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带移动奇异源热方程的移动网格方法
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]浙江大学数学系,浙江杭州310027
  • 相关基金：国家自然科学基金（10731060;10801120）;国家基础研究发展计划（2011CB309704）;高校科学基金（2010QNA3019）
作者： 胡志成[1], 王何宇[1]
关键词： 移动网格方法, 移动观察区域, 奇异源, 热方程, moving mesh methods, moving observed domain, singular sources, heat equa-tion
中文摘要：

研究了一个带若干奇异源热方程的数值求解，其源的移动由一个常微分方程描述．基于移动观察区域和区域分解思想提出了一个移动网格预估校正算法．网格方程可自然的通过并行高效求解，算法避免了跳跃信息M的计算而使物理方程的离散格式变得非常简单，且仍保持了空间上的二阶收敛性．数值例子验证了算法的收敛性和高效性，并模拟了非线性源函数带来的爆破现象．

英文摘要：

In this paper, a moving mesh method for heat equation with traveling singular sources on unbounded domain is presented. The position of the sources is determined through an ordinary differential equation perhaps coupled with the solution. Based on the moving observed domain and domain decomposition idea, a predictor-corrector algorithm is derived. The mesh equation can be solved very efficiently through parallel computing. It is also found that the computation of the jump [u] is avoided, thus the approximation scheme for the problem is greatly simplified. In addition, the method has an expected second-order convergence for space. Numerical examples are presented to demonstrate the convergence rates and efficiency of the proposed algorithm, blow up phenomenon are also observed.

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期刊信息
  • 《高校应用数学学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州市玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu@zjy.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1000-4424
  • 国内统一刊号：ISSN：33-1110/O
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3669