Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (12): 1897-1914.doi: https://doi.org/10.1007/s10483-020-2674-6

• 论文 • 上一篇    

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

Linchong CHEN1, Xiaolin LI2   

  1. 1. School of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China;
    2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • 收稿日期:2020-02-26 修回日期:2020-07-30 发布日期:2020-11-21
  • 通讯作者: Xiaolin LI E-mail:lxlmath@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (No. 11971085), the Innovation Research Group Project in Universities of Chongqing of China (No. CXQT19018), the Science and Technology Research Program of Chongqing Municipal Education Commission of China (No. KJZD-M201800501), and the Science and Technology Research Program of Chongqing University of Education of China (No. KY201927C)

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

Linchong CHEN1, Xiaolin LI2   

  1. 1. School of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China;
    2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • Received:2020-02-26 Revised:2020-07-30 Published:2020-11-21
  • Contact: Xiaolin LI E-mail:lxlmath@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (No. 11971085), the Innovation Research Group Project in Universities of Chongqing of China (No. CXQT19018), the Science and Technology Research Program of Chongqing Municipal Education Commission of China (No. KJZD-M201800501), and the Science and Technology Research Program of Chongqing University of Education of China (No. KY201927C)

摘要: The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.

关键词: meshless method, complex variable moving least-square approximation, boundary element-free method, Burton-Miller formulation, regularization, high frequency acoustic problem, large wavenumber

Abstract: The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.

Key words: meshless method, complex variable moving least-square approximation, boundary element-free method, Burton-Miller formulation, regularization, high frequency acoustic problem, large wavenumber

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