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Localized method of fundamental solutions for interior Helmholtz problems with high wave number

机译：高波数内亥姆霍兹问题基本解的局部化方法

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摘要

This paper introduces a localized version of the method of fundamental solutions (MFS) named as the localized MFS (LMFS) for two-dimensional (2D) interior Helmholtz problems with high wave number. Due to its full interpolation matrix, the traditional MFS is low-efficiency to solve the above-mentioned problem that requires a large number of boundary nodes for obtaining availably numerical results. For the LMFS, the computational domain is first divided into some overlap subdomains based on the distributed nodes. In each subdomain, physical variables are then represented as linear combinations of the fundamental solution of the governing equation as same as in the traditional MFS. A sparse and banded system matrix is finally formed for the LMFS by satisfying Helmholtz equation and boundary conditions, and thus the developed method is inherently efficient for large-scale problems. Three numerical examples are provided to verify the accuracy and the stability of the LMFS.
机译：本文介绍了一种基本解决方案（MFS）的本地化版本，称为高波数二维（2D）内部亥姆霍兹问题的本地化MFS（LMFS）。由于其完整的插值矩阵，传统的MFS解决上述问题的效率很低，而上述问题需要大量的边界节点才能获得可用的数值结果。对于LMFS，首先根据分布式节点将计算域划分为一些重叠子域。然后在每个子域中，将物理变量表示为控制方程式基本解的线性组合，与传统MFS中的线性组合相同。通过满足亥姆霍兹方程和边界条件，最终为LMFS形成了稀疏带状系统矩阵，因此所开发的方法本质上有效地解决了大规模问题。提供了三个数值示例来验证LMFS的准确性和稳定性。

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  • 来源
    《Engineering analysis with boundary elements》 |2019年第10期|25-32|共8页
  • 作者

    Qu Wenzhen; Fan Chia-Ming; Gu Yan;

  • 作者单位

    Qingdao Univ Sch Math & Stat Qingdao 266071 Shandong Peoples R China|Qingdao Univ Sch Automat Qingdao 266071 Shandong Peoples R China;

    Natl Taiwan Ocean Univ Dept Harbor & River Engn Keelung 20224 Taiwan|Natl Taiwan Ocean Univ Computat & Simulat Ctr Keelung 20224 Taiwan|Natl Taiwan Ocean Univ Ctr Excellence Ocean Engn Keelung 20224 Taiwan;

    Qingdao Univ Sch Math & Stat Qingdao 266071 Shandong Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Localized method of fundamental solutions; Meshless method; Interior Helmholtz problem; High wave number;

    机译：基本解决方案的本地化方法;无网格方法;内部亥姆霍兹问题;高波数;

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