Hypersingular meshless method using double-layer potentials for three-dimensional exterior acoustic problems

D L Young; K H Chen; T Y Liu; C S Wu

doi:10.1121/1.4939895

Hypersingular meshless method using double-layer potentials for three-dimensional exterior acoustic problems

J Acoust Soc Am. 2016 Jan;139(1):529-40. doi: 10.1121/1.4939895.

Authors

D L Young¹, K H Chen², T Y Liu¹, C S Wu¹

Affiliations

¹ Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei 10617, Taiwan.
² Department of Civil Engineering, National Ilan University, Ilan 26047, Taiwan.

PMID: 26827046
DOI: 10.1121/1.4939895

Abstract

Three-dimensional exterior acoustic problems with irregular domains are solved using a hypersingular meshless method. In particular, the method of fundamental solutions (MFS) is used to formulate and analyze such acoustic problems. It is well known that source points for MFS cannot be located on the real boundary due to the singularity of the kernel functions. Thus, the diagonal terms of the influence matrices are unobtainable when source points are located on the boundary. An efficient approach is proposed to overcome such difficulties, when the MFS is used for three-dimensional exterior acoustic problems. This work is an extension of previous research on two-dimensional problems. The solution of the problem is expressed in terms of a double-layer potential representation on the physical boundary. Three examples are presented in which the proposed method is compared to the MFS and boundary element method. Good numerical performance is demonstrated by the proposed hypersingular meshless method.