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

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.

A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers

“…Unfortunately, the BEM and the BCM encounter the singularity and hyper singularity difficulties [20][21][22] due to the application of the fundamental solutions. In recent years, many useful techniques are proposed to bypass this limitation, such as the logarithmic quadrature formulation [23], the rigid body motion method [24], the subtraction and adding-back technique (SAB) [25][26][27], the integration by parts [28], the analytical integration approach [29] and the contour method [30]. As a competitive strategy, the SAB technique was first proposed by Young et [31][32][33] in the regularized meshless method (RMM) [34][35][36].…”

3D meshless FEM-BEM model for prediction of sound fields in cabins due to external sound disturbances

“…In 2012, there were some new hybrid methods synthesizing of FE and meshless methods, the FE-LSPIM was applied to solve the interior SPL in 2D plane [12]. Recently, the meshless method was proposed to solve unbounded acoustic problems [13] and three-dimension exterior acoustic problems with irregular domains [14]. Meanwhile, the meshless method in mechanics [15] was introduced into the numerical acoustics for cabin sound field modeling [16] for author's research.…”