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计算数学  2018, Vol. 40 Issue (2): 135-148    DOI:
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Helmholtz问题的Robin型区域分解法
刘勇翔1,2, 许学军3,4
1. 中国工程物理研究院微系统与太赫兹研究中心, 成都 610200;
2. 中国工程物理研究院电子工程研究所, 绵阳 621999;
3. LSEC, 中国科学院数学与系统科学研究院, 北京 100190;
4. 同济大学数学科学学院, 上海 200092
ROBIN-TYPE DOMAIN DECOMPOSITION METHODS FOR THE HELMHOLTZ PROBLEM
Liu Yongxiang1,2, Xu Xuejun3,4
1. Microsystems and Terahertz Research Center, China Academy of Engineering Physics, Chengdu 610200, China;
2. Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621999, China;
3. LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China;
4. School of Mathematical Sciences, Tongji University, Shanghai 200092, China
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摘要 Helmholtz问题的数值模拟在科学工程计算领域有着广泛的应用,快速高效求解Helmholtz方程离散代数系统一直是科学计算的重要研究方向.本文简要回顾了Helmholtz方程的区域分解型求解器的发展历程,重点介绍了我们提出的Robin型区域分解算法,同时比较了各类算法的优劣和特点.近年来Helmholtz方程的求解效率有了极大的提升,然而仍有一些本质困难尚待突破,如何高效求解Helmholtz方程,仍是具有挑战意义的研究课题.
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关键词Helmholtz问题   区域分解算法     
Abstract: The Helmholtz problem has many applications and is widely used in engineering computation. How to efficiently solve this problem is a very important and challenging research topic. In this paper we first review and introduce some well-known domain decomposition solvers for this problem. Especially, we shall give a brief introduction of our Robin-type domain decomposition method. However till now there still exist some fundamental difficulties in designing efficient algorithms for solving the Helmholtz problem with high wave number.
Key wordsthe Helmholtz problem   domain decomposition methods   
收稿日期: 2017-08-17;
基金资助:

科学挑战计划基金(TZ2016003-1)和国家自然科学基金(11404300,11671302,11701536)资助.

引用本文:   
. Helmholtz问题的Robin型区域分解法[J]. 计算数学, 2018, 40(2): 135-148.
. ROBIN-TYPE DOMAIN DECOMPOSITION METHODS FOR THE HELMHOLTZ PROBLEM[J]. Mathematica Numerica Sinica, 2018, 40(2): 135-148.
 
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