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

doi:10.1007/s10483-020-2674-6

Abstract

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

2010 MSC Number:

65N38

Linchong CHEN, Xiaolin LI. Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1897-1914.

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