamiltonian partial differential equations (PDEs) characterized by solitons and rapid temporal variations. A novel framework, named the Energy Equidistribution Principles (EEPs), is introduced, highlighting the critical role of energy conservation in achieving accurate simulations. Building on EEPs, three kinds of energy-equidistributed moving mesh PDEs (EMMPDEs) are proposed, each grounded in different methodologies. These strategies are rigorously examined in terms of their convergence conditions and rates. Both theoretical analysis and numerical experiments demonstrate that the proposed EMMPDEs offer superior robustness and effectiveness in long-term simulations, compared to traditional arc-length-equidistributed MMPDEs.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.