Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected Domain

Abstract

In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with multiply-connected do- main. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental so- lutions (MFS) after using the proposed technique to reg- ularize the singularity and hypersingularity of the ker- nel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of in- fluence matrices are determined by employing the sub- tracting and adding-back technique. Spurious eigenval- ues are filtered out by using singular value decomposi- tion (SVD) updating term technique. The accuracy and stability of the RMM are verified through the numerical experiments of the Dirichlet and Neumann problems for domainswithmultipleholes. Themethod isfoundtoper- form pretty well in comparison with analytical solutions and numerical resultsof boundaryelement method, finite element method and the point-matching method. keyword: Regularized meshless method, Hypersingu- larity, Eigenvalue, Eigenmode, Method of fundamental solutions,Acoustics.