Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Qinjiao Gao, Zhengjie Sun, Zongmin Wu
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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.
模拟哈密顿偏微分方程的能量等分布移动网格策略
本文提出了一种新颖的能量等分布移动网格策略,用于模拟以孤子和快速时间变化为特征的哈密顿偏微分方程。介绍了一种新的框架,称为能量均分原则(EEPs),强调了节能在实现精确模拟中的关键作用。在此基础上,提出了三种能量等分布移动网格偏微分方程(EMMPDEs),每一种基于不同的方法。这些策略在其收敛条件和速率方面进行了严格的检查。理论分析和数值实验都表明,与传统的弧长等分布MMPDEs相比,所提出的EMMPDEs在长期模拟中具有更好的鲁棒性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
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.
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